Updated on 2024/04/01

写真a

 
TANAKA Ushio
 
Organization
Graduate School of Science Department of Mathematics Associate Professor
School of Science Department of Mathematics
Title
Associate Professor
Affiliation
Institute of Science

Position

  • Graduate School of Science Department of Mathematics 

    Associate Professor  2022.04 - Now

  • School of Science Department of Mathematics 

    Associate Professor  2022.04 - Now

Degree

  • Ph.D. （ Others ） (   The Graduate University for Advanced Studies )

Research Areas

  • Natural Science / Geometry  / Differential Geometry, Global Analysis, Shape Theory, Likelihood Geometry, Persistent Homology, The Theory of Point Processes

Research Interests

  • (Differentiable) Manifold, Bundle, Curvature, Topology, Diameter, Volume, Metric (Measure) Space; Shape Theory, Shape Space, Persistent Homology; Prime Number, Zeta; Likelihood Geometry; Point Process, Likelihood Analysis

Research subject summary

  • Analysis for Geometric Structures in Science, Arithmetic Point Processes

Research Career

  • Differential Topology, Global Analysis, Global Riemannian Geometry, Shape Theory, Geometric Analysis, Arithmetic Point Processes

    Bundle, Connection, Riemannian Manifold, Curvature, Topology, Diameter, Volume, Shape Space, Riemann Zeta Function, Intensity, Likelihood Geometry, Likelihood Analysis  Individual

    2001.04 - Now 

Professional Memberships

  • American Mathematical Society

    2020 - Now   Overseas

  • The Mathematical Society of Japan

    2015.04 - Now   Domestic

  • The Japan Society for Industrial and Applied Mathematics

    2016.07 - Now   Domestic

  • Japan Statistical Society

    2004 - Now   Domestic

Papers

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Books and Other Publications

  • Spatio-Temporal Statistical Analysis

    Yoshihiro Yajima, Ushio Tanaka（ Role： Joint author）

    KYORITSU SHUPPAN CO., LTD.  2019.05  （ ISBN:9784320113527 ）

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    Total pages：268   Book type：Scholarly book Participation form：Second Author

  • Mathematical Statistics from the Measure Theoretical Point of View

    Yoko Watamori, Hidekazu Tanaka, Ushio Tanaka （ Role： Joint author）

    KYORITSU SHUPPAN CO., LTD.  2023.09  （ ISBN:9784320114975 ）

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    Total pages：240   Book type：Textbook, survey, introduction

MISC

  • Simulation and Estimation of the Neyman-Scott Type Spatial Cluster Models Reviewed International journal

    U. Tanaka, M. Saga and J. Nakano

    CRAN   2023.03

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    Authorship：Lead author   Kind of work：Joint Work   International / domestic magazine：International journal  

  • Tables as graphs: the Ramanujan principle. Significance. Vol. 8, Issue 4, p. 183, Dec. 2011.

    Royal Statistical Society   65 ( 6 )   2014.06

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Presentations

  • Stein identity and Poincar´e inequality for a discrete metric measure space Domestic conference

    Tomonari Sei and Ushio Tanaka

    2024 The Mathematical Society of Japan ANNUAL MEETING  2024.03  The Mathematical Society of Japan

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    Presentation type：Oral presentation (general)  

    Venue：Osaka Metropolitan University 3–3–138 Sugimoto, Sumiyoshi-ku Osaka-shi, 558-8585, Japan  

  • Stein identity and Poincar´e inequality and exponential integrability on a metric measure space Invited International conference

    Tomonari Sei and Ushio Tanaka

    Statistical Theories and Machine Learning Using Geometric Methods  2023.12  Koichi Tojo (RIKEN AIP), Hideto Nakashima (ISM), Yoshihiko Konno (Osaka Metro.Univ.), Hideyuki Ishi (Osaka Metro.Univ.), Kenji Fukumizu (ISM)

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    Presentation type：Oral presentation (general)  

    Venue：Academic Extension Center (Osaka Metropolitan University)  

  • An isoperimetric inequality, an expansion coefficient and a lower bound for the Cheeger constant of a metric measure space

    Ushio Tanaka

    OCAMI Differential Geometry Seminar  2023.01  OCAMI Differential Geometry Seminar

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    Presentation type：Public lecture, seminar, tutorial, course, or other speech  

    Venue：F415, Department of Mathematics, Osaka Metropolitan University  

    The present study is intended to demonstrate an isoperimetric inequality in terms of Ledoux's expansion coefficient on a metric measure space with a certain functional inequality; the Ledoux's expansion coefficient gives rise to an exponential concentration. The result enables us to bound the Cheeger constant of the metric measure space from below in terms of the constant attributed to the functional inequality.

  • Stein-type distributions on Riemannian manifolds International conference

    T. Sei and U. Tanaka

    Mathematical Optimization and Statistical Theories using Geometric Methods  2022.10  H. Nakashima, Y. Konno, H. Ishi and K. Fukumizu

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    Presentation type：Oral presentation (general)  

    Venue：Academic Extension Center, Osaka Metropolitan University  

  • On Geometric Properties of the Textile Set and Strict Textile Set International conference

    T. Sei and U. Tanaka

    4th International Conference, GSI 2019  2019.08 

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    Presentation type：Oral presentation (general)  

    Venue：Toulouse, France  

    Other Link： https://link.springer.com/chapter/10.1007/978-3-030-26980-7_1

Works

Outline of collaborative research (seeds)

  • Differential Geometry; Shape Theory; Likelihood Geometry; Stochastic Geometry, The Theory of Point Processes and Spatial Statistics; Mathematics for Go and Go Art

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    Type of research exchange：Technical consultation,　Contract research,　Joint research,　Lecture

Grant-in-Aid for Scientific Research

  • Graphical modeling based on the information-geometric characterization of copulas

    Grant-in-Aid for Scientific Research(C)  2025

  • Graphical modeling based on the information-geometric characterization of copulas

    Grant-in-Aid for Scientific Research(C)  2024

  • Analysis for asymptotic theory of cluster point processes and GUI implementation of R package on point process analysis

    Grant-in-Aid for Young Scientists(B)  2013.04

Charge of on-campus class subject

  • 数理統計学1

    2024   Weekly class   Undergraduate

  • 数学特別研究2A

    2024   Intensive lecture   Graduate school

  • 数学特別研究1A

    2024   Intensive lecture   Graduate school

  • 数学特別研究5A

    2024   Intensive lecture   Graduate school

  • 数学特別研究4A

    2024   Intensive lecture   Graduate school

  • 数学特別研究3A

    2024   Intensive lecture   Graduate school

  • 数理統計学II

    2024   Weekly class   Undergraduate

  • Probability and Statistics II

    2021    

  • Probability and Statistics I

    2021    

  • Basic Statistics I

    2021    

  • Basic Statistics I

    2021    

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Social Activities　⇒ Link to the list of Social Activities

  • Mathematics based on a variational principle

    Role(s)： Lecturer

    Type： Seminar, workshop

    Osaka Metropolitan University  2022.04

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    Audience： High school students,　General public,　Civic organization

    Number of participants：106（人）

  • Professors Seminar, an isoperimetric inequality

    Role(s)： Lecturer

    Type： Visiting lecture

    Professors Seminar  2018.11

  • 府立泉北高等学校SSH (スーパーサイエンスハイスクール) 大学訪問研修 変分問題入門

    Role(s)： Lecturer

    2016.07

Visiting Lectures　⇒ Link to the list of Visiting Lectures

  • 等周問題

    Category：Science (mathematics, physics, chemistry, biology, geology, biochemistry)

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    Audience：Preschooler,　Schoolchildren,　Junior high school students,　High school students,　College students,　Teachers,　Researchers,　General,　Company,　Civic organization

    Keyword：等周不等式 

    物理法則は簡明に記述され，真理は単純である．この信念は，自然界の原理として古くから知られ，変分原理といわれる．変分問題は，変分原理に基づく問題であり，エネルギー最小を数学的に探る問題といえる．本セミナーでは，古代ローマの伝説上の女王Didoが臣下に命じた，変分問題の起源のひとつとして知られている等周問題を紹介する．

  • 変分問題入門

    Category：Science (mathematics, physics, chemistry, biology, geology, biochemistry)

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    Audience：Preschooler,　Schoolchildren,　Junior high school students,　High school students,　College students,　Teachers,　Researchers,　General,　Company,　Civic organization

    Keyword：微分幾何学，最小作用の原理，Plateau問題，平均曲率，Gauss曲率，極小曲面，平均曲率一定曲面，Computer Graphics 

    ミツバチの巣にみられるハニカム構造は，建築物をはじめ多様なものに応用されています．これはハニカム構造がコストの経済性や強度に優れていることに基づきますが，それは何故でしょうか．この問題の数学的定式化は今から約2000年以上前に予想され，2001年，長い年月を経て証明されました．

    さて，自然は作用を最小にする，といわれます．いわゆる「最小作用の原理」です．変分問題はこれらを数学的枠組みで捉え，出張講義ではこれに関する入門的講義をします．「極小曲面」(石鹸膜の幾何学的モデル) と「平均曲率一定曲面」(シャボン玉の幾何学的モデル) が変分問題において中心的な役割を果たします．

    ところで，数学は一般には物理的実験要素を含みませんが，変分問題はこの点において一線を画す分野といえます．加えて，近年Computer Graphicsの発展により，様々な様相を呈する極小曲面と平均曲率一定曲面の可視化が実現しました．変分問題を通して数学を視覚的に楽しめることも変分問題の醍醐味のひとつと思います．