Details of the Researcher

PHOTO

Nobuaki Obata
Section
Center for Data-driven Science and Artificial Intelligence
Job title
Specially Appointed Professor(Research)
Degree

  • 理学博士（名古屋大学）

Research History 3

  • 2023/04 - Present
    Tohoku University　Center for Data-driven Science and Artificial Intelligence

  • 2022/04 - Present
    Tohoku University

  • 2001/04 - 2023/03
    Tohoku University　Graduate School of Information Sciences　Professor

Committee Memberships 7

  • JST　ムーンショット型研究開発事業 数理科学分科会 委員

    2021/11 - Present

  • JST　ムーンショット型研究開発事業 目標３アドバイザー

    2020/06 - Present

  • 九州大学マス・フォア・インダストリ研究所　産業数学の先進的・基礎的共同研究拠点共同利用・共同研究委員会委員

    2013/04 - Present

  • Complex Analysis and Operator Theory　Editor

    2010/01 - Present

  • 筑波大学北アフリカ研究センター　客員研究員

    2005/10 - Present

  • Stochastic Analysis and Applications　Editor

    2002/01 - Present

  • Infinite Dimensional Analysis, Quantum Probability and Related Topics　Associate Editor

    1998/01 - Present

Show all ︎Show first 5

Professional Memberships 3

  • International Association of Infinite Dimensional Analysis and Quantum Probability

  • International Association of Mathematical Physics

  • 日本数学会

Research Interests 6

  • Stochastic Analysis

  • Functional Analysis

  • Networks

  • Spectral analysis

  • White noise calculus

  • Quantum probability

Research Areas 4

  • Informatics / Statistical science / Statistics

  • Natural sciences / Applied mathematics and statistics / Mathematics in General (including Probability Theory and Mathematical Statistics)

  • Natural sciences / Basic mathematics / Mathematics in General (including Probability Theory and Mathematical Statistics)

  • Natural sciences / Basic analysis / Basic Analysis

Awards 1

  1. ロレアル・アート・アンド・サイエンス奨励賞

    1998/10　ロレアル・アート・アンド・サイエンス財団

Papers 138

  1. Quantum probability approach to spectral analysis of growing graphs Invited Peer-reviewed

    Nobuaki Obata

    Groups and Graphs, Designs and Dynamics (R. A. Bailey, Peter J. Cameron and Yaokun Wu, Eds.)　87-175　2024/05/11

    Publisher: Cambridge University Press

    DOI： 10.1017/9781009465939 　

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    This collection of four short courses looks at group representations, graph spectra, statistical optimality, and symbolic dynamics, highlighting their common roots in linear algebra. It leads students from the very beginnings in linear algebra to high-level applications: representations of finite groups, leading to probability models and harmonic analysis; eigenvalues of growing graphs from quantum probability techniques; statistical optimality of designs from Laplacian eigenvalues of graphs; and symbolic dynamics, applying matrix stability and K-theory. An invaluable resource for researchers and beginning Ph.D. students, this book includes copious exercises, notes, and references.

  2. A classification of graphs through quadratic embedding constants and clique graph insights

    Edy Tri Baskoro, Nobuaki Obata

    Communications in Combinatorics and Optimization　2024

    DOI： 10.22049/CCO.2024.29159.1869 　

  3. Complete multipartite graphs of non-QE class Peer-reviewed

    Nobuaki Obata

    Electronic Journal of Graph Theory and Applications　11　(2)　511-527　2023/10/24

    Publisher: The Institute for Research and Community Services (LPPM) ITB

    DOI： 10.5614/ejgta.2023.11.2.14 　

    eISSN： 2338-2287

  4. Primary Non-QE Graphs on Six Vertices Peer-reviewed

    Nobuaki OBATA

    Interdisciplinary Information Sciences　29　(2)　141-156　2023/07

    Publisher: Graduate School of Information Sciences, Tohoku University

    DOI： 10.4036/iis.2023.r.01 　

    ISSN： 1340-9050

    eISSN： 1347-6157

  5. Quadratic Embedding Constants of Graph Joins Peer-reviewed

    Zhenzhen Lou, Nobuaki Obata, Qiongxiang Huang

    Graphs and Combinatorics　38　(5)　2022/09/17

    Publisher: Springer Science and Business Media LLC

    DOI： 10.1007/s00373-022-02569-w 　

    ISSN： 0911-0119

    eISSN： 1435-5914

  6. Scaling Limits for the Gibbs States on Distance-Regular Graphs with Classical Parameters Peer-reviewed

    Masoumeh Koohestani, Nobuaki Obata, Hajime Tanaka

    Symmetry, Integrability and Geometry: Methods and Applications　17　104-104　2021/11/26

    Publisher: SIGMA (Symmetry, Integrability and Geometry: Methods and Application)

    DOI： 10.3842/sigma.2021.104 　

    eISSN： 1815-0659

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    We determine the possible scaling limits in the quantum central limit theorem with respect to the Gibbs state, for a growing distance-regular graph that has so-called classical parameters with base unequal to one. We also describe explicitly the corresponding weak limits of the normalized spectral distribution of the adjacency matrix. We demonstrate our results with the known infinite families of distance-regular graphs having classical parameters and with unbounded diameter.

  7. Determining finite connected graphs along the quadratic embedding constants of paths Peer-reviewed

    Edy Tri Baskoro, Nobuaki Obata

    Electronic Journal of Graph Theory and Applications　9　(2)　539-539　2021/10/16

    Publisher: The Institute for Research and Community Services (LPPM) ITB

    DOI： 10.5614/ejgta.2021.9.2.23 　

    eISSN： 2338-2287

  8. Multivariate orthogonal polynomials: Quantum decomposition, deficiency rank and support of measure Peer-reviewed

    Ameur Dhahri, Nobuaki Obata, Hyun Jae Yoo

    Journal of Mathematical Analysis and Applications　485　(1)　123775-123775　2020/05

    Publisher: Elsevier BV

    DOI： 10.1016/j.jmaa.2019.123775 　

    ISSN： 0022-247X

  9. The Elements of Multi-Variate Analysis for Data Science Invited Peer-reviewed

    Mohammad Samy BALADRAM, Nobuaki OBATA

    Interdisciplinary Information Sciences　26　(1)　41-86　2020

    Publisher: Graduate School of Information Sciences, Tohoku University

    DOI： 10.4036/iis.2020.a.02 　

    ISSN： 1340-9050

    eISSN： 1347-6157

  10. On quadratic embedding constants of star product graphs Peer-reviewed

    Wojciech Mlotkowski, Nobuaki Obata

    Hokkaido Math. J.　49　(1)　129-163　2020

  11. Asymptotic joint spectra of Cartesian powers of strongly regular graphs and bivariate Charlier–Hermite polynomials Peer-reviewed

    John Vincent S. Morales, Nobuaki Obata, Hajime Tanaka

    Colloquium Mathematicum　162　(1)　1-22　2020

    Publisher: Institute of Mathematics, Polish Academy of Sciences

    DOI： 10.4064/cm7724-7-2019 　

    ISSN： 0010-1354

    eISSN： 1730-6302

  12. Quantifying heterogeneity of stochastic gene expression Peer-reviewed

    Keita Iida, Nobuaki Obata, Yoshitaka Kimura

    Journal of Theoretical Biology　465　56-62　2019/03

    Publisher: Elsevier BV

    DOI： 10.1016/j.jtbi.2019.01.003 　

    ISSN： 0022-5193

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    The heterogeneity of stochastic gene expression, which refers to the temporal fluctuation in a gene product and its cell-to-cell variation, has attracted considerable interest from biologists, physicists, and mathematicians. The dynamics of protein production and degradation have been modeled as random processes with transition probabilities. However, there is a gap between theory and phenomena, particularly in terms of analytical formulation and parameter estimation. In this study, we propose a theoretical framework in which we present a basic model of a gene regulatory system, derive a steady-state solution, and provide a Bayesian approach for estimating the model parameters from single-cell experimental data. The proposed framework is demonstrated to be applicable for various scales of single-cell experiments at both the mRNA and protein levels and is useful for comparing kinetic parameters across species, genomes, and cell strains.

  13. Distance matrices and quadratic embedding of graphs Peer-reviewed

    Nobuaki Obata, Alfi Y. Zakiyyah

    Electronic Journal of Graph Theory and Applications　6　(1)　37-60　2018

    Publisher: Indonesian Combinatorics Society

    DOI： 10.5614/ejgta.2018.6.1.4 　

    ISSN： 2338-2287

  14. Quadratic embedding constants of wheel graphs Peer-reviewed

    OBATA Nobuaki

    Interdiscip. Inform. Sci.　23　(2)　171-174　2017/12

    DOI： 10.4036/iis.2017.S.02 　

  15. Asymptotic behavior of a rotational population distribution in a molecular quantum-kicked rotor with ideal quantum resonance Peer-reviewed

    Leo Matsuoka, Etsuo Segawa, Kenta Yuki, Norio Konno, Nobuaki Obata

    PHYSICS LETTERS A　381　(21)　1773-1779　2017/06

    DOI： 10.1016/j.physleta.2017.03.032 　

    ISSN： 0375-9601

    eISSN： 1873-2429

  16. Quantum probability aspects to lexicographic and strong products of graphs Peer-reviewed

    Nobuaki Obata

    Interdiscip. Inform. Sci.　22　(2)　143-146　2016/10

    Publisher: Graduate School of Information Sciences, Tohoku University

    DOI： 10.4036/iis.2016.S.1 　

    ISSN： 1347-6157

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    The adjacency matrix of the lexicographic product of graphs is decomposed into a sum of monotone independent random variables in a certain product state. The adjacency matrix of the strong product of graphs admits an expression in terms of commutative independent random variables in a product state. Their spectral distributions are obtained by using the monotone, classical and Mellin convolutions of probability distributions.

  17. An implementation problem for boson fields and quantum Girsanov transform Peer-reviewed

    Un Cig Ji, Nobuaki Obata

    JOURNAL OF MATHEMATICAL PHYSICS　57　(8)　083502　2016/08

    DOI： 10.1063/1.4960454 　

    ISSN： 0022-2488

    eISSN： 1089-7658

  18. Calculating normal-ordered forms in Fock space by quantum white noise derivatives Peer-reviewed

    Un Cig Ji, Nobuaki Obata

    Interdiscip. Inform. Sci.　19　(2)　201-211　2013/12

    Publisher: Tohoku University

    DOI： 10.4036/iis.2013.201 　

    ISSN： 1340-9050

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    The normal-ordered form of the composition of the exponential of a quadratic annihilation operator and its adjoint is derived by means of a new method based on quantum white noise calculus. Our method consists of two steps: (i) to derive a system of differential equations consisting of quantum white noise derivatives and Wick products; and (ii) to solve explicitly the system of differential equations.

  19. Localization of the Grover Walks on Spidernets and Free Meixner Laws Peer-reviewed

    Norio Konno, Nobuaki Obata, Etsuo Segawa

    COMMUNICATIONS IN MATHEMATICAL PHYSICS　322　(3)　667-695　2013/09

    DOI： 10.1007/s00220-013-1742-x 　

    ISSN： 0010-3616

  20. DISTANCE-k GRAPHS OF HYPERCUBE AND q-HERMITE POLYNOMIALS Peer-reviewed

    Hun Hee Lee, Nobuaki Obata

    INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS　16　(2)　1350011　2013/06

    DOI： 10.1142/S0219025713500112 　

    ISSN： 0219-0257

  21. Asymptotic spectral distributions of distance-k graphs of Cartesian product graphs Peer-reviewed

    Yuji Hibino, Hun Hee Lee, Nobuaki Obata

    Colloquium Mathematicum　132　(1)　35-51　2013

    DOI： 10.4064/cm132-1-4 　

    ISSN： 0010-1354 1730-6302

  22. THE KARLIN-MCGREGOR FORMULA FOR PATHS CONNECTED WITH A CLIQUE Peer-reviewed

    Nobuaki Obata

    PROBABILITY AND MATHEMATICAL STATISTICS-POLAND　33　(2)　451-466　2013

    ISSN： 0208-4147

  23. Quantum white noise calculus and applications Invited Peer-reviewed

    Un Cig Ji, Nobuaki Obata

    Real and Stochastic Analysis: Current Trends　269-353　2013/01/01

    Publisher: World Scientific Publishing Co.

    DOI： 10.1142/9789814551281_0004 　

  24. One-mode interacting Fock spaces and random walks on graphs Peer-reviewed

    Nobuaki Obata

    STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES　84　(2-3)　383-392　2012

    DOI： 10.1080/17442508.2010.550919 　

    ISSN： 1744-2508

  25. Asymptotic spectral distributions of distance k-graphs of large-dimensional hypercubes Peer-reviewed

    Nobuaki Obata

    Banach Center Publications　2012

  26. Manhattan product of digraphs

    Nobuaki Obata

    京都大学数理解析研究所講究録　1819　125-134　2012

    Publisher:

    ISSN： 1880-2818

  27. MANHATTAN PRODUCTS OF DIGRAPHS: CHARACTERISTIC POLYNOMIALS AND EXAMPLES Peer-reviewed

    Nobuaki Obata

    ANNALS OF FUNCTIONAL ANALYSIS　3　(2)　135-143　2012

    ISSN： 2008-8752

  28. Spectra of Manhattan products of directed paths P_n#P_2 Peer-reviewed

    Nobuaki Obata

    Interdiscip. Inform. Sci.　18　(1)　43-54　2012

    Publisher: The Editorial Committee of the Interdisciplinary Information Sciences

    DOI： 10.4036/iis.2012.43 　

    ISSN： 1340-9050

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    The Manhattan product of directed paths Pn and Pm is a digraph, where the underlying graph is the n×m lattice and each edge is given direction in such a way that left and right directed horizontal lines are placed alternately, and so are up and down directed vertical lines. Unless both m and n are even, the Manhattan product of Pn and Pm is unique up to isomorphisms, which is called standard and denoted by Pn#Pm. If both m and n are even, there is a Manhattan product which is not isomorphic to the standard one. It is called non-standard and denoted by Pn#′Pm. The characteristic polynomials of Pn#P2 and Pn#′P2 are expressed in terms of the Chebychev polynomials of the second kind, and their spectra (eigenvalues with multiplicities) are thereby determined explicitly. In particular, it is shown that ev (P2n-1#P2)=ev (P2n#P2) and ev (P2n#′P2)=ev (P2n+2#P2). The limit of the spectral distribution of Pn#<i>P<i></sub>2</sub> as n→∞ exists in the sense of weak convergence and its concrete form is obtained.

  29. A NOTE ON CONVOLUTION OPERATORS IN WHITE NOISE CALCULUS Peer-reviewed

    Nobuaki Obata, Habib Ouerdiane

    INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS　14　(4)　661-674　2011/12

    DOI： 10.1142/S0219025711004535 　

    ISSN： 0219-0257

  30. MARKOV PRODUCT OF POSITIVE DEFINITE KERNELS AND APPLICATIONS TO Q-MATRICES OF GRAPH PRODUCTS Peer-reviewed

    Nobuaki Obata

    COLLOQUIUM MATHEMATICUM　122　(2)　177-184　2011

    DOI： 10.4064/cm122-2-2 　

    ISSN： 0010-1354

    eISSN： 1730-6302

  31. Implementation problem for the canonical commutation relation in terms of quantum white noise derivatives Peer-reviewed

    Un Cig Ji, Nobuaki Obata

    JOURNAL OF MATHEMATICAL PHYSICS　51　(12)　123507-15pp　2010/12

    DOI： 10.1063/1.3516477 　

    ISSN： 0022-2488

  32. QUANTUM WHITE NOISE DERIVATIVES AND ASSOCIATED DIFFERENTIAL EQUATIONS FOR WHITE NOISE OPERATORS Peer-reviewed

    Un Cig Ji, Nobuaki Obata

    QUANTUM PROBABILITY AND INFINITE DIMENSIONAL ANALYSIS　25　42-+　2010

    ISSN： 1793-5121

  33. Quantum stochastic derivatives and applications

    Nobuaki Obata

    Proceedings of TJASSST 10 (A. Ghorbel, A. Ben Salem, S. Bouzayene, Eds.)　289-291　2010

  34. Quantum stochastic gradients Peer-reviewed

    Un Cig Ji, Nobuaki Obata

    Interdisciplinary Information Sciences　15　(3)　345-359　2009/11

    Publisher: Graduate School of Information Sciences, Tohoku University

    DOI： 10.4036/iis.2009.345 　

    ISSN： 1340-9050

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    We obtain regularity properties of the quantum stochastic gradients (creation, annihilation and conservation gradients) by systematic study of their various domains. Accordingly, regularity properties of the (non-adapted) quantum stochastic integrals of Hitsuda–Skorohod type follow by duality.

  35. 量子確率論とグラフのスペクトル解析 Invited

    尾畑伸明

    数理物理2009「ベキ乗則の数理」　1-40　2009/08

  36. Annihilation-Derivative, Creation-Derivative and Representation of Quantum Martingales Peer-reviewed

    Un Cig Ji, Nobuaki Obata

    COMMUNICATIONS IN MATHEMATICAL PHYSICS　286　(2)　751-775　2009/03

    DOI： 10.1007/s00220-008-0702-3 　

    ISSN： 0010-3616

    eISSN： 1432-0916

  37. グラフのスペクトル解析における量子確率論の手法 Invited

    尾畑伸明

    第26回代数的組合せ論シンポジウム報告集　102-125　2009

  38. Quantum stochastic integral representations of Fock space operators Peer-reviewed

    Un Cig Ji, Nobuaki Obata

    STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC REPORTS　81　(3-4)　367-384　2009

    DOI： 10.1080/17442500902919645 　

    ISSN： 1744-2508

    eISSN： 1744-2516

  39. Spectral properties of the threshold network model Peer-reviewed

    Yusuke Ide, Norio Konno, Nobuaki Obata

    Internet Mathematics　6　(2)　173-187　2009/01/01

    Publisher: Taylor and Francis Inc.

    DOI： 10.1080/15427951.2009.10129183 　

    ISSN： 1542-7951

  40. Notions of independence in quantum probability and spectral analysis of graphs Peer-reviewed

    Nobuaki Obata

    Amer. Math. Soc. Transl.　223　115-136　2008/10

  41. Dew development in white noise analysis Invited

    Nobuaki Obata

    量子情報の数理に関する研究～エントロピー・ゆらぎ・ミクロとマクロ・アルゴリズム・生命情報～ 高等研報告書　0801　173-192　2008/06

  42. Generalized white noise operators fields and quantum white noise derivatives Peer-reviewed

    Un Cig Ji, Nobuaki Obata

    Seminaires et Congres　16　17-33　2008/01

  43. Asymptotic spectral analysis of growing regular graphs Peer-reviewed

    Akihito Hora, Nobuaki Obata

    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY　360　(2)　899-923　2008

    DOI： 10.1090/S0002-9947-07-04232-8 　

    ISSN： 0002-9947

    eISSN： 1088-6850

  44. Hitsuda--Skorohod quantum stochastic integrals in terms of quantum stochastic gradients

    Un Cig Ji, Nobuaki Obata

    京都大学数理解析研究所講究録　1565　143-156　2007/10

  45. Quantum Levy Laplacian and associated heat equation Peer-reviewed

    Un Cig Ji, Nobuaki Obata, Habib Ouerdiane

    JOURNAL OF FUNCTIONAL ANALYSIS　249　(1)　31-54　2007/08

    DOI： 10.1016/j.jfa.2007.04.006 　

    ISSN： 0022-1236

  46. Partial unitarity arising from quadratic quantum white noise Peer-reviewed

    W. Ayed, N. Obata, H. Ouerdiane

    Mathematical Analysis of Random Phenomena　2007/04

  47. Growing networks and random matrices: A quantum probabilistic aspect Invited

    Nobuaki Obata

    数理科学　524　18-23　2007/02

  48. Positive Q-matrices of graphs Peer-reviewed

    Nobuaki Obata

    STUDIA MATHEMATICA　179　(1)　81-97　2007

    DOI： 10.4064/sm179-1-7 　

    ISSN： 0039-3223

  49. Asymptotic spectral analysis of generalized Erdos-Renyi random graphs Peer-reviewed

    Song Liang, Nobuaki Obata, Shuji Takahashi

    NONCOMMUTATIVE HARMONIC ANALYSIS WITH APPLICATIONS TO PROBABILITY　78　211-229　2007

    ISSN： 0137-6934

  50. Asymptotic spectral analysis of growing graphs: Odd graphs and spidernets Peer-reviewed

    Daisuke Igarashi, Nobuaki Obata

    Banach Center Publications　73　245-265　2006/11

  51. A note on Konno's paper on quantum walk Peer-reviewed

    N Obata

    INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS　9　(2)　299-304　2006/06

    DOI： 10.1142/S0219025706002366 　

    ISSN： 0219-0257

  52. Asymptotic spectral analysis of growing graphs: A quantum probabilistic approach Peer-reviewed

    Nobuaki Obata

    Methods and Applications of Infinite Dimensional Analysis　62-85　2006

  53. An interacting Fock space with periodic Jacobi parameters obtained from regular graphs in large scale limit Peer-reviewed

    Akihito Hora, Nobuaki Obata

    Quantum Information V, World Scientific　121-144　2006/01

  54. Unitarity of generalized Fourier-Gauss transforms Peer-reviewed

    Un Cig Ji, Nobuaki Obata

    STOCHASTIC ANALYSIS AND APPLICATIONS　24　(4)　733-751　2006

    DOI： 10.1080/07362990600751837 　

    ISSN： 0736-2994

  55. Admissible white noise operators and their quantum white noise derivatives Peer-reviewed

    Un Cig Ji, Nobuaki Obata

    Infinite Dimensional Analysis III, World Scientific　213-232　2005/10

  56. Concepts of independence and spectral analysis on graphs Invited Peer-reviewed

    Nobuaki Obata

    Sugaku Expository　57　(1)　1-20　2005/01/26

    Publisher:

    DOI： 10.11429/sugaku1947.57.1 　

    ISSN： 0039-470X

  57. Monotone independence, comb graphs and Bose-Einstein condensation Peer-reviewed

    L Accardi, A Ben Ghorbal, N Obata

    INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS　7　(3)　419-435　2004/09

    DOI： 10.1142/S0219025704001645 　

    ISSN： 0219-0257

    eISSN： 1793-6306

  58. A role of Bargmann-Segal spaces in characterization and expansion of operators on Fock space Peer-reviewed

    BUC Ji, N Obata

    JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN　56　(2)　311-338　2004/04

    DOI： 10.2969/jmsj/1191418632 　

    ISSN： 0025-5645

  59. Quantum probabilistic approach to spectral analysis of star graphs Peer-reviewed

    Nobuaki Obata

    Interdisciplinary Information Sciences　10　41-52　2004/03

    Publisher: Tohoku University

    DOI： 10.4036/iis.2004.41 　

    ISSN： 1340-9050

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    A general method for obtaining a vacuum spectral distribution of the adjacency matrix of a star graph is established within the framework of quantum probability theory. The spectral distribution tends asymptotically to the Bernoulli distribution as the number of leaves of a star graph tends to the infinity.

  60. Unitarity of Kuo's Fourier-Mehler transform Peer-reviewed

    UC Ji, N Obata

    INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS　7　(1)　147-154　2004/03

    DOI： 10.1142/S0219025704001487 　

    ISSN： 0219-0257

  61. Heat equation associated with Levy Laplacian Peer-reviewed

    N Obata, H Ouerdiane

    PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON STOCHASTIC ANALYSIS AND APPLICATIONS　53-68　2004

  62. A unified characterization theorem in white noise theory Peer-reviewed

    UC Ji, N Obata

    INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS　6　(2)　167-178　2003/06

    DOI： 10.1142/S0219025703001122 　

    ISSN： 0219-0257

  63. Quantum decomposition and quantum central limit theorem Peer-reviewed

    A Hora, N Obata

    FUNDAMENTAL ASPECTS OF QUANTUM PHYSICS　17　284-305　2003

    ISSN： 1793-5121

  64. Central limit theorems for large graphs: Method of quantum decomposition Peer-reviewed

    Y Hashimoto, A Hora, N Obata

    JOURNAL OF MATHEMATICAL PHYSICS　44　(1)　71-88　2003/01

    DOI： 10.1063/1.1528275 　

    ISSN： 0022-2488

  65. Cauchy Processes and the Levy Laplacian Peer-reviewed

    Nobuaki Obata, Kimiaki Saito

    Non-Commutativity, Infinite-Dimensionality and Probability at the Crossroads　360-373　2002/12

  66. Quantum white noise calculus Peer-reviewed

    Un Cig Ji, Nobuaki Obata

    Non-Commutativity, Infinite-Dimensionality and Probability at the Crossroads　143-191　2002/12

    Publisher:

  67. 量子分解法による隣接作用素のスペクトル解析 I: 個数作用素が現れない場合

    Nobuaki Obata, Hora Akihito

    数理解析研究所講究録　1291　11-44　2002/10

    Publisher:

    ISSN： 1880-2818

  68. Analytic characterization of generalized fock space operators as two-variable entire functions with growth condition Peer-reviewed

    Un Cig Ji, Nobuaki Obata, Habib Ouerdiane

    Infinite Dimensional Analysis, Quantum Probability and Related Topics　5　(3)　395-407　2002/09

    DOI： 10.1142/S0219025702000912 　

    ISSN： 0219-0257

  69. Analytic characterization of generalized Fock space operators as two-variable entire functions with growth condition Peer-reviewed

    UC Ji, N Obata, H Ouerdiane

    INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS　5　(3)　395-407　2002/09

    DOI： 10.1142/S0219025702000912 　

    ISSN： 0219-0257

  70. Diagonalization of the levy laplacian and related stable processes Peer-reviewed

    HH Kuo, N Obata, K Saito

    INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS　5　(3)　317-331　2002/09

    DOI： 10.1142/S0219025702000882 　

    ISSN： 0219-0257

    eISSN： 1793-6306

  71. Inverse S-transform, Wick product and overcompleteness of exponential vectors Peer-reviewed

    Nobuaki Obata

    Quantum Information IV　147-176　2002/08

  72. Quantum white noise calculus based on nuclear algebras of entire functions

    Nobuaki Obata

    京都大学数理解析研究所講究録　1278　130-157　2002/08

    Publisher: Kyoto University

    ISSN： 1880-2818

  73. Segal-Bargmann transform of white noise operators and white noise differential equations

    Un nCig Ji, Nobuaki Obata

    京都大学数理解析研究所講究録　1266　59-81　2002/05

    Publisher: Kyoto University

    ISSN： 1880-2818

  74. Quantum stochastic analysis via white noise operators in weighted Fock space Peer-reviewed

    DM Chung, UC Ji, N Obata

    REVIEWS IN MATHEMATICAL PHYSICS　14　(3)　241-272　2002/03

    DOI： 10.1142/S0129055X0200117X 　

    ISSN： 0129-055X

  75. 量子分解法によるスペクトル解析 Peer-reviewed

    Nobuaki Obata

    物性研究　77　(5)　784-805　2002/02

    Publisher:

    ISSN： 0525-2997

  76. A quantum aspect of asymptotic spectral analysis of large Hamming graphs Peer-reviewed

    Yukihiro Hashimoto, Nobuaki Obata, Nobuyuki Tabei

    Quantum Information III, World Scientific　45-57　2001/10

    Publisher:

  77. Unitarity criterion in white noise calculus and nonexistence of unitary evolutions driven by higher powers of quantum white noises Peer-reviewed

    Nobuaki Obata

    Aportaciones Mat. Investig.　16　251-269　2001/10

  78. Multi-variable white noise functions : Standard setup revisited

    Nobuaki Obata

    京都大学数理解析研究所講究録　1227　184-198　2001/08

    Publisher: Kyoto University

    ISSN： 1880-2818

  79. white noise analysis based on the Levy Laplacian

    H.-H. Kuo, Nobuaki Obata, Kimiaki saito

    京都大学数理解析研究所講究録　1227　170-183　2001/08

    Publisher: Kyoto University

    ISSN： 1880-2818

  80. Quadratic quantum white noises and Lévy Laplacian Peer-reviewed

    N. Obata

    Nonlinear Analysis, Theory, Methods and Applications　47　(4)　2437-2448　2001/08

    DOI： 10.1016/S0362-546X(01)00367-4 　

    ISSN： 0362-546X

  81. 複素ホワイトノイズとコヒーレント状態表示 Peer-reviewed

    Nobuaki Obata

    物性研究　75　(5)　901-917　2001/02

    Publisher:

    ISSN： 0525-2997

  82. Coherent state representation and unitarity condition in white noise calculus Peer-reviewed

    OBATA Nobuaki

    J. Korean Math. Soc.　38　297-309　2001

  83. Unitarity criterion in white noise calculus and nonexistence of unitary evolutions driven by higher powers of quantum white noises Peer-reviewed

    Nobuaki Obata

    Aportaciones Matematicas Investigacion　16　251-269　2001

  84. Quantum stochastic analysis via white noise operator theory

    Nobuaki Obata

    Proceedings of the International Conference on Probability and Statistics and Their Applications, Hanoi Institute of Mathematics　41-64　2000/10

  85. Complex white noise and coherent state representations Peer-reviewed

    Nobuaki Obata

    Acta Applicandae Mathematicae　63　(1-3)　283-291　2000/09

    DOI： 10.1023/A:1010771919136 　

    ISSN： 0167-8019

  86. Normal-ordered white noise differential equations I : Existence of solutions as Fock space operators Peer-reviewed

    D. M. Chung, Un Cig Ji, Nobuaki Obata

    Trends in Contemporary Infinite Dimensional Analysis and Quantum Probability　115-135　2000/06

    Publisher:

  87. Color-coding reveals tandem repeats in the Escherichia coli genome Peer-reviewed

    Tetsuhiko Yoshida, Nobuaki Obata, Kenji Oosawa

    Journal of Molecular Biology　298　(3)　343-349　2000/05/05

    Publisher: Academic Press

    DOI： 10.1006/jmbi.2000.3667 　

    ISSN： 0022-2836

  88. Initial-value problem for white noise operators and quantum stochastic processes Peer-reviewed

    Un Cig Ji, Nobuaki Obata

    Infinite Dimensional Harmonic Analysis (H. Heyer, T. Hirai and N. Obata, eds.)　203-216　2000/05

  89. A note on coherent state representations of white noise operators

    Nobuaki Obata

    Quantum Information II, World Scientific　135-147　2000/05

  90. Coherent state representations in white noise calculus Peer-reviewed

    OBATA Nobuaki

    Can. Math. Soc. Proceedings Series　29　517-531　2000

  91. Wick product of white noise operators and quantum stochastic differential equations Peer-reviewed

    N Obata

    JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN　51　(3)　613-641　1999/07

    ISSN： 0025-5645

  92. Some new trends and questions in white noise calculus

    Nobuaki Obata

    京都大学数理解析研究所講究録　1099　1-16　1999/06

    Publisher: Kyoto University

    ISSN： 1880-2818

  93. 作者の統計的識別の一例

    堀江亮次, 奥田康誠, 山下准, 河村和人, 尾畑伸明

    統計数理研究所シンポジウム報告集「人文科学における数量的分析(4)」　51-60　1999/03

  94. Normal-ordered white noise differential equations II : Regularity properties of solutions Peer-reviewed

    D. M. Chung, U. C. Ji, Nobuaki Obata

    Probability Theory and Mathematical Statistics (B. Grigolionis et al Eds.)　157-174　1999

    Publisher:

  95. ホワイトノイズと量子確率解析の非線型拡張 Peer-reviewed

    OBATA Nobuaki

    物性研究　72　(3)　345-360　1999

    Publisher:

    ISSN： 0525-2997

  96. A method of sequencial analysis by 2D-pattern formation with coloration Peer-reviewed

    OBATA Nobuaki

    Amino Acids　17　121　1999

  97. Higher powers of quantum white noises in terms of integral kernel operators Peer-reviewed

    DM Chung, UC Ji, N Obata

    INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS　1　(4)　533-559　1998/10

    ISSN： 0219-0257

  98. Notions of independence related to the free group Peer-reviewed

    L Accardi, Y Hashimoto, N Obata

    INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS　1　(2)　201-220　1998/04

    ISSN： 0219-0257

    eISSN： 1793-6306

  99. Notions of independence related to the free group II : From singleton condition to singleton independence

    Luigi Accardi, Yukihiro Hashimoto, Nobuaki Obata

    RIMS Kokyuroku　1035　82-94　1998/04

    Publisher: Kyoto University

    ISSN： 1880-2818

  100. A note on transformations on white noise functions -Hida's whiskers revisited

    Nobuaki Obata

    RIMS Kokyuroku　1035　155-169　1998/04

    Publisher: Kyoto University

    ISSN： 1880-2818

  101. Transformations on white noise functions associated with second order differential operators of diagonal type Peer-reviewed

    DM Chung, UC Ji, N Obata

    NAGOYA MATHEMATICAL JOURNAL　149　173-192　1998/03

    ISSN： 0027-7630

  102. 色彩パターン化による1次元配列の情報解析法

    大澤研二, 吉田徹彦, 尾畑伸明

    統計数理研究所シンポジウム報告集「人文科学における数量的分析(3)」　77-82　1998/03

  103. Harmonic functions on Hilbert space and the Levy Laplacian

    Nobuaki Obata

    京都大学数理解析研究所講究録　642　213-228　1998/02

  104. Singleton independence Peer-reviewed

    OBATA Nobuaki

    Banach Center Publications　43　9-24　1998

  105. A role of singletons in quantum central limit theorems Peer-reviewed

    OBATA Nobuaki

    J. Korean Math. Soc.　35　675-690　1998

  106. Quantum stochastic differential equations in terms of quantum white noise Peer-reviewed

    N Obata

    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS　30　(1)　279-290　1997/12

    ISSN： 0362-546X

  107. White noise distributions and quantum stochastic differential equations Invited

    Nobuaki Obata

    物性研究　69　19-38　1997/10

  108. Integral kernel operators on fock space - Generalizations and applications to quantum dynamics Peer-reviewed

    N Obata

    ACTA APPLICANDAE MATHEMATICAE　47　(1)　49-77　1997/04

    ISSN： 0167-8019

  109. Generalization of integral kernel operators

    Nobuaki Obata

    京都大学数理解析研究所講究録　980　137-149　1997/02

    Publisher: Kyoto University

    ISSN： 1880-2818

  110. Constructing one-parameter transformations on white noise functions in terms of equicontinuous generators Peer-reviewed

    N Obata

    MONATSHEFTE FUR MATHEMATIK　124　(4)　317-335　1997

    ISSN： 0026-9255

  111. Generalized hypergroups and orthogonal polynomials Peer-reviewed

    N Obata, NJ Wildberger

    NAGOYA MATHEMATICAL JOURNAL　142　67-93　1996/06

    ISSN： 0027-7630

  112. 量子ホワイトノイズの数学的基礎 Peer-reviewed

    OBATA Nobuaki

    物性研究　66　(1)　76-94　1996

    Publisher:

    ISSN： 0525-2997

  113. Generalized quantum stochastic processes on Fock space Peer-reviewed

    N Obata

    PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES　31　(4)　667-702　1995/12

    ISSN： 0034-5318

  114. DERIVATIONS ON WHITE-NOISE FUNCTIONALS Peer-reviewed

    N OBATA

    NAGOYA MATHEMATICAL JOURNAL　139　21-36　1995/09

    ISSN： 0027-7630

  115. OPERATOR CALCULUS ON VECTOR-VALUED WHITE-NOISE FUNCTIONALS Peer-reviewed

    N OBATA

    JOURNAL OF FUNCTIONAL ANALYSIS　121　(1)　185-232　1994/04

    ISSN： 0022-1236

  116. ホワイトノイズによる量子確率積分 Peer-reviewed

    OBATA Nobuaki

    物性研究　62　82-85　1994

  117. AN ANALYTIC CHARACTERIZATION OF SYMBOLS OF OPERATORS ON WHITE-NOISE FUNCTIONALS Peer-reviewed

    N OBATA

    JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN　45　(3)　421-445　1993/07

    ISSN： 0025-5645

  118. WHITE-NOISE DELTA FUNCTIONS AND CONTINUOUS VERSION THEOREM Peer-reviewed

    N OBATA

    NAGOYA MATHEMATICAL JOURNAL　129　1-22　1993/03

    ISSN： 0027-7630

  119. TRANSFORMATIONS FOR WHITE-NOISE FUNCTIONALS Peer-reviewed

    T HIDA, HH KUO, N OBATA

    JOURNAL OF FUNCTIONAL ANALYSIS　111　(2)　259-277　1993/02

    ISSN： 0022-1236

  120. INFINITE DIMENSIONAL ROTATIONS AND LAPLACIANS IN TERMS OF WHITE-NOISE CALCULUS Peer-reviewed

    T HIDA, N OBATA, K SAITO

    NAGOYA MATHEMATICAL JOURNAL　128　65-93　1992/12

    ISSN： 0027-7630

  121. ROTATION-INVARIANT OPERATORS ON WHITE-NOISE FUNCTIONALS Peer-reviewed

    N OBATA

    MATHEMATISCHE ZEITSCHRIFT　210　(1)　69-89　1992/05

    ISSN： 0025-5874

  122. ISOMETRIC OPERATORS ON L1-ALGEBRAS OF HYPERGROUPS

    N OBATA

    PROBABILITY MEASURES ON GROUP X　315-328　1991

  123. PERMUTATIONS PRESERVING CESARO MEAN, DENSITIES OF NATURAL-NUMBERS AND UNIFORM-DISTRIBUTION OF SEQUENCES Peer-reviewed

    M BLUMLINGER, N OBATA

    ANNALES DE L INSTITUT FOURIER　41　(3)　665-678　1991

    ISSN： 0373-0956

  124. LEVY LAPLACIAN OF GENERALIZED-FUNCTIONS ON A NUCLEAR SPACE Peer-reviewed

    HH KUO, N OBATA, K SAITO

    JOURNAL OF FUNCTIONAL ANALYSIS　94　(1)　74-92　1990/11

    ISSN： 0022-1236

  125. CONSTRUCTION OF IRREDUCIBLE UNITARY REPRESENTATIONS OF AMALGAMS OF DISCRETE ABELIAN-GROUPS Peer-reviewed

    N OBATA

    JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN　42　(4)　585-603　1990/10

    ISSN： 0025-5645

  126. A CHARACTERIZATION OF THE LEVY LAPLACIAN IN TERMS OF INFINITE DIMENSIONAL ROTATION GROUPS Peer-reviewed

    N OBATA

    NAGOYA MATHEMATICAL JOURNAL　118　111-132　1990/06

    ISSN： 0027-7630

  127. INTEGRAL EXPRESSION OF SOME INDECOMPOSABLE CHARACTERS OF THE INFINITE SYMMETRIC GROUP IN TERMS OF IRREDUCIBLE REPRESENTATIONS Peer-reviewed

    N OBATA

    MATHEMATISCHE ANNALEN　287　(3)　369-375　1990

    ISSN： 0025-5831

  128. SOME REMARKS ON INDUCED REPRESENTATIONS OF INFINITE DISCRETE-GROUPS Peer-reviewed

    N OBATA

    MATHEMATISCHE ANNALEN　284　(1)　91-102　1989

    ISSN： 0025-5831

  129. THE LEVY LAPLACIAN AND MEAN-VALUE THEOREM Peer-reviewed

    N OBATA

    LECTURE NOTES IN MATHEMATICS　1379　242-253　1989

    ISSN： 0075-8434

  130. DENSITY OF NATURAL-NUMBERS AND THE LEVY GROUP Peer-reviewed

    N OBATA

    JOURNAL OF NUMBER THEORY　30　(3)　288-297　1988/11

    ISSN： 0022-314X

  131. Analysis of the Levy Laplacian Peer-reviewed

    Nobuaki Obata

    Soochow J. Math.　14　105-109　1988/06

  132. A NOTE ON CERTAIN PERMUTATION-GROUPS IN THE INFINITE DIMENSIONAL ROTATION GROUP Peer-reviewed

    N OBATA

    NAGOYA MATHEMATICAL JOURNAL　109　91-107　1988/03

    ISSN： 0027-7630

  133. Harmonic functions on Hilbert space and the L\\'evy Laplacian

    Nobuaki Obata

    京都大学数理解析研究所講究録　642　213-228　1988

    Publisher: Kyoto University

    ISSN： 1880-2818

  134. CERTAIN UNITARY REPRESENTATIONS OF THE INFINITE SYMMETRICAL GROUP .2. Peer-reviewed

    N OBATA

    NAGOYA MATHEMATICAL JOURNAL　106　143-162　1987/06

    ISSN： 0027-7630

  135. CERTAIN UNITARY REPRESENTATIONS OF THE INFINITE SYMMETRICAL GROUP .1. Peer-reviewed

    N OBATA

    NAGOYA MATHEMATICAL JOURNAL　105　109-119　1987/03

    DOI： 10.1017/S0027763000000775 　

    ISSN： 0027-7630

  136. Configuration space and unitary representations of the group of diffeomorphisms

    Nobuaki Obata

    京都大学数理解析研究所講究録　615　129-153　1987/03

    Publisher: Kyoto University

    ISSN： 1880-2818

  137. Configuration space and unitary representations of the group of diffeomorphisms

    Nobuaki Obata

    京都大学数理解析研究所講究録　615　129-153　1987

  138. A characterization of the Levy group and related topics

    Nobuaki Obata

    Levy Seminar No.2　63-88　1987

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Misc. 11

  1. On Overcompleteness of Coherent Vectors (Analytical Study of Quantum Information and Related Fields)

    Obata Nobuaki

    RIMS Kokyuroku　1196　63-77　2001/04

    Publisher: Kyoto University

    ISSN： 1880-2818

  2. Quantum Stochastic Process as Continuous Flow of Fock Space Operators

    OBATA NOBUAKI

    RIMS Kokyuroku　982　196-208　1997/03

    Publisher: Kyoto University

    ISSN： 1880-2818

  3. Wick Product of White Noise Operators and Its Application to Quantum Stochastic Differential Equations(Quantum Stochastic Analysis and Related Fields)

    OBATA NOBUAKI

    RIMS Kokyuroku　957　167-185　1996/08

    Publisher: Kyoto University

    ISSN： 1880-2818

  4. Towards a Non-linear Extension of Stochastic Calculus(Quantum Stochastic Analysis and Related Fields)

    ACCARDI LUIGI, LU YUN-GANG, OBATA NOBUAKI

    RIMS Kokyuroku　957　1-15　1996/08

    Publisher: Kyoto University

    ISSN： 1880-2818

  5. CONDITIONAL EXPECTATION IN CLASSICAL AND QUANTUM WHITE NOISE CALCULI(Analysis of Operators on Gaussian Space and Quantum Probability Theory)

    OBATA NOBUAKI

    RIMS Kokyuroku　923　154-190　1995/09

    Publisher: Kyoto University

    ISSN： 1880-2818

  6. Fock空間上の量子確率過程:ホワイトノイズの観点から(無限次元空間上の測度論、無限次元群の表現および関連した話題)

    尾畑 伸明

    数理解析研究所講究録　887　72-96　1994/10

    Publisher: 京都大学

    ISSN： 1880-2818

  7. ON VECTOR-VALUED WHITE NOISE FUNCTIONALS

    Obata Nobuaki

    RIMS Kokyuroku　885　120-138　1994/09

    Publisher: Kyoto University

    ISSN： 1880-2818

  8. White Noise Approach to Quantum Stochastic Integrals(White Noise Analysis and Quantum Probability)

    OBATA NOBUAKI

    RIMS Kokyuroku　874　156-167　1994/06

    Publisher: Kyoto University

    ISSN： 1880-2818

  9. White Noise Calculus with Finite Degree of Freedom(White Noise Analysis and Quantum Probability)

    OBATA NOBUAKI

    RIMS Kokyuroku　874　137-155　1994/06

    Publisher: Kyoto University

    ISSN： 1880-2818

  10. Derivation property of the Levy laplacian(White Noise Analysis and Quantum Probability)

    ACCARDI LUIGI, OBATA NOBUAKI

    RIMS Kokyuroku　874　8-19　1994/06

    Publisher: Kyoto University

    ISSN： 1880-2818

  11. Toward Harmonic Analysis on Gaussian Space(Problems on structure and representations of Lie groups)

    OBATA NOBUAKI

    RIMS Kokyuroku　855　118-141　1993/12

    Publisher: Kyoto University

    ISSN： 1880-2818

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Books and Other Publications 16

  1. Pythonで学ぶ確率統計

    尾畑, 伸明, 荒木, 由布子

    共立出版　2023/10

    ISBN: 9784320125216

  2. 量子確率論の基礎（復刊）

    Accardi, Luigi, 尾畑, 伸明

    オーム社　2021/09

    ISBN: 9784274227578

  3. Probability and Statistics for Data Science

    Nobuaki Obata

    2021/07

    ISBN: 9784320125186

  4. 集合・写像・数の体系 - 数学リテラシ―として

    尾畑 伸明

    牧野書店　2019/02

    ISBN: 9784434256936

    More details Close

    集合と写像、およびそこから派生する基本的な諸概念を系統的に解説。現代数学で共通に使われる言葉遣いを習得し、高等学校レベルの数学リテラシーを強化する。宮城教育大学での数学の入門講義を元に書籍化。

  5. Spectral Analysis of Growing Graphs - A Quantum Probability Point of View

    OBATA Nobuaki

    Springer　2017/02

  6. 数理統計学の基礎

    尾畑伸明

    共立出版　2014

    ISBN: 9784320111189

  7. 確率モデル要論

    尾畑伸明

    牧野書店　2012

    ISBN: 9784434167393

  8. 情報数理の基礎と応用

    尾畑伸明

    サイエンス社　2008/07

  9. Quantum Probability and Spectral Analysis of Graphs

    Akihito Hora, Nobuaki Obata

    Springer　2007/05

  10. Mathematical Analysis of Random Phenomena

    A. B. Cruzeiro, N. Obata, H. Ouerdiane

    2007/04

  11. Probability and Statistics

    Nobuaki Obata

    Makino Shoten　2007/01

  12. Foundations of Quantum Probability Theory

    Luigi Accardi, Nobuaki Obata

    Makino Shoten　2003/09/10

  13. Non-Commutativity, Infinite-Dimensionality and Probability at the Crossroads

    Nobuaki Obata, Akihito Hora, Taku Matsui

    World Scientific　2002/12

  14. Trends in Contemporary Infinite Dimensional Analysis and Quantum Probability

    L. Accardi, H.-H. Kuo, Nobuaki Obata, Kimiaki Saito, Si Si, L. Streit

    Instituto Italiano di Cultura, Kyoto　2000/06

  15. 代数的確率論入門

    OBATA Nobuaki

    1999

  16. White Noise Calculus and Fock Space

    Nobuaki Obata

    Springer-Verlag　1994/04

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Presentations 117

  1. A quantitative approach to quadratic embedding constants of graphs Invited

    Nobuaki Obata

    The 7th Tunisian-Japanese Conference: Geometric and Harmonic Analysis on Homogeneous Spaces and Applications

  2. On quadratic embedding constants of graphs Invited

    Nobuaki Obata

    The 25th Indonesia-Japan Conference on Discrete and Computational Geometry, Graphs and Games (IJCDCG3 2023)

  3. Positivity of Q-matrices and quadratic embedding constants of graphs

    Nobuaki Obata

    10th International Congress on Industrial and Applied Mathematics (ICIAM2023)

  4. Quadratic embedding of graphs and positivity of their Q-matrices Invited

    Nobuaki Obata

    Workshop on Quantum Probability and Infinite Dimensional Analysis in honor of Professor Hui-Hsiung Kuo　2023/06/02

  5. Positive definite Q-matrices and primary non-QE graphs Invited

    Nobuaki Obata

    19th Workshop: Noncommutative Probability, Noncommutative Harmonic Analysis and Related Topics, with Applications　2022/08/02

  6. Some recent results on quadratic embedding constants of graphs Invited

    Nobuaki Obata

    International Conference on Graph Theory and Information Security V2022　2022/05/22

  7. Asymptotic spectral distributions for growing distance-regular graphs

    Nobuaki Obata

    AMS Spring Eastern Virtual Sectional Meeting: Special Session on Quantum Probability, Orthogonal Polynomials, and Special Functions　2022/03/19

  8. Quadratic embedding constants of graphs Invited

    Nobuaki Obata

    International Conference on Mathematics, Geometry, Statistics, and Computation (IC-MaGeStiC) 2021　2021/11/27

  9. Spectral analysis of growing graphs: A quantum probability point of view Invited

    Nobuaki Obata

    International Conference and PhD-Master Summer School on Groups and Graphs, Designs and Dynamics (G2D2)　2019/08/15

  10. Quadratic embedding constants of graphs International-presentation Invited

    OBATA Nobuaki

    Second International Conference on Pure and Applied Mathematics 2018 (2nd ICPAM)　2018/12/17

  11. Quantitative modeling of stochastic gene expression

    Keita IIDA, Nobuaki OBATA, Yoshitaka KIMURA

    2018年度応用数学合同研究集会　2018/12/15

  12. Quadratic embedding constants of graphs International-presentation

    OBATA Nobuaki

    International Workshop on Algebraic Combinatorics　2018/11/24

  13. Component sizes in random graphs International-presentation

    OBATA Nobuaki

    International Conference on Control, Games and Stochastic Analysis　2018/10/30

  14. Theoretical framework for single-cell gene expression analysis

    Keita Iida, Nobuaki Obata, Yoshitaka Kimura

    第15回生物数学の理論とその応用　2018/09/12

  15. Asymptotic spectral analysis of growing graphs: Review and bivariate extension International-presentation

    OBATA Nobuaki

    18th Workshop: Noncommutative Probability, Operators Algebras, Random Matrices and Related Topics, with Applications　2018/07/16

  16. グラフのスペクトル解析における量子確率論の手法 Invited

    尾畑 伸明

    日本数学会年会函数解析学分科会特別講演　2018/03/18

  17. 量子分解法の2変数化の試み Invited

    OBATA Nobuaki

    量子論にまつわる数学と数論の連携探索2018　2018/03/03

  18. グラフ理論の深みを覗く Invited

    OBATA Nobuaki

    東北大学大学院情報科学研究科シンポジウム: 「情報科学」から「交通ネットワーク」を考える　2018/02/18

  19. Asymptotic spectral analysis of growing graphs International-presentation Invited

    OBATA Nobuaki

    Colloquium at Department of Mathematics, Ohio State University　2018/01/18

  20. Asymptotic spectral analysis of graphs and orthogonal polynomials in two variables. International-presentation Invited

    OBATA Nobuaki

    Joint Mathematics Meetings San Diego AMS Special Session on Orthogonal Polynomials, Quantum Probability, and Stochastic Analysis　2018/01/13

  21. Central limit theorems for growing graphs: revisited International-presentation Invited

    OBATA Nobuaki

    Workshop on Quantum Probability, Infinite Dimensional Analysis and Related Topics　2017/12/28

  22. Component sizes in random graphs: Mathematical analysis and simulation International-presentation

    OBATA Nobuaki

    International Conference on Stochastic Analysis, Stochastic Control and Applications　2017/10/24

  23. 距離行列とグラフの2次埋め込み Invited

    OBATA Nobuaki

    名城大学理工学部数学科談話会　2017/09/27

  24. Distance Matrices and quadratic embedding of graphs International-presentation Invited

    OBATA Nobuaki

    International Conference on Graph Theory and Information Security (ICGTIS 2017)　2017/08/07

  25. 量子ウォークに関係する諸分野のチュートリアルレクチャー「直交多項式とスペクトル」

    量子系の数理と物質制御への展開II：量子ウォークを架け橋に　2016/10/20

  26. Distance matrices and quadratic embedding of graphs International-presentation

    12th Sendai Workshop on Non-commutative Stochastic Analysis and Applications　2016/10/17

  27. Quadratic embedding of graphs International-presentation

    Special Week Concentrated on IDAQP　2016/09/07

  28. Intensive Lectures: Introduction to Quantum White Noise International-presentation

    Special Week Concentrated on IDAQP　2016/09/07

  29. Counting walks: A quantum probability viewpoint International-presentation

    17th Workshop: Non-Commutative Probability, Levy Processes and Operator Algebras, with Applications　2016/07/24

  30. Graph products and counting walks International-presentation

    Tunisia-Japan Symposium on Science, Society and Technology (TJASSST2015)　2016/02/23

  31. Graph products and counting walks: A quantum probability viewpoint International-presentation

    The 14th Korea-Japan Workshop on Algebra and Combinatorics　2016/01/28

  32. Counting walks: A quantum probabilistic viewpoint International-presentation

    The 2nd International Conference on Mathematical Models (ICAMM 2016)　2016/01/05

  33. Algebraic central limit theorems for growing graphs International-presentation

    The 8th International Conference on Science and Mathematics Education in Developing Countries　2015/12/04

  34. On Stieltjes transform for augmented Jacobi parameters of Chebyshev type International-presentation

    11th Sendai Workshop on Infinite Dimensional Analysis and Quantum Probability　2015/10/26

  35. Quantum white noise derivatives and characterization of white noise operators International-presentation

    Quantum Markov Semigroups in Analysis, Physics and Probability　2015/08/18

  36. Quantum white noise derivatives and quantum Girsanov transform International-presentation

    10th Jikji Workshop on Infinite Dimensional Analysis and Quantum Probability　2015/07/29

  37. 量子確率論の最近の話題から

    統計数理研究所共同研究集会「科学における確率」　2015/07/06

  38. Quantum white noise derivatives and quantum Girsanov transform International-presentation

    2015 International Conference of the Chungcheong Mathematical Society　2015/06/12

  39. 量子確率論の最近の展開～スペクトルグラフ理論から量子場理論まで

    日本数学会東北支部会　2015/02/14

  40. Synchronization of coupled oscillators International-presentation

    International Conference on Mathematical and Stochastic Analysis and its Applications (ICMSAA-2014)　2014/12/18

  41. Spectral analysis of digraphs and applications to coupled oscillators International-presentation

    International Conference on Mathematics and its Applications (ICMAA-2014)　2014/12/15

  42. Transforms in quantum white noise calculus

    量子場の数理とその周辺　2014/10/06

  43. Transforms in quantum white noise calculus International-presentation

    Satellite Conference of the International Congress of Mathematicians 2014　2014/08/22

  44. Spectral analysis of digraphs and coupled oscillators with self-adaptive dynamics International-presentation

    16th Workshop on Non-Commutative Harmonic Analysis:Random Matrices, representation theory and free probability, with applications　2014/07/07

  45. Lee's analytic version theorem and development of complex white noise theory International-presentation

    Workshop on Probability and Analysis in honor of Professor Yuh-Jia Lee　2014/04/30

  46. Coupled oscillators on digraphs with self-adaptive dynamics International-presentation

    Pattern Formation: Mathematics & Materials　2014/04/30

  47. Free Meixner laws and localization of quantum walks on spidernets International-presentation

    Non-commutative and infinite dimensional harmonic analysis: representation theory and probability theory　2014/02/17

  48. Coupled oscillators on digraphs with self-adaptive dynamics International-presentation

    International Joint Research Week on Non-Commutative Stochastic Systems: Analysis, Modelling, and Applications　2014/02/03

  49. Spectral analysis of digraphs and coupled oscillators International-presentation

    3rd Tunisian-Japanese Conference: Geometric and Harmonic Analysis on Homogeneous Spaces and Applications　2013/12/18

  50. Spectral analysis of Manhattan street networks International-presentation

    Tunisian Japanese Symposium on Science, Society and Technology (TJASSST2013)　2013/11/15

  51. Quantum White Noise Derivatives and Their Applications International-presentation

    International Conference on Stochastic Analysis and Applications　2013/10/14

  52. Spectra of Manhattan street digraphs for synchronization of coupled oscillators International-presentation

    NIMS Hot Topics Workshops and The 8th Jikji workshop: Infinite Dimensional Analysis and Quantum Probability　2013/08/19

  53. Asymptotic spectral distributions of distance k-graphs of Cartesian product graphs International-presentation

    International Conference in Honour of Sixtieth Birthday of Rajendra Bhatia: Matrices and Operators　2012/12/27

  54. Quantum probability and asymptotic spectral analysis of growing graphs International-presentation

    International Conference on mathematical modeling and its aplications 2012　2012/12/22

  55. Asymptotic spectral analysis of growing graphs: A quantum probabilistic approach International-presentation

    International Conference on Frontiers of Statistics and its Applications　2012/12/21

  56. Quantum probability and asymptotic spectral analysis of growing graphs International-presentation

    International Conference on Stochastic Modelling and Simulation (ICSMS2012)　2012/12/17

  57. Recent developments of quantum white noise calculus: Quantum stochastic derivatives and their applications

    数理解析研究所研究集会「量子場の数理とその周辺」　2012/11/14

  58. Distance k-graphs of direct product graphs and their asymptotic spectral distributions International-presentation

    QP 33 "Quantum Probabilities and Related Fields"　2012/10/01

  59. Localization of quantum walks on spidernets International-presentation

    15th Workshop on Non-Commutative Harmonic Analysis: Random Matrices, representation theory and free probability, with applications　2012/09/24

  60. Random walks, quantum walks and free Meixner laws International-presentation

    Random Media II　2012/09/03

  61. An introduction to quantum white noise calculus International-presentation

    The 7th Jikji Workshop: Infinite Dimensional Analysis and Quantum Probability　2012/07/22

  62. Random walk, quantum walk, and quantum probability International-presentation

    6th KMS Probability Workshop　2012/06/01

  63. Spectral analysis of digraphs International-presentation

    Workshop on Non-Commutative Harmonic Analysis with Applications to Real World Complex Phenomena　2012/01/16

  64. Quantum probabilistic spectral analysis of graphs

    数理解析研究所研究集会「独立性と従属性の数理 -- 代数と確率の出会い --」　2011/12/19

  65. Quantum probabilistic spectral analysis of large graphs International-presentation

    The 2nd Tunisian--Japanese Conference: Geometric and Harmonic Analysis on Homogeneous Spaces and Applications　2011/12/12

  66. Transformations of Fock space operators in terms of quantum white noise calculus International-presentation

    Tunisian Japanese Symposium on Science, Society and Technology (TJASSST11)　2011/11/11

  67. Spectral analysis of product graphs International-presentation

    3rd Conference of Settat on Operator Algebras and Applications　2011/11/01

  68. Quantum probabilistic spectral analysis of networks and applications International-presentation

    International Conference on Stochastic Analysis and Applications　2011/10/10

  69. Spectral analysis of Manhattan products of digraphs International-presentation

    14th Workshop: Non-commutative Harmonic Analysis　2011/09/25

  70. Convolution operators in white noise calculus: Revisited International-presentation

    2nd International Conference on Quantum Probability and Related Topics　2011/05/29

  71. Asymptotic Spectral Analysis of Large Graphs --- A Quantum Probabilistic Approach

    Analysis on Graphs in Sendai 2011　2011/02/21

  72. Quantum probabilistic approach to spectral analysis of networks: Some recent results International-presentation

    Japan-Korea Workshop on Algebra and Combinatorics　2011/01/24

  73. Quantum probability theory: Notions of independence and applications to spectral analysis of graphs International-presentation

    The 3rd ILJU School of Mathyematics: Banach spaces & Related Topics　2011/01/16

  74. Join of one-mode interacting Fock spaces and applications to random walks International-presentation

    The 6th Jikji Workshop on Infinite Dimensional Analysis and Quantum Probability　2011/01/10

  75. Non-commutative independence and structure of graphs

    京都大学数理解析研究所研究集会「独立性と従属性の数理 --- 函数解析学の視点から」　2010/12/20

  76. Join of one-mode interacting Fock spaces and applications International-presentation

    10th Sendai Workshop on Infinite Dimensional Analysis and Quantum Probability　2010/12/17

  77. Deformed Vacuum States and Q-Matrices of Graphs International-presentation

    Symposium on Analysis and Probability 2010　2010/08/10

  78. Quantum probabilistic aspect to random walks on graphs International-presentation

    13th Workshop on Noncommutative Harmonic Analysis　2010/07/11

  79. Some New Aspects of Bogoliubov Transformations from Quantum White Noise Calculus International-presentation

    The 5th Jikji Workshop on Infinite Dimensional Analysis and Quantum Probability　2010/01/06

  80. Quantum white noise derivatives and implementation problem International-presentation

    International Conference on Mathematical Quantum Field Theory and Renormalization Theory　2009/11/26

  81. Quantum stochastic derivatives and applications International-presentation

    チュニジア-日本 文化・科学・技術学術会議 第10回記念大会 (TJASSST 10)　2009/11/11

  82. Quantum white noise derivatives and applications International-presentation

    International Conference on Stochastic Analysis and Applications　2009/10/12

  83. Quantum white noise calculus: Quantum white noise derivatives and applications International-presentation

    12th Workshop on Noncommutative Harmonic Analysis with Applications to Probability　2009/08/16

  84. Recent developments in quantum white noise calculus:Quantum white noise derivatives and implementation problem International-presentation

    2009 NIMS Hot Topics Workshop on Infinite Dimensional Analysis and Related Topics　2009/06/22

  85. 量子確率論とグラフのスペクトル解析

    第26回代数的組合せ論シンポジウム　2009/06/22

  86. Spectral analysis of random complex networks International-presentation

    The 3rd Cheongju Workshop on Infinite Dimensional Analysis and Quantum Probability　2009/01/12

  87. 量子確率解析からの展望

    「離散幾何学から提案する新物質創成と物性発現の解明」キックオフシンポジウム　2008/12/26

  88. Recent developments in quantum white noise theory: Stochastic integrals and transformations International-presentation

    29th Conference on Quantum Probability and Related Topics　2008/10/13

  89. Quantum probabilistic approach to spectral analysis of growing graphs International-presentation

    Korea Operator Theory and Its Applications Conference (KOTAC 2008)　2008/06/19

  90. Questions on quantum stochastic integrals International-presentation

    KOSEF-JSPS workshop on Infinite Dimensional Analysis and Quantum Probability　2007/12/03

  91. Quantum stochastic gradients and quantum Hitsuda-Skorokhod integrals International-presentation

    International Conference on Stochastic Analysis and Applications　2007/11/05

  92. Asymptotic spectral analysis and applications to complex networks International-presentation

    Conference on Infinite-Dimensional Harmonic Analysis　2007/09/10

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    Japan-Germany Research Cooperative Program A. Hora (Nagoya University)

  93. Asymptotic spectral analysis of random graphs -- Towards complex networks International-presentation

    10th Workshop: Non-Commutative Harmonic Analysis with Applications to Probability　2007/08/06

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    Mathematical Research and Conference Center Institute of Mathematics Polish Academy of Sciences Marek Bo\\.zejko

  94. 量子確率論によるグラフのスペクトル解析

    量子解析におけるミクロ・マクロ双対性　2006/12/25

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    京都大学数理解析研究所・共同研究 小嶋 泉(京都大学数理解析研究所)

  95. Quantum probability and random graphs International-presentation

    The 2nd KOSEF--JSPS Joint Workshop on Infinite Dimensional Analysis and Quantum Probability　2006/11/14

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    Dankook University Un Cig Ji (Chungbuk National University)

  96. Asymptotic spectral analysis of growing graphs and application to quantum walks International-presentation

    9th Workshop: Non-Commutative Harmonic Analysis with Applications to Probability　2006/09/29

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    Mathematical Research and Conference Center, Institute of Mathematics, Polish Academy of Sciences (B\\cdlewo, Poland) \\par Marek Bo\\.zejko

  97. Asymptotic spectral analysis of growing graphs and application to quantum walks International-presentation

    Current Status of Rigorous Statistical Mechanics and Mathematical Quantum Field Theory　2006/09/04

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    Kyushu University Taku Matsui

  98. Positive definite kernels on graphs and applications International-presentation

    KOSEF-JSPS Joint Research Project: Noncommutative Aspects in Stochastic Analysis and Applications to Mathematical Models　2006/06/22

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    Department of Mathematics Chungbuk National University Un Cig Ji (Research Institute of Mathematical Finance, % Department of Mathematics, Chungbuk National University)

  99. Quantum white noise calculus --- Some unitarity problems International-presentation

    International Conference on White Noise Analysis and Quantum Information　2006/02/21

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    Meijo University

  100. Unitarity questions in white noise theory International-presentation

    KOSEF-JSPS Joint Workshop IDAQP-WEEK　2006/02/06

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    Tohoku University Nobuaki Obata, Fumio Hiai, Song Liang (Tohoku University) Un Cig Ji (Chungbuk National University)

  101. Quadratic quantum white noise International-presentation

    KOSEF-JSPS Joint Workshop on Infinite Dimensional Analysis and Quantum Probability　2005/12/22

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    Department of Mathematics Chungbuk National University Un Cig Ji (Research Institute of Mathematical Finance, Department of Mathematics, Chungbuk National University)

  102. Quantum white noise calculus

    量子情報の数理　2005/12/01

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    大矢雅則（東京理科大学） 国際高等研究所

  103. Quantum white noise derivatives International-presentation

    6th Tunisia-Japan Seminar on Culture, Science and Technology 2005　2005/11/10

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    Session ``Information Technology and Mathematics" Universit\\'e de Sousse

  104. Quantum probability and spectral analysis of graphs International-presentation

    International Conference on Mathematical Analysis of Random Phenomena　2005/09/12

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    Hotel Abou Nawas Hammamet (Tunisia) Habib Ouerdiane (University of Tunis El Manar), Ana Bela Cruzeiro (University of Lisbon)

  105. Asymptotic spectral analysis of growing regular graphs International-presentation

    8th Workshop on Noncommutative Harmonic Analysis with Applications to Probability　2005/08/29

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    Mathematical Research and Conference Center Institute of Mathematics, Polish Academy of Sciences, B\\cdlewo, Poland Marek Bo\\.ejko (University of Wroc{\\l}aw, Poland)

  106. Asymptotic spectral analysis of growing graphs International-presentation

    Madeira Mathematics Encounters XXIX: Infinite Dimensional Analysis, Networks and Mathematical Topics in Quantum Control and Quantum Entanglement　2005/08/03

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    L. Streit (Universidade da Madeira) Centro de Ci\\^encias Mathem\\'aticas Universidade da Madeira

  107. Quantum probabilistic approach to spectral analysis on large graphs International-presentation

    4th Jagna International Workshop "Method and Applications of Infinite Dimensional Analysis"　2005/01/03

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    C. C. Bernido and M. V. C.-Bernido (RCTP, CVIF)

  108. 量子確率論とグラフのスペクトル解析

    量子情報の数理　2004/11/19

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    大矢雅則（東京理科大学） 国際高等研究所

  109. Kesten measures, Wigner semicircle and beyond International-presentation

    3rd Sendai Workshop: Free Probability and Random Matrices　2004/11/01

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    F. Hiai and N. Obata GSIS Tohoku University

  110. Quantum probability and spectral analysis on graphs International-presentation

    Volterra--CIRM International School: Quantum probability and spectral analysis on large graphs　2004/09/19

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    L. Accardi, A. Hora, N. Obata Levico Terme, Italy

  111. Recent development of quantum white noise calculus International-presentation

    6th Pan-African Congress of Mathematicians　2004/09/01

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    Institut National des Sciences Appliqu\\'ees et de la Technologie (INSAT), Tunis, Tunisia

  112. Spectral analysis on graphs: A quantum probabilistic viewpoint International-presentation

    International Conference on Probability Theory on Groups and Related Structures　2004/08/02

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    Budapest University of Technology and Economics, Hungary (Gyula Pap)

  113. Independence, central limt theorems and interacting Fock spaces related to graphs International-presentation

    25th Conference on Quantum Probability and Related Topics　2004/06/21

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    Mathematical Research and Conference Center B\\cdlewo, Poland (Marek Bo\\.zejko)

  114. Spectral analysis on graphs: A quantum probabilistic viewpoint International-presentation

    4th Workshop on Operator Algebras and Quantum Probability　2004/06/18

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    University of \\L\\'od\\'z, Poland (Staszek Goldstein)

  115. Quantum white noise derivatives International-presentation

    Tunisia-Japan Symposium on Culture, Science and Technology 2004　2004/05/24

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    Workshop "Stochastic Analysis and Applications" Universit\\'e de Tunis El Manar (Habib Ouerdiane) Tunisia- Japan Symposium on Culture, Science and Technology 2004 Sfax University (Moncef and Tetsuo Ida)

  116. 量子確率論とグラフのスペクトル解析

    量子系の数理とその量子コンピュータへの応用　2004/02/23

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    京都大学数理解析研究所短期共同研究（東京理科大学：大矢雅則）

  117. Quantum probability and spectral analysis of graphs

    第12回 凝縮系物理(非平衡系の統計物理)シンポジウム　2003/12/17

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    筑波大学物理学系(有光敏彦)

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Industrial Property Rights 2

  1. Method and Apparatus for Revealing Latent Characteristics Existing in Symbolic Sequences

    US 6438496 B1

    Property Type: Patent

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    3149824

    Property Type: Patent

Research Projects 60

  1. ネットワーク数理の学際的研究 Competitive

    2007/04 - Present

  2. Quantum Probability Theory Competitive

    System: Grant-in-Aid for Scientific Research

    1997/04 - Present

  3. Quantum White Noise Calculus Competitive

    1990/04 - Present

  4. 新たな複雑系データのための関数データ解析手法の開発と適用

    荒木 由布子, 尾畑 伸明, 今泉 允聡, 川野 秀一, 山本 倫生, 岩田 欧介

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業

    Category: 基盤研究(B)

    Institution: 東北大学

    2023/04/01 - 2027/03/31

  5. 新たな複雑系データのための関数データ解析手法の開発と適用

    荒木 由布子, 尾畑 伸明, 今泉 允聡, 岩田 欧介, 川野 秀一, 山本 倫生

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業

    Category: 基盤研究(B)

    Institution: 東北大学

    2023/04/01 - 2027/03/31

  6. Quantum probability and asymptotic analysis of large finite systems

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Tohoku University

    2019/04/01 - 2023/03/31

  7. Non-commutative stochastic analysis and mathematical study of networks

    Obata Nobuaki

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Tohoku University

    2016/04/01 - 2019/03/31

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    Non-commutative stochastic analysis, originally as a mathematical framework for statistical problems in quantum physics, has developed providing new aspects and methods for classical problems. We initiated a multi-variate extention of quantum decomposition, which has been a central issue for a long time, through spectral analysis of a pair of strong regular graphs. Some important operators are characterized by differential equations involving quantum white noise derivatives. We studied the graph isomorphism problem in terms of quantum walks and collaborated for application in the field of quantum engineering and quantum physics. By a large scale simulation we examined statistical properties of connected components of the configuration model and found a power law at the critical point with an index which is different from the known results.

  8. New development of theory of generalized functionals, an infinite dimensional stochastic analysis and applications to theory of quantum dynamical system

    Saito Kimiaki, ICHIHARA Kanji, OBATA Nobuaki, HIBINO Yuji, ACCARDI Luigi, KUO Hui-Hsiung

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (C)

    Institution: Meijo University

    2015/04/01 - 2018/03/31

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    We researched new developments of theory of generalized functionals, an infinite dimensional stochastic analysis based on the theory,and its applications.We obtained remarkable results:①We constructed spaces of generalized functionals from new spaces consisting of distributions that are closed in the product of distributions,and also obtained an integral expressions of the higher order Levy Laplacians.Moreover,we obtained a SDE including random directional differentiations induced from the delta distribution centered at powers of an infinite dimensional Brownian motion.②We initiated the new method of stochastic integral for instantly independent stochastic processes,and proved the Doob-Meyer type decomposition theorem. ③We proved that the nuclearity of the space of test functionals for infinite dimensional distributions is a necessary and sufficient condition for a characterization of the S-transform.The result is the breakthrough as an answer for an unsolved problem.

  9. Interdisciplinary Approach to mathematical network theory

    obata nobuaki, KONNO Norio, SEGAWA Etsuo, NAKAZAWA Takashi

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Tohoku University

    2014/07/18 - 2017/03/31

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    Based on the non-commutative analysis, we aimed at developing an interdisciplinary approach to mathematical theory of networks. The long-time behaviour of energy levels in the lazor experiment of isotope separation was obtained by means of spectral analysis of quantum walk and we examined a good fitting to the physical experiment. We derived complex spectra of some Manhattan products of directed paths. The Gauss-Poisson distributions were derived as the asymptotic spectral distributions of strong regular graphs by means of two-variable orthogonal polynomials. Applying the Kronecker product to two-dimensional restricted lattices, we obtained the spectral density in terms of elliptic integrals. We derived the distribution of connected components at the critical phase of percolation on the Cayley tree. We analyzed the mechanism of the outbreak for an infection model with multiple sources of infection.

  10. Quantum probabilistic analysis of dynamics on complex networks

    obata nobuaki, KONNO Norio, HASEGAWA Takehisa

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Challenging Exploratory Research

    Institution: Tohoku University

    2014/04/01 - 2017/03/31

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    From quantum probability point of view we aimed at developing mathematical approach to complex networks. We obtained formulas for spectral distributions of certain graph products. These are applied to counting walks on two-dimensional restricted lattices and the density functiones are expressed in terms of elliptic integrals. We obtained the long-time asymptotics of quantum walks on the semi-infinite line by means of Chebyshev polynomials and examined the experimental data. We obtain the eigenvalues of the adjacency matrices and Laplacians of the Manhattan product of directed paths and, with the aid of numerical analysis, examined the behaviour of coupled oscillators. As for multi-variable polynomials, we obtained Gauss-Poisson distribution as a limit spectral distribution of strong regular graphs by means of two-variable Krautchuk polynomials.

  11. Discrete Geometric Analysis for Quantum Spin System

    Kotani Motoko, Obata Nobuaki, Tate Tatsuya, Miyaoka Reiko

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (A)

    Institution: Tohoku University

    2012/04/01 - 2017/03/31

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    We study mathematical framework for Quantum spin system. Physics on topological Insulator and topologically protected surface/edge state is formulated in K-theory. By using the non-commutative geometry, we generalized it to disordered systems. We also develop discrete surface theory to study the relation of microscopic structural data and macroscopic properties and apply it to carbon networks.

  12. New developments on quantum information theory by an infinite dimensional stochastic analysis and applications to dynamical system theory

    SAITO KIMIAKI, MIMACHI Yuko, ICHIHARA Kanji, OBATA Nobuaki, HIBINO Yuji

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (C)

    Institution: Meijo University

    2012/04/01 - 2015/03/31

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    ①We introduced an infinite dimensional Brownian motions associated with higher real order derivatives of white noise and proved that their generators of this stochastic processes are given by exotic Laplacians. We also proved that higher real order Cesaro Theorem, and that the exotic Laplacian coincides with the Levy Laplacian associated with higher real order derivative of white noise. ② Constructing a space of distributions on which the product is well-defined, we formulated powers of an infinite dimensional Brownian motion without any renormalization as mathematics. This implies a generalization of the Ito formula in stochastic analysis. On the space of distributions the divergent part in the theory of quantum field is also formulated as mathematics. ③ We gave a method of triangulation decomposition of the transition probability matrix of the G-W branching process, and obtained a limiting probability distribution of the process. We also developed a new algorism of the method.

  13. Quantum stochastic analysis - Transforms and spectral analysis

    OBATA Nobuaki, FUKUIZUMI Reika, HASEGAWA Takehisa, SEGAWA Etsuo, KUBO Hideo, HIAI Fumio, SUZUKI Kanako

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Tohoku University

    2011/04/01 - 2015/03/31

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    For the development of quantum stochastic analysis we focused on 'quantum white noise calculus' from analytic aspect and 'spectral analysis of complex networks' from algebraic aspect. We aimed at the establishment of the mathematical fundamentals and the paradigm for collaborating with other research fields for applications. By means of quantum white noise calculus, the Bogoliubov transform and the Girsanov transform are characterized by the white noise differential equations of new types. A quantum probabilistic method is applied to the spectral analysis of digraphs such as Manhattan product. The phase transition of various dynamics on networks is studied in detail with the help of numerical computation. New statistical properties of quantum walks on graphs such as localization are obtained by generalizing the existing method of spectral analysis.

  14. Non-perturbative spectral analysis of quantum system by stochastic method

    HIROSHIMA Fumio, ITO Keiichi, HIROKAWA Masao, MATSUI Taku, OBATA Nobuaki, SASAKI Itaru, SUZUKI Akito

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Kyushu University

    2011/04/01 - 2014/03/31

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    Spectrum of non-relativistic QED, the Nelson model and spin-boson models in quantum field theory are studied by functional inegrations. We can investigate QFT on manifold, enhanced binding and non-enhanced binding, non-local PF model, removal of UV cutoff and infinite volume limit of Gibbs measure in the sense of local weak in a non-perturbative way.

  15. Spectral analysis of complex networks and modeling methods by statistics

    OBATA Nobuaki, HORA Akihito, KONNO Norio

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Challenging Exploratory Research

    Institution: Tohoku University

    2011 - 2013

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    (1) Spectral analysis of networks: The asymptotic spectral distribution of the distance-k graph of the cartesian product graph is derived as a combinatorial central limit theorem. The asymptotic spectral distribution of weighted hypercubes are described in terms of q-deformed Hermite polynomials. The spectral distribution is completely determined for the Manhattan product of directed paths of small orders, and thier asymptotic behaviors are obtained in the infinite length. (2) Statistical and asymptotic behaviors of dynamics for the modeling methods: A quantum probabilistic method is applied to classical random walks for reconstructing transition probability and recurrence probability. A necessary and sufficient condition is obtained for a quantum walk (Grover walk) on a spidernet in order to exhibit the localization.

  16. Study on decomposition of unitary representations of groups and harmonic functions on branching graphs

    HORA Akihito, ISHI Hideyuki, MATSUMOTO Sho, OBATA Nobuaki

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (C)

    2011 - 2013

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    We intend to develop harmonic analysis on a large group, which plays a role in clarifying complex phenomena involving a huge number of factors. Our project aims at establishing a concrete framework by which one clearly understands decomposition of representations of a large group. For wreath products of a compact group, including the infinite symmetric group and infinite complex reflection groups, we took interactive approach from probability theory, group representations and potential theory, and obtained concrete and detailed results on such objects as group character formulas and their characterization, boundaries of the branching graph and minimal harmonic functions, and description of ergodic probabilities on the path space of the graph.

  17. New development of harmonic maps

    URAKAWA Hajime, ICHIYAMA Toshiyuki, ITOH Jinichi, OBATA Nobuaki, INOGUCHI Junichi, HIAI Fumio

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (C)

    Institution: Tohoku University

    2009 - 2012

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    In 1986, the concept of the bi-harmonic map which is an extension of harmonic maps was introduced. We raised the new notion of the bi-Yang-Mills field, which is an analog of the bi-harmonic map, and showed its isolation phenomena. That is, bi-Yang-Mills fields with some square-integral norm over compact manifolds with positive Ricci curvature must be Yang-Mills fields. We showed bi-harmonic maps which have a bounded square-integral norm must be harmonic if the target space has non-positive curvature. We classified all the bi-harmonic maps for cases where the target space is a compact Lie group or compact symmetric spaces.

  18. Generalizations of infinite dimensional Laplacians, construction methods of stochastic processes and developments in quantum information analysis

    SAITO Kimiaki, MATSUZAWA Tadato, ICHIHARA Kanji, MIMACHI Yuko, NISHI Kenjiro, OBATA Nobuaki, HIBINO Yuji

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (C)

    Institution: Meijo University

    2009 - 2011

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    In this research, we considered a quantization and a new approach to a quantum information analysis by researching the infinite dimensional stochastic analysis jointly from major fields : probability theory, analysis, graph theory, number theory and computer science. Especially we succeeded in constructing the theory of higher order derivatives of white noise based on the stochastic analysis associated with exotic Laplacians defined by higher order Cesaro means of the second differentiation. It is a quite important progress and a creative point that a quantum information analysis in this direction can be constructed.

  19. Quantum Probability Theory and Infinite Dimensional Analysis

    OBATA Nobuaki, HIAI Fumio, URAKAWA Hajime, SUZUKI Kanako, LIANG Song, HORA Akihito, SAITO Kimiaki, HOROSHIMA Fumio, YOSHIDA Hiroaki

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Tohoku University

    2008 - 2010

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    We investigated mathematical models of random phenomena by revealing and utilizing non-commutative structures hidden behind. We introduced the new concept of quantum white noise derivative and applied to generalization of quantum stochastic integrals, integral representation of Fock space operators, representation of quantum martingales, and characterization of Bogoliubov transformation. For the structural analysis of complex networks, we developed the quantum probabilistic approach to spectral analysis and transition probability of random walks, and studied free probability, free entropy, and matrix inequalities.

  20. Non-perturbative analysis of quantum interaction systems

    HIROSHIMA Fumio, ITOU Keiichi, HIROKAWA Masao, MATSUI Taku, NAKANO Fumihiko, OBATA Nobuaki, HATTORI Tetsuya

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Kyushu University

    2008 - 2010

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    Ground states of quantum interaction systems are investigated. By means of functional integral representations quantum systems are studied in non-perturbative way. We show the existence and absence of ground states of the so-called Nelson model defined on a Lorentz manifold, we remove the UV cutoff by means of micro-local analysis. The asymptotic completeness of the Pauli-Fierz model defined on an indefinite Hilbert space is also established. We investigate enhanced bindings. We specify the no-binding regime of the Pauli-Fierz model and show the enhanced binding of the relativistic Nelson model. We next consider functional integrations. The heat semi-group generated by the relativistic Schroedinger operator with spin 1/2 is represented in terms of Brownian motions, Poisson processes and subordinators. By this we can derive a non-trivial energy comparison inequality. Moreover we extend this path integral representation to the Bernstein functions of the Laplacian, and apply this to a spin-boson model to show the uniqueness of the ground state. We furthermore succeeded to construct an infinite volume limit of the Gibbs measure with double stochastic integral as potential.

  21. Integrated study of probability and representation theory towards harmonic analysis on huge groups

    HORA Akihito, OKADA Soichi, TATE Tatsuya, HIRAI Takeshi, OBATA Nobuaki, SHIMOMURA Hiroaki, KAWAZOE Takeshi, YAMADA Hirofumi, ARAI Hitoshi, NISHIYAMA Kyo, ISHI Hideyuki, MATSUMOTO Sho, INAHAMA Yuzuru

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Nagoya University

    2007 - 2010

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    Towards developing harmonic analysis on huge groups, we did integrated studies of probability theory and group representations. Harmonic analysis is a discipline which seeks deep mathematical structures by looking at symmetries of the objects and develops analysis relying on them. In this study, we are led to huge groups describing the symmetries because our objects are so big as to have an infinite degree of freedom. Main results among the ones we obtained are (i) classification and explicit formulas of the characters which are building blocks of harmonic analysis, and (ii) a series of theorems which construct a bridge between asymptotic behavior of representations of groups and probabilistic limit theorems.

  22. ランダムグラフの量子確率論的スペクトル解析

    尾畑 伸明, 洞 彰人

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業

    Category: 挑戦的萌芽研究

    Institution: 東北大学

    2007 - 2009

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    グラフ(有限または無限)に付随する様々な行列や作用素(隣接行列・Q-行列・ラプラシアン・推移行列など)のスペクトルはグラフの構造をさまざまに反映し、代数的グラフ理論の中心的なテーマである。近年、(a)多様な独立性(b)量子分解法(c)分割の統計、などの量子確率論的手法によるスペクトル解析が大きく発展している。本研究では、これらの手法をランダムグラフに適用できるように拡張し、複雑ネットワークへの応用を視野にいた具体的なモデルのスペクトル分布を導出することが重要である。特に、ワッツ・ストロガッツ模型の修正モデル(一般化エルデシュ・レニーモデルと呼ぶ)とランダム閾値グラフについて研究を重ねた。今年度は、今野氏・井手氏との共同研究によって、一般的な閾値グラフのスペクトルを計算し、ランダム閾値グラフの平均スペクトル分布を導出したことが大きな成果である。ランダム閾値グラフはランダム成長グラフととらえることができ、その成長の仕方に対応する独立性の定式化は非常に興味深く、研究を続行している。ボロバシュの流れをくむウチャック氏を招聘し、ランダムグラフの連結成分の挙動についてスペクトル的アプローチを議論した。残念ながら、エルデシュ-レニーのランダムグラフに対する希薄極限のスペクトル密度の導出には至らなかった。第26回代数的組合せ論シンポジウム(山形)と数理物理サマースクール2009(東京)において、量子確率論的手法について総合報告をするとともに、いくつかの国際会議で成果の一部を発表した。日本と韓国の代数的組合せ論研究者との研究交流が始まり、新しい展開が期待できる環境が整ってきた。

  23. Constructive research on infinite dimensional stochastic Processes and its applications to quantum information analysis

    SAITO Kimiaki, MATSUZAWA Tadato, OBATA Nobuaki, HIBINO Yuji, MIMACHI Yuko, NISHI Kenjiro

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (C)

    Institution: Meijo University

    2007 - 2008

  24. Study of free probability and operator algebras based on random matrices

    HIAI Fumio, OBATA Nobuaki, URAKAWA Hajime, OZAWA Masanao, KOSAKI Hideki, YAMAGAMI Shigeru, HORA Akihito, UEDA Yoshimichi, NAKAMURA Makoto

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Tohoku University

    2005 - 2008

  25. Mathematical study of quantum information and quantum computing

    MASANAO Ozawa, HIAI Fumio, OBATA Nobuaki, TANAKA Kazuyuki, HOTTA Masahiro, KANEKO Makoto, HIAI Fumio, OBATA Nobuaki, TANAKA Kazuyuki, HOTTA Masahiro

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    2005 - 2008

  26. Spectral Analysis of infinite grapgs with discrete group actions

    KOTANI Motoko, SHIOYA Takashi, IZEKI Hiroyasu, OBATA Nobuaki, SUNADA Toshikazu, NAYATANI Shin

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Tohoku University

    2004 - 2007

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    We discuss ed a long time behavior of periodic random walks on a crystal lattice in view of geometry, a large deviation property in particular, and relate it to a rational convex polyhedron in the first homology group of a finite graph, which, as remarkable combinatorial features,. A crystal lattice has a metric structure with the graph distance. By changing scale of the distance, we obtain a one-parameter family of metric spaces. The Gromov-Hausdorff limit of the sequence is called the asymptotic cone at the infinity of the crystal lattice. As the scale go to zero., because of the periodicity of the crystal lattice, the asymptotic cone exists and we determinded its unit ball explicitely in terms of combinatorial data. We also published a survey article on discrete geometric analysis of crystal lattice from Sugaku Expository, Amer.Math.Soc. In there, we discussed spectral properties and geometry of random walks on a crystal lattice, such as the law of large number, the central limit theorem, large deviation and spectrum of magnetic Schroedinger operators from non-commutative geometry.

  27. Global analysis of the heat kernels on Riemannian manifolds and graphs

    URAKAWA Hajime, ASOH Tohl, MUNEMASA Akihiro, KANEKO Makoto, OBATA Nobuaki, ITOH Jin-ichi

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Tohoku University

    2004 - 2006

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    The heat kernels of compact Riemannian manifolds converge to the equilibrium when time goes to infinity. We studied the rates of the heat kernels how do they reflect from the geometric structures of Riemannian manifolds. We showed the convergence rates are Lipshitz continuous on the deformation of Riemannian manifolds, we gave their upper estimation in terms of Ricci curvature and diameter, and also the upper estimation in terms of the non-zero first eigenvalue of the Laplacian. We gave their precise lower and upper estimations in the case of compact Riemannian symmetric spaces of rank one. A Yang-Mills connection is a critical point of the Yang-Mills functional, and this is an analogue of harmonic map which is a critical point of the energy functional. Recently, the notion of biharmonic map was introduced which is a critical point of the 2-energy functional. We introduced the notion of 2-Yang-Mills connection which is a critical point of the 2-Yang-Mills functional. This notion is a natural generalization of Yang-Mills connection, and many further studies would be expected. We introduced quite new method to visualize the Dirichlet or Neumann boundary eigenvalue problem of the Laplacian on plane domains. This method improved 20 percents fast comparing the known methods and reduced many steps input the data into computers. This new method made visualizations of the eigenvalue problems of the Laplacian on compact surfaces and bounded three dimensional domains. We applied to get patent of this method for programming of computer.

  28. Nonlinear theory of quantum white noise and its non-Gaussian extension

    OBATA Nobuaki, HIAI Fumio, URAKAWA Hajime, HORA Akihito, ARIMITSU Toshihico, SAITO Kimiaki

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Tohoku University

    2003 - 2005

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    Stochastic analysis has developed considerably keeping profound applications to mathematical analysis of random phenomena, where the traditional framework, called the Ito calculus, is based upon functionals of Brownian motion. We start, in this research project, with the new aspect of quantum white noise which is obtained by applying quantum decomposition and time derivative to the Brownian motion. Since the quantum white noise is more primary, we come naturally to two lines of research beyond the traditional stochastic analysis : nonlinear theory and non-Gaussian extension. We developed quantum white noise theory by making research collaboration, workshops, summer schools, international conferences. The research subjects are as follows : (1) Nonlinear white noise equations : We developed white noise operator theory by means of a newly obtained characterization theorem and introduced the notion of quantum white noise derivatives. (2) Complex white noise : Unitarity of the Fourier-Gauss transform is proved. We found that the solution to normal-ordered white noise equation involving quadratic quantum white noise possesses partial unitarity. (3) Levy Laplacian and higher powers of quantum white noises : Associated stochastic processes are constructed and the relation between them is established through the heat equation. (4) Interacting Fock space : We established a systematic approach to asymptotic spectral analysis of graphs, in particular, for growing regular graphs and graphs related to notions of independence. (5) Non-Gaussian stochastic processes : We are continuing the study of interacting Fock space of multi-mode towards quantum decomposition of stochastic processes. (6) Infinite dimensional harmonic analysis : The method of quantum decomposition is applied to prove a generalization of the Kerov central limit theorem. The asymptotic representation theory of the symmetric groups and the infinite wreath products have been developed. (7) Application to quantum physics : We promoted collaboration with physicists through quantum stochastic differential equations, statistical properties of turbulence, Bose-Einstein condensation on graphs.

  29. Mathematical Research of Quantum Information and Quantum Computing

    OZAWA Masanao, HIAI Fumio, OBATA Nobuaki, TAYA Hisao

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Tohoku University

    2002 - 2004

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    1.Heisenberg's uncertainty principle, which gives the trade-off between measurement noise and disturbance, has been reconsidered. Its limitation of the validity has been clarified and the universally valid generalization (universal uncertainty principle) has been established. If any measuring apparatus measures an observable A with noise ε(A) and disturbance η(B) on B, we have the relation ε(A)η(B)+ε(A)σ(B)+σ(A)η(B)≧(1/2)|<[A,B]>|, where σ stands for the standard deviation in the state just before the measurement. 2.It has been shown that, if the noise ε(A) and the disturbance η(B) are statistically independent from the initial state of the measured object, we have the original Heisenberg relation ε(A)η(B)≧(1/2)|<[A,B]>|. 3.From the universal uncertainty principle, Wigner-Araki-Yanase (WAY), found in 1952 to set a limitation of measurements under conservation law, has been quantitatively generalized to a reciprocal relation between the mean-square-noise of the measurement and the variance of the conserved quantity. 4.As a consequence from the universal uncertainty principle, it has been shown that the angular momentum conservation law sets a limitation to the accuracy of quantum gate operations, the accuracy of the CNOT gate controlled by an interaction with n qubit ancilla system is limited with error probability at least 1/(4n^2), and the CNOT controlled by the electro-magnetic field with average photon N is limited with error probability at least 1/(16N).

  30. Study of noncommutative analysis and free probability theory on operator algebras

    HIAI Fumio, YAMAGAMI Shigeru, OBATA Nobuaki, URAKAWA Hajime, UEDA Yoshimnichi

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (C)

    Institution: Tohoku University

    2002 - 2003

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    We studied operator theory and operator algebra theory on Hubert spaces with applications to noncommutative probability theory. In recent years, free probability theory initiated by D.Voiculescu has been extensively developed as a branch of noncommutative probability theory. We investigated large deviation theory for random matrices and free relative entropy related to free probability theory. We investigated automorphsims on (interpolated) free group factors by the method of free products. Moreover, we studied norm inequalities for means of operators and obtained a number of inequalities extending the arithmetic-geometric norm inequalities for operators. More concretely, (1)We obtained a new norm inequality for matrices involving operator monotone functions and unitarily invariant norms. (2)We investigated free relative entropy extending free entropy into two variables We gave its two definitions by double logarithmic integral and by matrix approximation, and proved their coincidence by making use of large deviation for the empirical eigenvalue distribution of relevant random matrices. (3)We showed that there are continuously many different aperiodic automorphisms on each (interpolated) free group factor by the method of free products and clarified the structure of their crossed-products. (4)Based on theory of double integral transformation and the method of Schur multipliers, we obtained norm inequalities for unitarily invariant nroms of operators, which strengthen the arithmetic-geometric mean inequality. (5)We gave an inequality for positive semidefinite matrices, comparing submultiplicativity with subadditivity for unitarily invariant norms. (6)We re-proved the free probabilistic analog of Talagrand transportation cost inequality for measures due to Biane and Voiculescu by means of random matrix approximation.

  31. 代数的確率論における組合せ数学

    尾畑 伸明, ORAVECZ Ferenc

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業

    Category: 特別研究員奨励費

    Institution: 東北大学

    2002 - 2003

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    代数的確率論の研究動向を踏まえながら、主に以下の4項目について研究した。研究成果は、本学で開催した「第2回仙台ワークショップ:量子確率と量子情報」、ハンガリーで開催された国際会議「フォンノイマン生誕100年記念会議」などで口頭発表し、また、論文によって公表した。 1 フェルミ合成積とブール合成積。モーメント・キュミュラント公式から示唆される組合せ論的構造に着目して、そのような公式と自然な合成積が両立するための条件を求めた。結果として、ブール合成積とフェルミ合成積の特徴づけを得た。 2 変形ポアソン分布と変形ガウス分布の関係。ガウス分布の1径数変形(たとえばq-変形)とポアソン分布の1径数変形を相互に変換させあう公式について継続研究し、合成積に共通する性質を組合せ論的観点から導いた。さらに、直交多項式やモーメント問題に関する古典的な結果との関連で研究を継続させている。 3 有限グラフの隣接作用素。代数的確率論における相互作用フォック空間の手法を応用し、有限グラフの隣接作用素のスペクトル問題にアプローチするため、予備的考察としていくつかの具体例を計算した。特に、スペクトルの間隔分布についていくつかの例を計算した。 4 量子カオスに関連する話題。多変数の三角多項式のゼロ点の分布に関する般的な結果を得た。特に、1変数の場合に、その間隔の分布の特徴を考察し、その最大間隔の評価を与えた。また、d次元トーラス上のラプラシアンのスペクトル分布の漸近的一様性を示した。この手法を(3)と関連付けることを目指して研究を継続している。

  32. 凸体の幾何とファジー力学系

    浦川 肇, 日合 文雄, 金子 誠, 麻生 透, 尾畑 伸明, 大野 芳希

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業

    Category: 萌芽研究

    Institution: 東北大学

    2001 - 2003

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    3次元空間内のネットの幾何学である離散曲面を考察し、その中で、離散非固有アファイン球面を定義し、その分類を行った。これらの離散曲面の連続極限が滑らかな非固有アファイン球面が回復されることを示した。離散及び滑らかな非固有アファイン球面のループ群表示定理を示し、ベックルンド変換を与え、システマティックに大量の例が構成出来ることを示した。 平面有界領域上のディリクレ固有値問題の固有値と固有関数を具体的に数値計算する有限要素法における剛性行列と質量行列を完全に書き下すことに成功し、剛性行列や質量行列とグラフ理論における隣接行列との間の深い関係を明示する定理を示した。この結果、ディリクレ固有値問題の固有値と固有関数がグラフ理論における隣接行列の固有値と固有ベクトルと関係していることを示した。さらにその応用として、数値計算のためのプログラムの計算時間の短縮に役立つことが期待できる。 無限グラフの熱核とグリーン核を無限準正則グラフの場合に具体的に計算した。この結果に熱核とグリーン核比較定理とを合わせて、極めてシャープな熱核とグリーン核の評価定理を得ることが出来た。 ファジー力学系の定式化として、ファジー・ユークリッド空間内の「太鼓の音」の問題を定式化する試みを行い、ファジー・ユークリッド空間上の測度・可測関数、微分形式と外微分、内積と余微分などを厳密に定義することが出来た。ファジー・ドラム理論の新たな進展が出来るものと期待している。

  33. Global Analysis of the heat kernel and Green kernel of an Infinite Graph

    URAKAWA Hajime, ARISAWA Mariko, KANEKO Makoto, ASOH Tohl, OBATA Nobuaki, OHNO Yoshiki

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Tohoku University

    2001 - 2003

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    We have obtained the following results: (1)We constructed the theory of Yang-Mills connections over compact symplectic manifolds. (2)We estimated the Cheeger constant, the heat kernel and the Green kernel for an infinite graph in terms of the volume growth, growth of in and out degree. (3)We determined the stiffness and mass matrices of the finite element method for the Dirichlet eigenvalue problem for a plane domain. (4)We calculated the Cheeger constant, the heat kernel and Green kernel of semi-regular infinite graphs and gave the explicit comparison theorem for every infinite graph. (5)We extended Yang-Mills theory to Weyl structure, and established Atiya-Hitchin-Singer theory to Weyl manifolds, and to affine connections. (6)We formulated discrete improper affine surface theory and show its loop group description. (7)We showed the relation in affine differential geometry, Weyl geometry, Yang-Mills theory. (8)We defined the notion of pseudoharmonic maps from CR manifolds to a Riemanninan manifold, and showed the first variation formula and the second variation formula. (9)We clarified the relation of each Yang-Mills theory on Kaehler manifolds, CR manifolds, and symplectic manifolds, and characterized the minimizers of the Yang-Mills functional over compact symplectic manifolds.

  34. Information Analysis of Symbolic sequences Competitive

    1998/04 - 2002/03

  35. Quantum white noise and nonlinear infinite dimensional analysis

    OBATA Nobuaki, SAITO Kimiaki, URAKAWA Hajimo, HIAI Fumio, TASAKI Shuichi, ARIMITSU Toshihico

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    2000 - 2002

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    We developed quantum white noise calculus within which Brownian motion and Poisson process are unified and extended quantum Ito calculus due to Hudson and Parthasarathy. Below are the main subjects of this research project (1) Normal-ordered white noise differential equations: We developed white noise operator theory by examining detailed structure of the operator symbols. We thereby proved existence, uniqueness and regularity of a solution to a white noise differential equation which is a white noise extension of a quantum stochastic differential equation (2) Higher powers of quantum white noises and the Levy Laplacian: We clarified a relation between the square of quantum white noises and the Levy Laplacian. A stochastic process associated with the Levy Laplacian was constructed by means of diagonalization and a direct integral (3) Complex white noise. Extending the Segal-Bargmann transform to a white noise operator, we proved a new characterization of operator symbols without assuming the nuclearity of the space of white noise functions. We obtained a unitarity criterion for a white noise operator and derived a necessary and sufficient condition for a solution to a normal-ordered white noise equation to be unitary (4) Application to physics: We studied relation among verious kinds of quantum stochastic differential equations which describe models of quantum dissipation and formulated mathematical problems. We observed emergence of an analogue of Bogoliubov transformation in a chain of Fock spaces (5) Algebraic probability theory: We established a new method of asymptotic spectral analysis of a large graph by means of quantum decomposition. We constructed new examples and derived a necessary condition satisfied by the probability measures emerging in particular scaling limits. We studied this condition to obtain another class of probability measures such as q-Gaussian distributions. Moreover, we proved another type of limit theorems

  36. Analytic Integral and its applications

    MIYAKE Masatake, NAKANISHI Tomoki, KIMURA Yoshihumi, AOMOTO Kazuhiko, MINAMI Kazuhiko, OKADA Soichi

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Nagoya University

    1999 - 2002

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    K.Aomoto studied integral representation of special functions and obtained the following results : 1) He established an integral formulas for quasi hypergeometric functions and obtained monodromy formulas, and gave an explicit formula of singular point by using Picard-Lefschetz transform. 2) He extended the notion of LR transform and density matrices into multi dimensional case. More explicitly, he defined Gram-Schmidt orthogonal polynomials with a given density and he dfined its LR transform. M.Miyake studied partial differential equatons in complex domain and obtained the following results : 3) He characterized the Borel summability of divergent formal solution of the Cauchy problem of certain non-Kowalevski type equations. He also gave an integral representation of the Borel sum. 4) He characterized a notion of singular equation or singular point for a nonlinear partial differential equation which depends on each solution. Moreover, the characterization of the singulaity is given by showing the convergent or the divergent criterion of the formal solutions.

  37. 新しい統計科学としての量子情報論

    尾畑 伸明, 大矢 雅則, 青本 和彦, 日合 文雄, 齋藤 公明, 有光 敏彦

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業

    Category: 基盤研究(C)

    Institution: 東北大学

    2001 - 2001

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    情報科学あるいは情報学として新しい学問領域が、旧来の研究分野を横断する形で形成されてきているが、基礎理論も無限次元解析や量子確率の融合を受けて大きく発展している。本企画調査では、これまでに確立している量子確率論における手法に基づき量子情報論を構築し、統計科学に新しい方向性を与えることと、境界諸分野における非線形現象・散逸・ゆらぎの認識・計算量・量子系の観測などの課題を整理することにあった。研究代表者・分担者ともに多くの研究会を主催・または参加し、外国から多数の研究者を招聘し、研究を遂行した。その結果、次の研究課題の重要性を認識するに至り、そのための研究組織を構築することとなった。 1. 量子ホワイトノイズ解析。確率変数の量子分解の確立、複素ホワイトノイズによる作用素の表現、ホワイトノイズの高次冪の定式化などによって、幅広い応用が期待できる。特に、新しい量子確率解析として量子情報論の基礎を担うためには、情報力学の定式化や新しい情報モデルの構築が課題となる。 2. 量子情報論の実験的側面が急速に発展していることから、「量子性と散逸」の問題を理論的に掘り下げてゆく必要がある。量子計算における困難であるデコヒーレンスなどがその典型例である。非平衡熱場理論に示唆される有限温度における量子確率解析やフィルタリングの手法などで制御する理論の構築は興味深い。量子アルゴリズムの高速化・計算量の問題などについては今後の課題である。 3.代数的確率論。統計解析における最も重要な概念である「独立性」および中心極限定理について新しい高い観点から統一することを試みた。離散グラフの隣接作用素の漸近的スペクトル解析への応用され、新しいノイズに基づく確率モデルの構成への道が拓かれた。

  38. 二次元色彩化によるゲノムデータベースの解析

    大澤 研二, 大沢 健夫, 吉田 徹彦, 尾畑 伸明

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業

    Category: 特定領域研究(C)

    Institution: 名古屋大学

    2001 - 2001

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    ・ヒト21番染色体中のタンデムリピートの解析:ヒト21番染色体中のタンデムリピートの解析を行い、28Mbセグメント中に30塩基長以上の周期をもつタンデムリピートを約300ヶ所同定した。見つかったうちで最も長い周期は639塩基であった。全体に渡る分布では、ある領域に集中する傾向が見られるとともに、かなりの長さに渡ってタンデムリピートが存在しない領域が見られた。 ・多くの細菌ゲノム中のタンデムリピートの探索:弘前大学の清水俊夫教授との共同研究により、大腸菌以外の細菌についても探索を行い、多くの知見を得た。特に一部の細菌ゲノムでは、非常に多くのタンデムリピートの存在が明らかとなった。また、ピロリ菌の一つのゲノムでは、大きなinverted repeatsの存在が明らかとなった。 ・他の探索手法との比較:Bensonの開発したタンデムリピート探索法との比較により、二次元色彩化でのみ発見できるタンデムリピートの存在を確認した。ヒト21番染色体のRepeatMaskerによる反復配列の解析結果と比較し、多くのタンデムリピートが二次元色彩化でのみ見出される事を確認した(二次元色彩化により発見されたタンデムリピートのうち約40%がRepeatMaskerでは発見されていない)。

  39. 二次元色彩化によるゲノムデータベースの解析

    大澤 研二, 尾畑 伸明

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業

    Category: 特定領域研究(C)

    Institution: 名古屋大学

    2000 - 2000

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    二次元色彩化を用いてゲノム中のタンデムリピートを探索する目的で開発した方法を、インフルエンザ菌に適用し、30塩基以上の反復長のタンデムリピートを30個見いだした。インフルエンザ菌では大腸菌とは異なり100塩基前後の長さのリピートは割合として多くないなどの特徴を示した。一方、ゲノム全体に関して特徴を見いだすために、表示幅を一定にして単一の彩色図を作成する手法を用いて、様々なゲノムを解析した。すると、細菌において、それぞれに特徴的な色パターンを示しているのに加えて、枯草菌ゲノムではGC相対比などに応じたパターンが顕在化したのに対して、大腸菌ゲノムではそれが明確にならなかった。これは、色彩化においてそれぞれの塩基の種類に対応する色彩の選択が特徴の顕在化に重要な因子の一つであることを示しており、現在それらのさらなる検討を進めている。また、ヒトゲノムについては、幅の設定により顕在化するパターンがあった。 二次元色彩化によるパターン顕在化は色彩の選択によるところが大きいが、今後顕在化されたパターンの分類や探索の自動化などを行ううえで重要な要素の一つにパターンの形の抽出・分類があることが、明らかになりつつある。この方面の研究をさらに発展させるためには、形の認識などに詳しい視覚心理学の分野との共同研究を実施して行く必要がある。一方、タンデムリピートの探索などに用いる配列の自動処理に関しても、ウェブサイト上での構築を視野に入れて開発・検討を行っている.

  40. 配列情報の基礎数理

    尾畑 伸明, 大澤 研二, 勝又 義直, 井原 俊輔

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業

    Category: 萌芽的研究

    Institution: 名古屋大学

    1999 - 2000

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    文字や数字の1次元配列のデータ解析にあたり、特に、4種類のアルファベットから成るDNAの塩基配列、タンパク質のアミノ酸配列、特定の規則で作られた数字の無限列、単語配列でできている文章などを念頭に置き、分野融合的な研究を試みた。本研究における課題は大きく分けて2つある。第一は個別の問題で、配列が与えられたとき(通常は極めて長大である)その配列の中に隠されている規則性を見いだすこと。第二は配列が多数与えられたときに、それらの類似性を判定することである。具体的な研究対象は、DNAの塩基配列やタンパク質のアミノ酸配列、および単語配列としての文章である。 長大な配列に潜む規則性を探査する為に「色彩パターン化法」(平成12年12月に特許査定)を開発し、大腸菌DNA配列に応用し、これまでに見つかっていなかった局所的な循環配列を検出した。タンパク質に対しては、アミノ酸の親水性・疎水性による標準的な指標を用いた色彩パターンが、大まかな分類には有効であることが示唆された。著者の個性を識別するという観点から、日本語文章における類似性の計量化を検討し、読点の付け方によって著者の癖が識別できる(クラスター分析による)ことが強く示唆される結果を得た。同一著者の経年変化を含め精査するために、約50万語からなる形態素分解データベースを作成中であるが校正に膨大な時間を要している。データ解析の理論面を強化するために、配列の「複雑さ」「階層性」「自己組織化度」を表す特性量として、配列エントロピーに付け加えるべきものを探索すべきであるが、形態素解析データベースの完成を待って、理論と実験を融合させ、この目標に向けた試論を展開する予定である。このように、いくつかの具体的な成果に加え、多くの課題を掘り起こすこととなり、より組織的な研究が必要となっっている。

  41. Establishment of paternity test system in Japan

    KATSUMATA Yoshinao, ITO Kensuke, UCHIHI Rieko, YAMAMOTO Toshimichi, NUDESHIMA Jiro, OBATA Nobuaki

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (A).

    Institution: Nagoya University

    1999 - 2000

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    The first one of results in the present study was "The guideline of paternity test in Japan" fixed up by the working group of paternity test in the Japanese Society of Legal Medicine. The head investigator of this study organized this group as the chairperson to make the guideline in cooperation with the other investigators. This guideline is the first and overall one in Japan concerning the parentage testing, which includes not only technical protocol but also sample collection and storage, the formula of expert report, and ethical guideline. We also recommended the three tests, homozygosity test, likelihood ratio test and exact test for the Hardy-Weiberg equilibrium by re-verification, and constructed a highly reliable database in Japanese at general STR loci available by commercially released multiplex amplification and typing kits. As more practical studies, we applied some specimens such as saliva, plucked hairs and cells from toothbrushes to multiplex STR genotyping thoroughly, and expanded the potential limitation of specimens. Furthermore, we tried to apply the minisatellite variant repeat mapping by PCR (MVR-PCR) to paternity tests. On the other hand, we discussed about the mutation of STRs which has considerably high rates with multiplex STR systems, and calculated the rate using a multiplex system. Addition of this rate in calculating the probabilities makes it possible to construct a more reliable system for parentage testings. In the present study, we have almost established a reliable paternity test system in Japan. It is necessary to make efforts to recognize the courts and society about the rightful paternity tests in future.

  42. Integrated Research on Equilibrium Random Phenomena

    KUBO Izumi, MAEJIMA Makoto, OKABE Yasunori, FUNAKI Tadahisa, AIDA Shigeki, OBATA Nobuaki

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (A).

    Institution: Hiroshima University

    1998 - 2000

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    Various important random phenomena are considered as equilibrium states. In this point of view, we have researched for three years. In the period, we held 24 symposia by the grant. Here some of our results are described along key words below. 1 Stochastic Analysis : Aida got very deep results on loop spaces especially about log-Sobolev inequalities, spectral gaps, Clark-Ocone formula etc. 2 Non-Linear and Stochastic Analysis : Funaki researched on Burger equations with fractal Laplacian, especially about the existence of global solution, the uniqueness, the regularities etc. Further, he researched progressive wave solutions and self-similar solutions. 3 White Noise Analysis : Kubo gave a new method of construction of white noise spaces, which is very clear and general. He gave also good characterization theorems. Those results were presented in the symposium held at Indian Statistical Institute in Calcutta. Obata researched the characterization of operators on the spaces by means of their symbols. He applied it stochastic differential equations. 4 Informatic Analysis : Ihara researched very general Gaussian channels with feed back and proved a general formula of mutual information. He discussed applications of large deviation theory to information theory. ue obtained the minimum coding rate for error in the case of stationary Gaussian source. Okabe developed an integrated system of various tests which had been proposed by him to analyze time series under the principle of "Fluctuation and Deviation Theorem". Further he constructed KM_20-Langevin equation for flow in metric vectors and applied it. 5 Self Similar Process : Takenaka showed the deterministic property of distribution of SaS-processes by its finite dimensional distributions. Maejima introduced the concept of semi-self-similar distributions and extended it to that of semi-self-similar processes, operator semi-self-similar distributions and etc. He researched them very deeply. Other results are found in the report and lists of papers by co-researchers.

  43. Quantum White Noise and Infinite Dimensional Harmonic Analysis

    OBATA Nobuaki, ARIMATSU Toshihiko, MINAMI Kazuhiko, AOMOTO Kazuhiko, HORA Akihito

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Nagoya University

    1997 - 1999

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    (1) Normal-Ordered White Noise Equations. On the basis of white noise calculus traditional quantum stochastic differential equations of Ito type are extended to normal-ordered white noise equations and properties of their solutions are described by means of white noise distributions. Cauchy problems on white noise space are solved through one-parameter transformation groups with new aspect to infinite dimensional harmonic analysis. (2) Higher Powers of White Noises and Renormalized Ito Formula. The Ito formula associated with normal-ordered white noise equations involving higher powers of quantum white noises emerges with renormalization and its structure is investigated by means of white noise operator theory. It is applied to (quantum) stochastic differential equations with very singular coefficients. (3) Stochastic Limit of Quantum Theory. Quantum noises and quantum stochastic differential equations are derived through stochastic limit from standard Hamiltonian models such as Anderson model in solid state physics and models of quantum electrodynamics without dipole approximation. Such direct treatment of very strong nonlinear interaction motivate to construct theory of interaction Fock module to give a unified aspect to new phenomenon. (4) Mathematical Analysis of Dissipative Quantum Systems. In order to describe the transition from micro-systems to macro -systems within the framework of canonical operator formalism, the theory of Non-Equilibrium Thermo Field Dynamics is developed. Relationship among equations describing dissipative quantum systems is clarified with a unified point of view. (5) Central Limit Theorems. Within the framework of algebraic probability the new concept of singleton independence is introduced and the associated central limit theorems and limit processes are derived towards mathematical origin of quantum noises. Connection with random walks on discrete graphs is investigated through analogues of the creation and annihilation operators. (6) Others. Quantum Markov chains, complex white noise and coherent state representation, inversion formulas of S-transform and operator symbols, quantum reality and locality, statistical invariance.

  44. Studies of Turbulence as a Nonlinear Science

    KIMURA Yoshifumi, NAWA Hayato, OBATA Nobuaki, OHTA Hiroshi, KIDA Shigeo, NAITO Hisashi

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (A)

    Institution: Nagoya University

    1996 - 1999

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    (1) Vortex Formation and Diffusion in Rotating Stratified Turbulence : Rotation and Stratification are two fundamental physical mechanisms in atmospheres and oceans. Studies of vortex formation and diffusion in such flows play a vital role in improving our understanding of geophysical and astrophysical turbulent phenomena. We examine results of direct numerical simulation of the Navier-Stokes equations with the effects of rotation and stably stratification. Both rotation and stratifications tend to make flows two dimensional (or two components), but we verified that they work in different ways in generating vertical structures. As for diffusion, we observed that stratification suppresses the particle migration in the vertical direction and so does rotation, and that the linear growth in time for single particle dispersion persists in the horizontal direction under strong rotation and/or stratification. (2) Vortex Motion on Surfaces with Constant Curvature : Vortex motion on two- dimensional Riemannian surfaces with constant curvature is formulated. By way of the stereographic projection, the relation and difference between the vortex motion on a sphere and on a hyperbolic plane can be clearly analyzed. The Hamiltonian formalism is presented for the motion of point vortices on a sphere and a hyperbolic plane. As an example of analytic solutions, the motion of a vortex pair (dipole) is considered. It is shown that a dipole draws a geodesic curve as its trajectory on both surfaces. (3) Evolution of decaying two-dimensional turbulence and self similarity : We examine the consequences of self-similarity of the energy spectrum of two-dimensional decaying turbulence, and conclude that traditional closures are consistent with this principle only if the regions of space contributing significantly to energy and enstrophy transfer comprise an ever diminishing region of space as time proceeds from the initial time of Gaussian chaos. (4) Axisymmetrization process for a non-uniform elliptic vortex : The axisymmetrization of a 2D non-uniform elliptic vortex is studied in terms of the growth of palinstrophy, the squared of the vorticity gradient. First, it is pointed out that the equation for the palinstrophy growth, if written in terms of the strain rate tensor, has a similar form to that of enstrophy growth in 3D - the vortex-stretching equation. Then palinstrophy production is analyzed particularly for non-uniform elliptic vortices. It is shown analytically and verified numerically that a non-uniform elliptic vortex in general has quadrupole structure for the palinstrophy production, and that in the positive production regions, vortex filaments are ejected following the gradient enhancement process for vorticity. (5) Pressure distribution for random Gaussian Velocities : Pressure distributions for random Gaussian velocities are studied both analytically and numerically. Arguments based on rotation symmetry allow to clarify the analytical structure of the characteristic function of pressure and to find the power of all its singularities, which in turn, allows to obtain the exact form of the PDF tail, including both exponent and power pre-exponent factors. For the narrow velocity spectrum (velocity restricted to a shell in k-space), the characteristic function is found explicitly, generating pressure cummulants of all orders.

  45. Infinite Dimensional Analysis and Quantum Probability Theory

    ACCARDI Luigi, OHYA Masamori, MINAMI Kazuhiko, AOMOTO Kazuhiko, OBATA Nobuaki

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (C)

    Institution: Nagoya University

    1997 - 1998

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    (1) Stochastic Limit of Quantum Theory Through the stochastic limit quantum noises and quantum stochastic differential equations are derived from canonical Hamiltonian models. This *ethod is applied to a model involving strong nonlinear interaction to obtain a new type of quantum noise. For example, a standard model of QED without dipole approximation yields a singular type of noncrossing diagrams and nonlinear deformation of Wigner's semicircle law. The concept of an interacting Fock module is introduced in order to unify this kind of phenomena. (2) Nonlinear Extension of Classical and Quantum Stochastic Calculus Motivated by (1) , we studied higher powers of quantum white noises which are considered as the first class of an infinite hierarchy of noises. Tha associated Ito formula is proved with renormalization. Moreover, unique existence of solutions is proved for a class of normal-ordered white noise equations involving higher powers of quantum white noises and a relation to quantum stochastic differential equations is established. (3) Central Limit Theorems Within the framework of algebraic probability theory, the existing concepts of independence have been unified and the new notion of singleton independence is introduced. The associated central limit theorem is proved and the limit stochastic process is obtained. This result is related to orthogonal polynomials, their q-deformations, and Gaussianization * probability measures. (4) Quantum Markov Chains Classification of quantum Markov states and lifting problems in quantum communication channels are discussed. An interesting connection between basic algorithyms appearing in quantum computing and quantum Markov chains is investigated. (5) Others Some conrete nonlinear models are discussed in detail in connection with quantum entropy and quantum communication. Questions in foundation of quantum theory related to Bell inequality and EPR paradox are clarified from the standpoint of algebraic probability theory.

  46. 無限次元解析と量子確率

    ACCARDI Luigi, 斉藤 公明, 千代延 大造, 南 和彦, 青本 和彦, 尾畑 伸明

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業

    Category: 基盤研究(C)

    Institution: 名古屋大学

    1997 - 1997

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    1.新しい独立性の概念 離散グラフ上の乱歩に付随するラプラシアンの研究に示唆されて、「シングルトン独立性」という新しい概念を導入した。これによって、これまでに議論されてきた様々な独立性(古典、ボゾン、フェルミ、自由、ほか)の概念を統一し、拡張することができた。さらに、量子論の確率極限から導出される様々なタイプの量子ノイズに組合せ論的視点が与えられた。 2.量子確率微分方程式 ホワイトノイズ解析と量子論の確率極限理論の成果を併せて、「量子確率微分方程式=正規順ホワイトノイズ方程式」を指導原理とする妥当性が得られた。さらに、凸体上の超関数論を発展させ、これまでの確率解析では極めて特異な対象であった高次ホワイトノイズを含む方程式の解の一意存在や解析的な性質を明らかにしつつある。 3.量子確率解析の非線形拡張 高次ホワイトノイズが自然に理論に取り込まれたため、生成・消滅過程(1次ホワイトノイズ)とゲージ過程(特別な2次ホワイトノイズ)に関する演算規則を与えてきた従来の量子伊藤公式は拡張された。実際、この拡張は「くりこみ」をともなったものとなり、新しい展開を見せている。この方向で、ノイズを含む非線形方程式の解析を進め、量子系の散逸や非平衡系との関連を見直すことが目下の課題である。 4.レヴィラプラシアンと無限次元解析 ヤンミルズ方程式とレヴィラプラシアンとの関係を基礎にして、新しいタイプの解を調和解析的に構成したり、逆に、レヴィラプラシアンの一般化を議論した。さらに、レヴィラプラシアンに付随する熱方程式・ブラウン運動を構成し、ディクレ形式を研究した。超関数を用いた作用素論の直接の応用として、無限次元ラプラシアンと無限次元回転群の関係を調和解析的視点から研究した。

  47. DNA塩基配列の二次元パターン化による解析

    大澤 研二, 尾畑 伸明

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業

    Category: 萌芽的研究

    Institution: 名古屋大学

    1997 - 1997

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    DNA塩基配列を色彩化し、二次元平面上に並べることにより、配列の中に含まれる情報を決まったパターンとして顕在化することを試みた。変換法式としては、それぞれの塩基の種類に対して決まった色をあてはめる方法をとり、様々な配列の解析を試みた。その結果、ヒトのcDNA配列中のアミノ酸配列を決定する領域とそうでない領域の区別がつくことを示すとともに、DNA配列中に含まれる反復配列を繰り返しのあるパターンとして容易に顕在化できることを示した。特に後者では、最近報告された大腸菌のゲノムに関して、反復長が24塩基対から541塩基対までの反復配列が合計42個存在することを見いだした。また、この方法はタンパク質のアミノ酸配列の解析にも応用でき、疎水性の度合などといったアミノ酸残基の性質に応じた色彩化を行うことにより球状やロッド状といった全体的な構造の違いを示すとともに、αヘリックスやコラーゲンヘリックスなどの特徴も顕在化できることが示された。特徴の顕在化において重要となる要素の解析については、円周率などの無理数や循環小数などの有理数を数字列として扱って、この方法を適用することで、文字列の中のどのような特徴が明らかになるのかを調べ、反復配列などの繰り返しのパターンだけでなく、特定の文字や文字のグループの分布の偏りによって色彩パターンが顕在化することが明らかとなった。これらの結果は、日本生物物理学会年会、ゲノムインフォーマティックスワークショップ、国際シンポジウム「DNA解析技術の最近の進歩」等において発表した。

  48. Research of stochastic processes on fractals.

    KUMAGAI Takashi, SUGIURA Makoto, CHIYONOBU Taizo, OBATA Nobuaki, ICHIHARA Kanji

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Nagoya University

    1996 - 1997

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    1. We have obtained sharp estimates on the transition densities (heat kernels) for diffusion processes on p.c.f. self-similar sets, which correspond to finitely ramified self-similar fractals. It was known that if the fractal had a strong symmetry, then the heat kernel of the Brownian motion had Aronson type estimates. In our result, we show that the Aronson type estimates do not hold in general. This work will appear in J.London Math.Soc. 2. On infinitely ramified fractals, we have studied the heat kernel estimates for diffusion processes on random Sierpinski carpets. We obtained sharp esimates for each sample carpets (each environments). Further, we obtained almost sure estimates assuming strong ergodicity for the randomness of the carpets. One of the key idea was to obtain uniform Harnack inequality of the approximate processes using the coupling arguments due to Barlow-Bass. This work is now a preprint. 3. On the relations between fractals and Euclidean spaces, we studied homogenization problems. Since the joint work of the head investigator with Prof.Kusuoka, it was known that the stability of fixed points of the renormalization map was essential. In our research, we discussed with researchers of the same fields when we attended interational workshops and learned several new ideas and methods to search for the problem. But so far we could not apply the methods to our cases. This is the problem we should pursue in a near future.

  49. 量子確率過程の超関数論的研究

    尾畑 伸明, 杉浦 誠, 南 和彦, 市原 完治, 熊谷 隆, 三宅 正武

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業

    Category: 基盤研究(C)

    Institution: 名古屋大学

    1996 - 1996

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    ホワイトノイズ超関数に作用する作用素の統一理論は、94年に出版された私の著書で一通りの完成を見たが、最近のホワイトノイズ超関数論の発展に合わせて、理論を組み立て直す必要が出てきた。本研究では、まず、増大度の条件を緩めたホワイトノイズ超関数でベクトル値の場合も含むように、従来の理論を発展させた。応用として、量子適合過程・量子的マルチンゲ-ルの一般化と特徴づけが得られた。この理論では、ホワイトノイズの高次の巾乗を取り扱うことができるが、これは確率解析を非線形の方向で一般化するための基礎になるのではないか、という知見を得た。関連する量子的伊藤公式の導出は興味深い課題として残った。別の応用として、ある種の量子確率微分方程式の解の一意存在定理を証明し、ウィック指数関数による解の構成を論じた。また、散逸を含む量子系を記述する量子ランジュヴァン方程式もこの範疇で捉えることができた。解の滑らかさは、極めて興味深い問題である。本研究では、古典的な微分方程式における手法が応用できるか、との関連で研究を開始したが、今のところ手探りの状態である。量子系の中心極限定理も本研究に含まれる課題であったが、群や超群上のランダムウォークのスペクトル解析を背景に、新しい組合せ論的アプローチを開発した。その結果、新しい極限分布の族が構成され、ウィグナーの半円則とその変形が得られた。この流れでダイソンのランダム行列モデルを解析することは今後の課題となった。シュレ-ディンガー作用素の固有値問題・量子スピン系・フラクタル上の確率過程などを量子確率論の観点から見直すことで、これらは今後の研究の展開の上で重要であると認識を新たにした。 本研究遂行にあたり、研究代表者・分担者ともに海外も含め多くの研究集会で口頭発表し、周辺研究者との交流を深めた。また、来日中の外国人研究者や国内研究者多数をセミナーに招待することができ有意義な研究討論を行なった。

  50. q差分属と接続行列

    青本 和彦, 南 和彦, 尾畑 伸明

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業

    Category: 重点領域研究

    Institution: 名古屋大学

    1996 - 1996

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    Jackson積分を用いて定義される基底超幾何関数のみたす差分方程式と接続行列についての関連を明らかにすることが目標であった. q乗法関数のJackson積分の場合にはそのコホモロジーの構造を明らかにし,パラメータを特定方向に無限大にするとき,その漸近展開を与える安定サイクルを求める方法を与えた.一般のサイクルをこの安定サイクルを用いて表す表示式を与えた. 特に,対称A型Jackson積分で定義される基底超幾何関数はパラメータα,β,γ,X_1→X_mに依存するn変数q関数を格子上の和で定義したものである.α→±∞のときの漸近展開を与えるα安定(α不安定)サイクルを定義し,一般のサイクルをこれらの1次結合で表示する式を得た.又α安定サイクルとα不安定サイクルとの関係を与える接続行列をも与えた.その要素は楕円データ関数を用いた擬定数である.特にm=2ならば,この行列のGauss分解が陽に求められ,R行列が計算される.q-差分方程式のRiemann-Hilbert問題を解くことが出来てq差分方程式そのものも陽に求められる.

  51. Stochastic processes with applications to statistical mechanics

    ICHIHARA Kenji, SUGIURA Makoto, KUMAGAI Takasi, OBATA Nobuaki, AOMOTO Kazuhiko, FUNAKI Tadahisa

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Nagoya University

    1994 - 1996

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    T.Funaki firstly studied some basic problems (derivation of nonlinear equations, etc) in hydrodynamical limit for Hamiltonian systems and lattice gas. Then he took up singular limit problem for reaction-diffusion equations with noise as reaction term tends to infinity. It has been shown for the problem that the solutions of the equations approach +1 or -1 pointwise in space and time. Accordingly the generation of random interfaces between two phases +1, -1 occurs. As the third topic, Burgers equations were treated. He proved that non-Gaussian distributions appear as a scaling limit of solutions for Burgers equations with random initial value. Furthermore various properties of solutions for a class of generalized Burgers-type equations with a fractionl power of the Laplacian were studied. K.Ichihara established a global Harnack inequlity for a class of symmetrizable difference operators on finitely generated groups of polynomial growth order. It was then applied to show a Liouville-property such operators. He secondly introduced birth and death processes in a class of time-dependent random environments. The recurrence and transience problem for the above processes was discussed by means of a renormalization technique. In multi-dimensicnal lattices some examples of recurrent and transient processes have been constructed respectively.

  52. ホワイトノイズによる量子確率解析とその応用

    尾畑 伸明, 杉浦 誠, 市原 完治, 熊谷 隆, 三宅 正武, 青本 和彦

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業

    Category: 一般研究(C)

    Institution: 名古屋大学

    1995 - 1995

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    1.作用素論の精密化 積分核作用素はフォック空間(ホワイトノイズ超関数の空間)上の作用素論において最も基本的なものである。従来の議論では、積分核はスカラー値超関数のみを扱っていたが、これを作用素値超関数も扱えるように拡張し、フビニ型の定理を証明した。また、積分核作用素における部分積分を定式化して証明した。これらの成果は、各点毎の生成・消滅作用素が滑らかな作用素流をなすというホワイトノイズ解析の特徴を反映したものである。 2.量子確率過程の表現 まず、量子確率積分を超関数を用いて議論し、従来の伊藤型量子確率積分を著しく一般化した。さらに、フォック空間上の作用素を展開定理を応用して、任意の量子確率過程が生成過程・消滅過程の量子確率積分で与えられることを示した。これは、従来の伊藤型の理論に新しい発展の方向を与えるものである。この結果の応用として、量子適合過程や量子マルチンゲ-ルの表現を得た。物理への応用として、散逸量子系に典型的に現れる量子ランジュヴァン方程式をホワイトノイズ超関数の立場から議論した。 3.無限次元調和解析 フォック空間上の作用素論は、ガウス空間上の調和解析に一つの方向を打ち出している。作用素の展開定理の応用として、ホワイトノイズ関数上の(代数的)微分をすべて決定した。また、ある種の無限次元ラプラシアンを含む低次元リー環をすべて決定し、無限次元コ-シ-問題への応用を研究した。さらに、ベクトル場の作る無限次元リー環のフォック表現と量子ポワソン・ホワイトノイズの関連を明らかにした。

  53. ホワイトノイズ解析と量子確率論

    尾畑 伸明, 松尾 厚, 千代延 大造, 小澤 哲也, 舟木 直久, 青本 和彦

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業

    Category: 一般研究(C)

    Institution: 名古屋大学

    1993 - 1993

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    近年、ホワイトノイズ解析は無限次元空間(ガウス空間)上のシュヴァルツ型超関数論として枠組みの確立ととも、研究代表者はホワイトノイズ超関数に働く作用素の統一理論の確立と応用を研究してきた。従来、その研究はスカラー値の超関数を対象としてきたが、本年度の研究では、理論をベクトル値の場合に拡張することについて一定の成果を得た。すなわち、「標準的な」可算ヒルベルト空間という概念を導入し、その空間に値をとるホワイトノイズ(超)関数に対して、これまでの結果を拡張した。特に、ベクトル値ホワイトノイズ(超)関数に働く有界とは限らない作用素の生成・消滅演算子による一般展開定理を得た。この一般化は、量子確率論の主題の一つである開放系の問題や、ボゾン・フェルミオン空間上の解析(ディラク作用素等)などへの応用にむけて重要になると思われる。 量子確率論との関わりでは、量子的伊藤公式の超関数論的な再定式化・ある種のフィルトレイションに適合した確率過程の表現を、我々の作用素論の直接的な応用として研究した。さらに、マルチンゲール表現定理について研究中である。また、古典的な確率過程に対しても、その種の表現定理が作用素論から導けると思われるが、これについても現在研究中である。 関連する成果は、論文によって公表するが、それに先立ち京大数理研等の研究集会における発表・他大学のセミナーなどにおける討論も重要であった。特に、非平衡系の統計物理において、別の立場から、量子的確率過程が議論されているのを知り、相互の興味が増大している。今後は、この分野をはじめ、量子情報理論の研究者とも交流を図って研究を進める予定である。

  54. 解析的容量の研究

    村井 隆文, 尾畑 伸明, 伊藤 正之, 岸 正倫, 舟木 直久, 飛田 武幸

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業

    Category: 一般研究(C)

    Institution: 名古屋大学

    1990 - 1990

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    研究課題である解析的容量の研究は有界解析函数の構造論であり、完全流体のなす速度場論(ホドグラフ面論)でもある。2次元連結物体が引き起こす速度場の研究は補領域から単位円板への等角写像により単位円板内の解析函数(完全流体)の研究に帰着し、このRiemann写像はある極値問題の解として与えられる。このことから一般のコンパクト集合に対し同様の極値問題が定義される。この極値とそれを与える函数(Ahlfors函数)の構造を調べるのが我々の目的である。極値は与えられた多体が引き起こす力(揚力)と関係している。本研究の特徴は容量研究にHilbert変換とSzego^^¨核を使う所にある。論文〔1〕ではHilbert変換の立場から容量の研究を試みており,論文〔2〕,〔3〕ではSzego^^¨核の立場から容量の構造を調べている。完全流体を扱うのにGaussーGreenの公式(Cauchyの積分定理)を用い大域素解(Cauchy核,渦糸)の構造と結びつける手法は古典的である。この手法は簡明で局所構造を解明するのに適しているが,多体問題を扱うのにかならずしも便利とはいい難い。Szego^^¨は解休函数のなすあるHibert空間の再生核であり,Cauchyよりも大域的性質を解明するのに適している。従ってSzego^^¨の構造論文と容量を結びつけて論じた〔2〕,〔3〕は有意義であると考えている。論文〔4〕は若干の新しい結果を含んだ総合報告であり,Green函数を使うことなしに2次元飛行物体の揚力理論をまとめている。あらゆる方向からの風に対して揚力が作用しない物体を構成出来たことは,本研究が数学のみならず応用上も重要であることを示している。(文献番号は次ペ-ジ,上から順)

  55. Stochastic Analysis and Quantum Field Theory

    HIDA Takeyuki, KUO H. H., POTTHOFF Jurgen, ALBEVERIO Sergio, STREIT Ludwig, WATANABE Hisao, FUKUSHIMA Masatoshi, KUSUOKA Shigeo, TAKAHASHI Yoichiro, OBATA Nobuaki, SATO Ken-iti, ROCKNER Michael

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for international Scientific Research

    Institution: Nagoya University

    1989 - 1990

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    We have investigated several current topics in stochastic calculus and quantum dynamics. To fix the idea, we explain one of the most important topics of what we have studied. White noise analysis may be viewed as the harmonic analysis arising from the infinite dimensional rotation group 0*. Since the white noise measure, which is introduced on the space of the generalized functions, is invariant under the action of the rotation group, it is natural to think of an infinite dimensional analogue of the harmonic analysis on a finite dimensional sphery on which the finite dimensional rotation group acts. There are several steps for our harmonic analysis depending on the choice of subgroup of 0*. 1. Inductive limit of finite dimensional rotation groups, denoted by G*. The Fock space <symmetry>H_n, the Laplace-Beltrami operator DELTA*, class-one irreducible unitary representations of G* on H_n, and so forth, are well investigated. 2. There is a subgroup Y, called Levy group, which contains infinite dimensional rotations, far from the finite dimensional ones, defined by permutations of coordinates of the basic function space. To carry on a similar calculus as in 1, associated with the Levy group, we need to go one step ahead. Namely, a space of generalized white noise functionals should naturally be introduced, then we are led to discuss the Levy's Laplacian operator that acts effectively on the space of the generalized white noise functionals. 3. We then come to a very interesting subgroup W consisting of all the transformations that come from diffeomorphism of the parameter space. The W is quite different, in character, from G* and the Levy group. To introduce some analytic structure, We consider continuous one-parameter subgroups (called whiskers) of W. Then we take a family of random variables {X(C)}, where the parameter C runs through a certain subclass of analytic, closed, simple manifolds, and where C is deformed by actions of the subgroup of W. A general theory is not yet established, however we can find many interesting questions in analysis as well as several applications.

  56. ホワイトノイズ解析と確率場

    飛田 武幸, 尾畑 伸明, 竹原 茂夫, 砂田 利一, 土屋 昭博, 青本 和彦

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業

    Category: 一般研究(C)

    Institution: 名古屋大学

    1989 - 1989

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    計画通り次の2項目について研究を行った。 1.ホワイトノイズの超汎関数の解析 確率過程の中で最も基本的なものの1つであるホワイトノイズを基礎にして、その非線型汎関数の解析を行うため、準備として数学の種々の分野の手法を用いてアプロ-チを試みた。本年度の研究において最も有効と思われたものは無限次元回転群により調和解析の方法であった。ホワイトノイズの測度分回転不変であるため、この回転群を基にする立場から、自然に超汎関数を導入する新しい方法が見出された。また、有限次元の場合にならって、ラプラス作用素を導くことができるか、その特徴づけを行うことができた。無限次元であるため、いくつかのラプラス作用素が考えられるが、確率論的に興味のある2種類について、応用も含め比較的詳しい性質が知られた。 2.ガウス型確率場 一般論は今後の問題として、多次元パラメ-タ-のホワイトノイズの線型汎関数として表され、多次元多様体を変数とするガウス型確率場扱った。ホワイトノイズ解析で知られる積分表現を用いて、テスト関数の線型汎関数としてこの確率場を表わし、通常の関数解析の手法によって解析をすすめた。著しい結果は、変数が球面の場合で、無限次元回転群を用いてこの場の変換を行い、特に2次元のときには、具体的な記述が可能となり、与えられた場の従属性を論ずることができた。 さらに1と関連して、理論物理学へのいくつかの応用を見出すたとができた。それらはiファインマン積分、iiディリクレ形式、iiip(Φ)ユ-クリッド場である。iについては我々の立場から新しい定式化を、iiについては無限次元の特性を活かした展開を行った。iiiについては高次元の場合が今後の問題として残されている。

  57. 無限次元回転群とヒルベルト空間上の調和解析

    尾畑 伸明

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業

    Category: 奨励研究(A)

    Institution: 名古屋大学

    1988 - 1988

  58. 多次元パラメーターの確率場の表現とその応用

    竹中 茂夫, 尾畑 伸明, 舟木 直久, 飛田 武幸

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業

    Category: 一般研究(C)

    Institution: 名古屋大学

    1987 - 1987

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    本年度は特に, 一次元パラメータブラウン運動に重点を置いて研究を行った. 従来よりブラウン運動が, 種々の変換に対する不変性を有する事は知られているが, 特に次の3つの変換に着目した. T1)X_1(t)=B(t+h)-B(t), T2)X_2(t)=e^<-u/2>B(e^ut), T3)X_3(t)=tB(-1/). 勿論, B(t)をブラウン運動とする時, X_1, X_2, X_3各々が, 又ブラウン運動となる事と, T1)及びT2)が各々パラメータhとuに関して1パラメータ群となり, またそれらが群を構成する事は, 古くから知られているが, 今回はT3)をも合わせてさらに大きな群が構成される事を示した. すなわち, 定理g=(<a,b>/<c,d>)SL(2,R)とすると, B^g(t)=(ct+d)B((at+b)/(ct+d))-ctb(a/c)-dB(b/d)は又ブラウン運動になりSL(2,R)のブラウン運動に対して同様の事を考えると, 射影幾何(SL(n+1,R))よりも, むしろ共形幾何学との繋がりが存在する事が分かってきて, この幾何学的不変性とブラウン運動のホワイトノイズによる表現との関連に, 新たな見方をあたえてくれている.

  59. 無限離散群の表現論

    尾畑 伸明

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業

    Category: 奨励研究(A)

    Institution: 名古屋大学

    1986 - 1986

  60. 無限次元群の表現論

    尾畑 伸明

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業

    Category: 奨励研究(A)

    Institution: 名古屋大学

    1985 - 1985

Show all Show first 5

Teaching Experience 4

  1. マルコフ連鎖　東北大学大学院

  2. 線形代数学　東北大学

  3. 微分積分　東北大学

  4. 数理統計学　東北大学

Social Activities 4

  1. おおさき産業フェア2014・気軽に楽しめるセミナー「おおさきサイエンスサロン」

    2014/10/24 -

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    チャンスの法則：確率から見える世界

  2. 第97回東北大学サイエンスカフェ

    2013/10/25 -

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    チャンスの法則 ～確率で世界はまわる～

  3. 神奈川県立神奈川総合高等学校講演会

    2008/12/10 -

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    コイントスから広がる確率論の世界

  4. 東京弁護士会期成会夏合宿

    2005/08/19 -

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    「確率論と社会」と題する講演を行った。

Media Coverage 6

  1. 科学の泉:広がりゆく確率の世界(6) 掛け算順番で結果が変化

    河北新報朝刊

    2014/06/15

    Type: Newspaper, magazine

  2. 科学の泉:広がりゆく確率の世界(5) 新たな知見は偶然の中に

    河北新報朝刊

    2014/06/14

    Type: Newspaper, magazine

  3. 科学の泉:広がりゆく確率の世界 (4) 繰り返すほど正確な割合に

    河北新報朝刊

    2014/06/13

    Type: Newspaper, magazine

  4. 科学の泉:広がりゆく確率の世界 (3) 「往復書簡」が理論のルーツ

    河北新報朝刊

    2014/06/12

    Type: Newspaper, magazine

  5. 科学の泉:広がりゆく確率の世界 (2) 賭博を科学的に研究、道開く

    河北新報朝刊

    2014/06/11

    Type: Newspaper, magazine

  6. 科学の泉:広がりゆく確率の世界 (1) ルネサンス中ごろに誕生

    河北新報朝刊

    2014/06/10

    Type: Newspaper, magazine

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  1. 非可換確率解析：量子ホワイトノイズと量子ウォークの新展開

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    非可換確率解析：量子ホワイトノイズと量子ウォークの新展開

  2. 非可換確率システム：解析、モデリング、およびその応用

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    非可換確率システム：解析、モデリング、およびその応用

  3. 非可換無限次元調和解析：表現論と確率論の融合的アプローチ

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    非可換無限次元調和解析：表現論と確率論の融合的アプローチ

  4. 数学をコアとするスマート・イノベーション融合研究共通基盤の構築と展開

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    本学において、数学と諸分野との連携強化のためのプラットフォーム形成を行う。

  5. 非可換調和解析と実世界複雑現象への応用

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    非可換調和解析と実世界複雑現象への応用

  6. 離散構造上の非可換調和解析と確率論への応用

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    NA

  7. 非可換確率解析の新展開とネットワーク科学への応用

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    非可換確率解析の新展開とネットワーク科学への応用

  8. 確率解析における非可換的様相と数理モデルへの応用

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    最終目標は、確率解析に質的な変化を与え、ランダム現象に対する新しい数理モデルを構築することにある。そのために、伝統的な確率解析の代数的構造、特に、量子成分の非可換性の役割を探求し、揺らぎの数学的起源を探る。さらに解析的な手法を組み合わせて、量子成分の集積による漸近的な挙動を研究し、さまざまな極限定理をその精密評価とともに導く。こうして構成される揺らぎのモデルは、伝統的な確率解析によっては捉えることができない非可換性を反映することから、新しい数理モデルとなることが期待される。 われわれの目標を達成するための鍵は「量子ホワイトノイズ解析」とりわけ確率微分方程式の非可換拡張、量子ホワイトノイズの非線形関数、一般化されたフーリエ・ガウス変換、量子ホワイトノイズ微分の理論の発展にある。そのために、代数的手法から解析的手法へ、および理論から応用へという２本の軸に沿って問題解決に当たる。特に、次の項目を取り上げる：（I）大偏差原理（解析＋理論）；（II）自由確率論（代数＋理論）；（III）ネットワークのスペクトル（代数＋応用）；（IV）ファインマン積分（解析＋応用）。これらの４課題との境界領域に大きな成果が期待される。われわれの研究組織はそのような分野の専門家から成っていて、互いに強い相互作用が可能であり、これまでの研究実績はここに提案している研究計画が十分に実現可能であることを裏打ちしている。 ２年間の研究期間中に少なくとも８回の相互訪問を実施し、集中ワークショップを開催する。これらを通して両国における若手研究者を奨励することも念頭においている。さらに、異なったバックグラウンドをもつ研究者との交流を活発化する目的も含め、開かれた会議を両国において１回ずつ開催する。

  9. 無限次元解析と量子確率論の動向

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    研究会を開催

  10. 配列の情報解析ー特に文章の類似性解析とその確率モデル

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    文章の類似性解析とその確率モデル

  11. 無限次元調和解析

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    ポーランド・ヴロツワフ大学との無限次元調和解析に関する共同研究

  12. 無限次元調和解析

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    ドイツ・チュービンゲン大学との共同セミナー

  13. ホワイトノイズと微分方程式

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    ホワイトノイズと微分方程式

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