• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Computational Approaches for Mathematical Sciences

Research Project

Project/Area Number 19204008
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKobe University

Principal Investigator

TAKAYAMA Nobuki  Kobe University, 理学研究科, 教授 (30188099)

Co-Investigator(Kenkyū-buntansha) BRENDLE Joerg  神戸大学, システム情報学研究科, 准教授 (70301851)
FUCHINO Sakae  神戸大学, システム情報学研究科, 教授 (30292098)
FUKUYAMA Katsushi  神戸大学, 理学研究科, 教授 (60218956)
KAKIUCHI Itsuro  神戸大学, システム情報学研究科, 准教授 (90091248)
NORO Masayuki  神戸大学, 理学研究科, 教授 (50332755)
NOUMI Masatoshi  神戸大学, 自然科学系先端融合環重点研究部, 教授 (80164672)
ROSSMAN Wayne  神戸大学, 理学研究科, 教授 (50284485)
新井 敏康  神戸大学, 工学研究科, 教授 (40193049)
Co-Investigator(Renkei-kenkyūsha) ARAI Toshiyasu  千葉大学, 理学研究科, 教授 (40193049)
Project Period (FY) 2007 – 2011
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥42,380,000 (Direct Cost: ¥32,600,000、Indirect Cost: ¥9,780,000)
Fiscal Year 2010: ¥11,180,000 (Direct Cost: ¥8,600,000、Indirect Cost: ¥2,580,000)
Fiscal Year 2009: ¥10,270,000 (Direct Cost: ¥7,900,000、Indirect Cost: ¥2,370,000)
Fiscal Year 2008: ¥9,880,000 (Direct Cost: ¥7,600,000、Indirect Cost: ¥2,280,000)
Fiscal Year 2007: ¥11,050,000 (Direct Cost: ¥8,500,000、Indirect Cost: ¥2,550,000)
Keywordsグレブナ基底 / 推定 / 数学ソフトウエア / 特殊関数 / 組み合わせ論的集合論 / 重複対数の法則 / 中心極限定理 / 極小曲面 / ホロノミック勾配降下法 / 数学ソフトエウア / Fisher-Bingham分布 / 超幾何関数 / logarithmic cohomology / Sparse SDP / 離散極小曲面 / 無矛盾性 / 特異基数 / ノンパラメトリック推測法
Research Abstract

We hosted the 10th Asian logic conference and the third international congress on mathematical software and made broad contributions to communities to study computation and mathematical sciences. We have obtained several results. Among them, a result which could not be obtained without this project is an algorithm to find a local minimum of a given holonomic function by utilizing computer algebra algorithms and numerical algorithms for holonomic systems. We expect that this method can be applied to estimation problems in statistics, which is in progress in a new project.

Report

(5 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Self-evaluation Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (27 results)

All 2011 2010 2009 2008 2007 Other

All Journal Article (16 results) (of which Peer Reviewed: 13 results) Presentation (5 results) Book (2 results) Remarks (4 results)

  • [Journal Article] Holonomic Gradient Descent and its Application to the Fisher-Bingham Integral2011

    • Author(s)
      H.Nakayama, K.Nishiyama, M.Noro, K.Ohara, T.Sei, N.Takayama, A.Takemura
    • Journal Title

      Advances in Applied Mathematics (2011), to appear. 03

    • Related Report
      2010 Final Research Report
  • [Journal Article] Holonomic Gradient Descent and its Application to the Fisher-Bingham Integral2011

    • Author(s)
      H.Nakayama, et al
    • Journal Title

      Advances in Applied Mathematics (doi:10.1016/j.aam.2011.03.001)

      Volume: (印刷中)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Pure gaussian limit distributions of trigonometric series with bounded gaps2010

    • Author(s)
      K.Fukuyama
    • Journal Title

      Acta Mathematics Hungarica

      Volume: 129 Pages: 303-313

    • NAID

      120005980772

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Holomorphic Representation of Constant Mean Curvature Surfaces in Minkowski : Space Consequences of Non-Compactness in Loop Group Methods2010

    • Author(s)
      D.Brander, W.Rossman, N.Schmitt
    • Journal Title

      Advances in Mathematics

      Volume: 223 Pages: 949-986

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stratification associated with local b-functions2010

    • Author(s)
      K. Nishiyama, M. Noro
    • Journal Title

      Journal of Symbolic Computation 45

      Pages: 462-480

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Holonomic Rank of A-Hypergeometric Differential-Difference Equations2009

    • Author(s)
      K.Ohara, N.Takayama
    • Journal Title

      Journal of Pure and Applied Algebra 213

      Pages: 1536-1544

    • NAID

      120001506673

    • Related Report
      2010 Final Research Report
  • [Journal Article] The Computation of the Logarithmic Cohomology for Plane Curves,2009

    • Author(s)
      F.J.Castro-Jimenez, N.Takayama
    • Journal Title

      Journal of Algebra 322

      Pages: 3839-3851

    • Related Report
      2010 Final Research Report
  • [Journal Article] The Computation of the Logarithmic Cohomology for Plane Curves2009

    • Author(s)
      F. J. Castro-Jimenez, N. Takayama
    • Journal Title

      Journal of Algebra 322

      Pages: 3839-3851

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Holonomic Rank of A-Hypergeometric Differential-Difference Equations2009

    • Author(s)
      K. Ohara & N. Takayama
    • Journal Title

      Journal of Pure and Applied Algebra 213

      Pages: 1536-1544

    • NAID

      120001506673

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The law of the iterated logarithm for discrepancies of θ^nX2008

    • Author(s)
      K. Fukuyama
    • Journal Title

      Acta Mathematica Hungarica 118

      Pages: 155-170

    • NAID

      120005980770

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Non-elementary speed-ups in logic calculi2008

    • Author(s)
      T. Arai
    • Journal Title

      Mathematical Logic Quarterly 6

      Pages: 629-640

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The law of the iterated logarithm for discrepancies of {θ^nx}2008

    • Author(s)
      K. fukuyama
    • Journal Title

      Acta Mathematica Hungarica 118

      Pages: 155-170

    • NAID

      120005980770

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Delaunay ends of constant mean curvature surfaces2008

    • Author(s)
      M. Kilian & W. Rossman & N. Schmitt
    • Journal Title

      Compositio Math. 144

      Pages: 186-220

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The law of the iterated logarithm for discrepancies of {θ^nx}2008

    • Author(s)
      K. Fukuyama
    • Journal Title

      Acta Mathematica Hungarica 118

      Pages: 155-170

    • NAID

      120005980770

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Local Grobner Fan2007

    • Author(s)
      R. Bahloul & N. Takayama
    • Journal Title

      C. R. Acad. Sci. Paris, Ser. I 344

      Pages: 147-152

    • NAID

      120001506675

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Holomorphic Representation of Constant Mean Curvature Surfaces in Minkowski Space : Consequences of Non-Compactness in Loop Group Methods

    • Author(s)
      D. Brander, W. Rossman, N. Schmitt
    • Journal Title

      to appear in Advances in Mathematics

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Presentation] ホロノミック系と統計2011

    • Author(s)
      高山信毅
    • Organizer
      計算による数理科学の展開2011
    • Place of Presentation
      神戸大学(兵庫県)(招待講演)
    • Year and Date
      2011-01-07
    • Related Report
      2010 Annual Research Report
  • [Presentation] Holonomic graidient descent and its application to Fisher-Bingham integral2010

    • Author(s)
      N.Takayama
    • Organizer
      The second crest-sbm international conference "Harmony of Groebner bases and the modern industrial society"
    • Place of Presentation
      大阪
    • Year and Date
      2010-06-30
    • Related Report
      2010 Final Research Report
  • [Presentation] 統計学に現れるパラメータ付き積分のためのD-加群理論入門2009

    • Author(s)
      高山信毅
    • Organizer
      計算代数統計学の展開
    • Place of Presentation
      統計数理研究所
    • Year and Date
      2009-11-27
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] 不完全A超幾何関数-a first step2009

    • Author(s)
      西山絢太, 高山信毅
    • Organizer
      グレブナ基底と現代産業社会の調和
    • Place of Presentation
      鹿児島大学
    • Year and Date
      2009-02-18
    • Related Report
      2008 Annual Research Report
  • [Presentation] Iterating the recursively Mahlo operators2007

    • Author(s)
      T. Arai
    • Organizer
      Logic Methodology, Philosophy of Science
    • Place of Presentation
      Beijing, China
    • Related Report
      2007 Annual Research Report
  • [Book] Mathematical Software -ICMS 2010 Third International Congress on Mathematica Software, Kobe, Japan2010

    • Author(s)
      M.Joswig, K.Fukuda, J.Van der Hoeven, N.Takayama編集
    • Total Pages
      6327
    • Publisher
      Springer Lecture Notes in Computer Science
    • Related Report
      2010 Final Research Report
  • [Book] Mathematical Software-ICMS 2010 Third International Congress on Mathematica Software, LNCS 63272010

    • Author(s)
      M.Joswig, K.Fukuda,J.Van der Hoeven, N.Takayama
    • Total Pages
      368
    • Publisher
      Springer
    • Related Report
      2010 Annual Research Report
  • [Remarks] ホームページ等

    • URL

      http://www.math.kobe-u.ac.jp/cm

    • Related Report
      2010 Final Research Report
  • [Remarks]

    • Related Report
      2010 Annual Research Report
  • [Remarks]

    • URL

      http://www.math.kobe-u.ac.jp/cm

    • Related Report
      2008 Annual Research Report
  • [Remarks]

    • URL

      http://www.math.kobe-u.ac.jp/cm

    • Related Report
      2007 Annual Research Report

URL: 

Published: 2007-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi