Details of the Researcher

PHOTO

Yoji Akama
Section
Graduate School of Science
Job title
Associate Professor
Degree

  • 博士（理学）（東京工業大学）

Research History 5

  • 1997/12 - 2000/03
    ETL researcher

  • 1998/04 - 1999/03
    一橋大学教養部非常勤講師　非常勤講師

  • 1995/04 - 1999/03
    Graduate School of Science, Tokyo University　Research Associate

  • 1996/04 - 1996/09
    千葉大学文学部行動科学科非常勤講師　非常勤講師

  • 1992/04 - 1995/03
    JSPS Research Fellow

Education 5

  • Tokyo Institute of Technology　Graduate School, Division of Science and Engineering　情報科学

    1992/04 - 1995/03

  • Tokyo Institute of Technology

    1990/04 - 1992/03

  • Tokyo Institute of Technology

    1989/04 - 1990/03

  • The University of Tokyo　The Faculty of Engineering　Department of Mathematical Engineering and Information Physics

    1986/04 - 1989/03

  • The University of Tokyo

    1984/04 - 1986/03

Committee Memberships 8

  • American Mathematical Society　Reviewer

    2013/04 - Present

  • 情報処理学会　調査研究運営委員会 ナチュラルコンピューティング研究 グループ（NC）幹事

    2006/04 - Present

  • 情報処理学会　調査研究運営委員会 ナチュラルコンピューティング研究 グループ（NC）幹事

    2006/04 - Present

  • 日本応用数理学会　「数理的技法による情報セキュリティ」研究部会 幹事

    2006/04 - 2010/03

  • 日本応用数理学会　「数理的技法による情報セキュリティ」研究部会 幹事

    2006/04 - 2010/03

  • Workshop on Learning with Logics and Logics for Learning 2006　Program Committee

    2005/10 - 2006/10

  • Workshop on Learning with Logics and Logics for Learning 2006　Program Committee

    2005/10 - 2006/10

  • 学習理論における組合せ論に関する研究会　世話人

    2012/09 -

Show all ︎Show first 5

Professional Memberships 3

  • 日本数学会

  • 応用数理学会

  • 人工知能学会

Research Interests 2

  • Tilings and Quasicrystals

  • Statisitical Learning Theory

Research Areas 3

  • Natural sciences / Applied mathematics and statistics / 数学基礎・応用数学（数値解析・数理モデル（がん予測理論、最適化、データ解析）

  • Natural sciences / Basic mathematics / 数学基礎・応用数学（数値解析・数理モデル（がん予測理論、最適化、データ解析）

  • Natural sciences / Geometry / tiling

Awards 1

  1. 日本ソフトウェア科学会第3回プログラミングおよびプログラミング言語ワークショップ発表賞

    2001/03/23　日本ソフトウェア科学会 プログラミングおよびプログラミング言語ワークショップ　発表賞

Papers 61

  1. A Dichotomous Behavior of Guttman-Kaiser Criterion from Equi-Correlated Normal Population Peer-reviewed

    Yohji Akama, Atina Husnaqilati

    Journal of the Indonesian Mathematical Society　272-303　2022/11/30

    Publisher: Indonesian Mathematical Society

    DOI： 10.22342/jims.28.3.1158.272-303 　

    ISSN： 2086-8952

    eISSN： 2460-0245

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    We consider a $p$-dimensional, centered normal population such that all variables have a positive variance and any correlation coefficient between different variables is a given nonnegative constant $\rho<1$. Suppose that both the sample size $n$ and population dimension $p$ tend to infinity with $p/n \to c>0$. We prove that the limiting spectral distributions of the sample covariance matrices and the sample correlation matrices are Mar\v{c}enko-Pastur distribution of index $c$ and scale parameter $1-\rho$.By the limiting spectral distributions, we rigorously show the limiting behavior of widespread stopping rules Guttman-Kaiser criterion and cumulative-percentage-of-variation rule in PCA and EFA.As a result, we establish the following dichotomous behavior of Guttman-Kaiser criterion when both $n$ and $p$ are large, but $p/n$ is small: (1) the criterion retains a small number of variables for $\rho>0$, as suggested by Kaiser, Humphreys, and Tucker [Kaiser, H. F. (1992). On Cliff's formula, the Kaiser-Guttman rule and the number of factors. \emph{Percept. Mot. Ski.} 74]; and(2) the criterion retains $p/2$ variables for $\rho=0$, as in a simulation study [Yeomans, K. A. and Golder, P. A. (1982). The Guttman-Kaiser criterion as a predictor of the number of common factors. \emph{J. Royal Stat. Soc. Series D} 31(3)].

  2. On deformed dodecahedron tilings Peer-reviewed

    85　(1)　1-14　2022/09

  3. Hyperbolic polyhedral surface with regular faces Peer-reviewed

    Discrete Mathematics　2022

  4. Tilings of the sphere by congruent pentagons III: Edge combination a5 Peer-reviewed

    Yohji Akama, Erxiao Wang, Min Yan

    Advances in Mathematics　394　107881-107881　2022/01

    Publisher: Elsevier BV

    DOI： 10.1016/j.aim.2021.107881 　

    ISSN： 0001-8708

  5. Classification of spherical tilings by congruent quadrangles over pseudo-double wheels (II)—the isohedral case Peer-reviewed

    AKAMA Yohji

    Hiroshima Mathematical Journal　48　(1)　1-34　2019/03

  6. Phase Separation Dynamics of a Binary Fluid with a Closed-Loop Phase Diagram Peer-reviewed

    Masatoshi Toda, Shinji Kajimoto, Shuichi Toyouchi, Toshihiro Kawakatsu, Yohji Akama, Motoko Kotani, Hiroshi Fukumura

    Journal of Physical Society of Japan　88　024007　2019/01

    DOI： 10.7566/JPSJ.88.024007 　

  7. Time-Resolved Structured Illumination Microscopy for Phase Separation Dynamics of Water and 2-Butoxyethanol Mixtures: Interpretation of “Early Stage” Involving Micelle-Like Structures Peer-reviewed

    Shuichi Toyouchi, Shinji Kajimoto, Masatoshi Toda, Toshihiro Kawakatsu, Yohji Akama, Motoko Kotani, Hiroshi Fukumura

    Journal of Physical Chemistry B　122　(51)　12375-12385　2018/12

    DOI： 10.1021/acs.jpcb.8b10244 　

  8. The confluent terminating context-free substitutive rewriting system for the lambda-calculus with surjective pairing & terminal type Peer-reviewed

    Yohji Akama

    Leibniz International Proceedings in Informatics, LIPIcs　84　1-19　2017/09/01

    Publisher: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

    DOI： 10.4230/LIPIcs.FSCD.2017.6 　

    ISSN： 1868-8969

  9. Phase behavior of a binary fluid mixture of quadrupolar molecules Peer-reviewed

    Masatoshi Toda, Shinji Kajimoto, Shuichi Toyouchi, Toshihiro Kawakatsu, Yohji Akama, Motoko Kotani, Hiroshi Fukumura

    PHYSICAL REVIEW E　94　(5)　2016/11

    DOI： 10.1103/PhysRevE.94.052601 　

    ISSN： 2470-0045

    eISSN： 2470-0053

  10. Anisohedral spherical triangles and classification of spherical tilings by congruent kites, darts and rhombi

    Yudai Sakano, Yohji Akama

    Hiroshima Mathematical Journal　45　(3)　309-339　2015/11/01

    Publisher: Hiroshima University

    DOI： 10.32917/hmj/1448323768 　

    ISSN： 0018-2079

  11. 24pAQ-3 Phase separation dynamics of a binary mixture with a closed-loop phase diagram Peer-reviewed

    M. Toda, S. Kajimoto, S. Toyouchi, T. Kawakatsu, Y. Akama, M. Kotani, H. Fukumura

    Meeting Abstracts of the Physical Society of Japan　70.1　(0)　3438-3438　2015

    DOI： 10.11316/jpsgaiyo.70.1.0_3438 　

  12. Spherical tilings by congruent quadrangles: Forbidden cases and substructures Peer-reviewed

    Yohji Akama, Nico Van Cleemput

    ARS MATHEMATICA CONTEMPORANEA　8　(2)　297-318　2015

    ISSN： 1855-3966

    eISSN： 1855-3974

  13. Mesoscopic Dynamics of Laser-induced Phase Separation in Water and 2-Butoxyethanol Mixtures Revealed by Nanosecond Time-resolved Light Scattering Peer-reviewed

    Shuichi Toyouchi, Shinji Kajimoto, Masatoshi Toda, Toshihiro Kawakatsu, Yohji Akama, Motoko Kotani, Hiroshi Fukumura

    CHEMISTRY LETTERS　43　(12)　1838-1840　2014/12

    DOI： 10.1246/cl.140698 　

    ISSN： 0366-7022

    eISSN： 1348-0715

  14. Realizability interpretation of PA by iterated limiting PCA Peer-reviewed

    Yohji Akama

    MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE　24　(6)　1-34　2014/12

    DOI： 10.1017/S0960129513000856 　

    ISSN： 0960-1295

    eISSN： 1469-8072

  15. A Non-Uniformly C-Productive Sequence & Non-Constructive Disjunctions Peer-reviewed

    John Case, Michael Ralston, Yohji Akama

    Asian Logic Conference 2013　29-52　2014/10/01

    DOI： 10.1142/9789814678001_0002 　

  16. Classification of spherical tilings by congruent quadrangles over pseudo-double wheels(I) ―a special tiling by congruent concave quadrangles Peer-reviewed

    Yohji Akama

    Hiroshima Mathematical Journal　43　(3)　2013/11/01

  17. On Image Reconstruction Algorithms of Structured Illumination Microscopy(<Special Topic>A Mathematical Challenge to a New Phase of Materials Science)

    Akama Yohji, Kamijo Takanobu

    Bulletin of the Japan Society for Industrial and Applied Mathematics　23　(4)　160-165　2013

    Publisher: The Japan Society for Industrial and Applied Mathematics

    DOI： 10.11540/bjsiam.23.4_160 　

    ISSN： 0917-2270

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    A structured illumination microscopy (SIM) proposed by Gustafsson has resolution better than conventional resolution limit. SIM illuminates a sample with structured light several times by varying the phase, observes the resulting uorescence image from the sample, compute the Fourier transform of the sample's image from those of the observed uorescence images, and then compute the inverse-Fourier transform to construct the super-resolution image of the sample. The observed images are prone to independent image noises. Unless the observed images continuously join to a single image, the computed image will contain an artifact that does not really exist in the sample. We propose to calculate the weighted mean of the Fourier transforms of the observed images, to construct the super-resolution image of the sample. By a computer simulation, we illustrate that this image reconstruction algorithm can indeed enhance the resolution of SIM.

  18. Effect of molecular geometry on LCST-type phase separation Peer-reviewed

    M. Toda, S. Kajimoto, T. Kawakatsu, Y. Akama, M. Kotani, H. Fukumura

    Meeting Abstracts of the Physical Society of Japan　68.2.2　321-321　2013

    DOI： 10.11316/jpsgaiyo.68.2.2.0_321_3 　

  19. On image construction algorithms of structured illumination microscopy Peer-reviewed

    Yohji Akama, Takanobu Kamijo

    応用数理　23　(4)　16-21　2013

  20. Classification of spherical tilings by congruent quadrangles over pseudo-double wheels (I) - a special tiling by congruent concave quadrangles Peer-reviewed

    Yohji Akama

    Hiroshima Mathematical Journal　43　(3)　2013

  21. Random Fields on Model Sets with Localized Dependency and Their Diffraction Peer-reviewed

    Yohji Akama, Shinji Iizuka

    JOURNAL OF STATISTICAL PHYSICS　149　(3)　478-495　2012/11

    DOI： 10.1007/s10955-012-0588-5 　

    ISSN： 0022-4715

  22. A new order theory of set systems and better quasi-orderings Peer-reviewed

    Yohji Akama

    Progress in Informatics　9　(9)　9-18　2012/03

    DOI： 10.2201/NiiPi.2012.9.3 　

    ISSN： 1349-8614 1349-8606

  23. Set systems: Order types, continuous nondeterministic deformations, and quasi-orders Peer-reviewed

    Yohji Akama

    THEORETICAL COMPUTER SCIENCE　412　(45)　6235-6251　2011/10

    DOI： 10.1016/j.tcs.2011.08.010 　

    ISSN： 0304-3975

  24. VC Dimensions of Principal Component Analysis Peer-reviewed

    Yohji Akama, Kei Irie, Akitoshi Kawamura, Yasutaka Uwano

    DISCRETE & COMPUTATIONAL GEOMETRY　44　(3)　589-598　2010/10

    DOI： 10.1007/s00454-009-9236-5 　

    ISSN： 0179-5376

  25. 主成分分析の固有値の一致性について

    Yohji Akama, Yasutaka Uwano

    人工知能 学会研究会資料　SIG-DMSM-A903　101-105　2010/03/30

  26. VC Theory and a Concentration Inequality for Sums of Eigenvalues of Wishart Matrix Peer-reviewed

    Yohji Akama, Yasutaka Uwano

    Collection of Technical Reports of the 12th Workshop on Information-Based Induction Sciences (IBIS 2009)　2009/10/19

    More details Close

    4-9902248-4-1

  27. Gaussian Mixture Models and VC Dimensions

    Yohji Akama

    Proceedings of The Fourth International Workshop on Data-Mining and Statistical Science　2009/06/07

  28. Asymmetries of Cut-and-project Sets and Related Tilings Peer-reviewed

    Yohji Akama, Shinji Iizuka, Yutaka Akazawa

    Interdisciplinary Information Sciences　15　(1)　99-113　2009

    Publisher: Tohoku University

    DOI： 10.4036/iis.2009.99 　

    ISSN： 1340-9050

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    In order to characterize the (a)symmetries of cut-and-project sets, we prove the following: any cut-and-project set with the two projections being injective on the lattice is fixed by an affine transformation if and only if (1) the window restricted on the projection of the lattice is fixed by another affine transformation, and (2) both affine transformations induce via the two projections the same transformation on the lattice. By this theorem, we prove that any Pisot tilings are asymmetric with respect to any affine transformations.

  29. Commutative Regular Shuffle Closed Languages, Noetherian Property, and Learning Theory Peer-reviewed

    Yohji Akama

    LANGUAGE AND AUTOMATA THEORY AND APPLICATIONS　5457　93-104　2009

    DOI： 10.1007/978-3-642-00982-2_8 　

    ISSN： 0302-9743

  30. Consistent and coherent learning with delta-delay Peer-reviewed

    Yohji Akama, Thomas Zeugmann

    INFORMATION AND COMPUTATION　206　(11)　1362-1374　2008/11

    DOI： 10.1016/j.ic.2008.06.005 　

    ISSN： 0890-5401

  31. 主成分分析のＶＣ次元

    Yohji Akama, Kei Irie, Akitoshi Kawamura, Yasutaka Uwano

    日本応用数理学会2008年度年会予稿集　337-338　2008/09

  32. VC Dimensions of Statistical Inferences

    Yohji Akama, Kei Irie, Akitoshi Kawamura, Yasutaka Uwano

    人工知能学会　SIG-FPAI-A801　9-13　2008/07

  33. 主成分分析の汎化誤差などについて

    赤間陽二, 上野康隆

    人工知能基本問題研究会資料　SIG-FPAI-A703　2008/01

  34. Learning Integer Crystalline Structures

    Yohji Akama

    応用数理学会2007年度年会予稿　2007/09

  35. Omega-Rules and Learnability

    Yohji Akama

    Cooper, Kent, Lowe and Sorbi eds. Computation and Logic in the Real World(Technical report No. 487)　368　2007/06

  36. Omega-rules and Learnability

    Yohji Akama

    Proceedings of Computability and Logic in the Real World　2007

  37. Consistency conditions for inductive inference of recursive functions Peer-reviewed

    Yohji Akama, Thomas Zeugmann

    NEW FRONTIERS IN ARTIFICIAL INTELLIGENCE　4384　251-264　2007

    ISSN： 0302-9743

  38. Cut-and-project sets and their epsilon-duals Peer-reviewed

    Y. Akama, S. Iizuka

    PHILOSOPHICAL MAGAZINE　87　(18-21)　2847-2854　2007

    DOI： 10.1080/14786430701373698 　

    ISSN： 1478-6435

  39. Hierarchies of Consistency Learnings with Delay

    Yohji Akama

    JSAI SIG Notes, SIG-FPAI-A602-12　2006/10/31

  40. Inductive Inference of Lattices from Positive Data Peer-reviewed

    Yohji Akama

    Proceedings of Ninth Workshop on Information-Based Induction Sciences　2006/10/31

  41. Multiclass Multisurface Proximity Support Vector Machines Invited Peer-reviewed

    Yohji Akama, Taufik Sutanto

    Workshop on Learning with Logics and Logics for Learning　2006/06

  42. Case-Smith Hierarchy of Intrusion Detection System

    Yohji Akama

    JSAI SIG Notes, SIG-FPAI-A502-14　2005/11/25

  43. Learning Lambda-Terms in Limit Peer-reviewed

    赤間 陽二

    日本ソフトウェア科学会第22回大会論文集　2005/10

  44. Real number representations of graph-directed IFS attractors Peer-reviewed

    Yohji Akama, Shinji Iizuka

    Proceedings of Second International Conference on Computability and Complexity in Analysis　3-24　2005/06

  45. Radix Representation with Computable Irrational Number and Computable Real Numbers

    赤間 陽二, 飯塚 新司

    京都大学数理解析研究所, 数理解析研究所講究録, 数学解析の理論的展開の計算機による支援・遂行可能性, 数理解析研究所講究録　1381　159-167　2004/06

    Publisher:

    ISSN： 1880-2818

  46. An arithmetical hierarchy of the law of excluded middle and related principles Invited Peer-reviewed

    Y Akama, S Berardi, S Hayashi, U Kohlenbach

    19TH ANNUAL IEEE SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE, PROCEEDINGS　192-201　2004

    ISSN： 1043-6871

  47. Limiting partial combinatory algebras Peer-reviewed

    Y Akama

    THEORETICAL COMPUTER SCIENCE　311　(1-3)　199-220　2004/01

    DOI： 10.1016/S0304-3975(03)00360-8 　

    ISSN： 0304-3975

  48. Fine metric and Walsh function systems associated to beta-expansion

    赤間 陽二, 竹内 大輔

    京都大学数理解析研究所, 数理解析研究所講究録, 数学解析の理論的展開の計算機による支援・遂行可能性, 数理解析研究所講究録　1286　61-78　2002/06

  49. Limit-computable mathematics and its applications

    Susumu Hayashi, Yohji Akama

    Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)　2471　1　2002

    Publisher: Springer Verlag

    DOI： 10.1007/3-540-45793-3_1 　

    ISSN： 1611-3349 0302-9743

  50. Typed Limiting Calculi and the Category Theory Peer-reviewed

    Yohji Akama, Susumu Hayashi

    日本ソフトウェア科学会第18回大会論文集　2001/10

  51. Limiting Partial Combinatory Algebras

    Yohji Akama

    京都大学数理解析研究所, 数理解析研究所講究録, 圏論と証明論の新たな融合を目指して = Towards new interaction between category theory and proof theory　1217　1-22　2001/06

  52. A study, of Abramsky's Linear Chemical Abstract Machine Peer-reviewed

    S Mikami, Y Akama

    TYPED LAMBDA CALCULI AND APPLICATIONS　1581　243-257　1999

    ISSN： 0302-9743

  53. Translation of First-class Environments to Records Peer-reviewed

    Shinya Nishizaki Yohji Akama

    Proceedings of the First Workshop on Explicit Substitutions : Theory Applications to Programs and Proofs, Tsukuba　1998/03

  54. SN combinators and partial combinatory algebras Peer-reviewed

    Y Akama

    REWRITING TECHNIQUES AND APPLICATIONS　1379　302-316　1998

    DOI： 10.1007/BFb0052378 　

    ISSN： 0302-9743

  55. A lambda-to-CL translation for strong normalization Peer-reviewed

    Y Akama

    TYPED LAMBDA CALCULI AND APPLICATIONS　1210　1-10　1997

    DOI： 10.1007/3-540-62688-3_25 　

    ISSN： 0302-9743

  56. , In M. Takeichi and T. Ida, editors Peer-reviewed

    Yohji Akama

    Proceedings of Fuji International Workshop on Functional and Logic Programming　48-62　1996/06

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    World Scientific<br /> 多相型つきプログラミング言語の保守的拡大について調べた。

  57. Normal proofs and their grammar Peer-reviewed

    M Takahashi, Y Akama, S Hirokawa

    INFORMATION AND COMPUTATION　125　(2)　144-153　1996/03

    DOI： 10.1006/inco.1996.0027 　

    ISSN： 0890-5401

  58. Strong Normalization and PER Model

    Yohji Akama

    IPSJ SIG Notes, 95-PRO-4, IPSJ　95　(114)　1-6　1995/11

    Publisher: Information Processing Society of Japan (IPSJ)

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    強正規化性と部分同値類モデル、情報処理学会PRO

  59. Normal Proofs and Their Grammar Invited

    Masako Takahashi, Yohji Akama, Sachio Hirokawa

    Proceedings of International Conference on Theoretical Aspects of Computer Software, Lecture Notes in Computer Science, Springer-Verlag　789　465-494　1994/11

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    M. Hagiya and J. C. Mitchell, editors

  60. On Mints' Reduction for ccc-Calculus Peer-reviewed

    Yohji Akama

    Proceedings of the International Conference on Typed Lambda Calculi and Applications, Lecture Notes in Computer Science, Springer-Verlag　664　1-12　1993/03

  61. Deriving a Functional Knuth-Morris-Pratt Algorithm by Transformation Peer-reviewed

    Masato Takeichi, Yoji Akama

    Journal of Information Processing　13　(4)　522-528　1990/01/01

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Misc. 24

  1. Graphs on surfaces with positive Forman curvature or corner curvature

    Yohji Akama, Bobo Hua, Yanhui Su, Haohang Zhang

    2020/02/10

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    On one hand, we study the class of graphs on surfaces, satisfying tessellation properties, with positive Forman curvature on each edge. Via medial graphs, we provide a new proof for the finiteness of the class, and give a complete classification. On the other hand, we classify the class of graphs on surfaces with positive corner curvature.

  2. A curvature notion for planar graphs stable under planar duality

    Yohji Akama, Bobo Hua, Yanhui Su, Lili Wang

    2019/09/17

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    Woess \cite{Woess98} introduced a curvature notion on the set of edges of a planar graph, called $\Psi$-curvature in our paper, which is stable under the planar duality. We study geometric and combinatorial properties for the class of infinite planar graphs with non-negative $\Psi$-curvature. By using the discharging method, we prove that for such an infinite graph the number of vertices (resp. faces) of degree $k,$ except $k=3,4$ or $6,$ is finite. As a main result, we prove that for an infinite planar graph with non-negative $\Psi$-curvature the sum of the number of vertices of degree at least $8$ and the number of faces of degree at least $8$ is at most one.

  3. Hyperbolic polyhedral surfaces with regular faces

    Yohji Akama, Bobo Hua

    2018/07/28

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    We study hyperbolic polyhedral surfaces with faces isometric to regular hyperbolic polygons satisfying that the total angles at vertices are at least $2\pi.$ The combinatorial information of these surfaces is shown to be identified with that of Euclidean polyhedral surfaces with negative combinatorial curvature everywhere. We prove that there is a gap between areas of non-smooth hyperbolic polyhedral surfaces and the area of smooth hyperbolic surfaces. The numerical result for the gap is obtained for hyperbolic polyhedral surfaces, homeomorphic to the double torus, whose 1-skeletons are cubic graphs.

  4. Tilings of the Sphere by Congruent Pentagons III: Edge Combination $a^5$

    Yohji Akama, Erxiao Wang, Min Yan

    2018/05/17

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    There are exactly eight edge-to-edge tilings of the sphere by congruent equilateral pentagons: three pentagonal subdivision tilings with 12, 24, 60 tiles; four earth map tilings with 16, 20, 24, 24 tiles; and one flip modification of the earth map tiling with 20 tiles.

  5. Confluent terminating extensional lambda-calculi with surjective pairing and terminal type

    Yohji Akama

    2018/05/05

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    For the lambda-calculus with surjective pairing and terminal type, Curien and Di Cosmo were inspired by Knuth-Bendix completion, and introduced a confluent rewriting system that (1) extends the naive rewriting system, and (2) is stable under contexts. The rewriting system has (i) a rule that rewrites term of a terminal type rewrites to a term constant *, unless the term is not *, (ii) rewrite rules for the extensionality of function types and product types, and rewrite rules mediating the rewrite rules (i) and (ii). Curien and Di Cosmo supposed that because of (iii), any reducibility method cannot prove the strong normalization (SN) of Curien-Di Cosmo's rewriting system, and they left the SN open. By relativizing Girard's reducibility method to the *-free terms, we prove SN of their rewriting, and SN of the extension by polymorphism. The relativization works because: for any SN term t, and for any variable z of terminal type not occurring in $t$, t with all the occurrences of * of terminal type replaced by the variable z is SN.

  6. Areas of spherical polyhedral surfaces with regular faces

    Yohji Akama, Bobo Hua, Yanhui Su

    2018/04/30

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    For a finite planar graph, it associates with some metric spaces, called (regular) spherical polyhedral surfaces, by replacing faces with regular spherical polygons in the unit sphere and gluing them edge-to-edge. We consider the class of planar graphs which admit spherical polyhedral surfaces with the curvature bounded below by 1 in the sense of Alexandrov, i.e. the total angle at each vertex is at most $2\pi$. We classify all spherical tilings with regular spherical polygons, i.e. total angles at vertices are exactly $2\pi$. We prove that for any graph in this class which does not admit a spherical tiling, the area of the associated spherical polyhedral surface with the curvature bounded below by 1 is at most $4\pi - \epsilon_0$ for some $\epsilon_0 > 0$. That is, we obtain a definite gap between the area of such a surface and that of the unit sphere.

  7. Review of "Elisa et al. Wulff shape emergence in graphene, Math. Models Methods Appl. Sci. 26, 2016"

    AKAMA Yohji

    Mathematical Review　2017

  8. 書評「横浜発 確率・統計入門」

    赤間 陽二

    数理科学　626　59-59　2015/08

    Publisher: サイエンス社

  9. Review of "Cohen, Liron; Constable, Robert L. Intuitionistic ancestral logic as a dependently typed abstract programming language. Logic, language, information, and computation, 14--26, Lecture Notes in Comput. Sci., 9160, Springer, Heidelberg, 2015. (Re

    Yohji Akama

    Mathematical Review　2015

  10. Review of "Salvati and Walukiewicz. Using models to model-check recursive schemes, Log. Methods Comput.l Sci. 11 (2015)"

    AKAMA Yohji

    Mathematical Review　2015

  11. On Deformed Dodecahedron Tiling

    Yohji Akama, Min Yan

    2014/03/27

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    There is only one type of tilings of the sphere by $12$ congruent pentagons. These tilings are isohedral.

  12. Review of "Fujita, Ken-etsu. Type problems for lambda calculi: from the theory of mathematical foundations to the structure of programming languages. (Japanese) Sūgaku 66 (2014), no. 1, 78–89"

    Yohji Akama

    Mathematical Review　2014

    Publisher: American Mathematical Society

  13. Review of "Czédli, Gábor. Finite convex geometries of circles. Discrete Math. 330 (2014), 61–75."

    Yohji Akama

    Mathematical Review　2014

    Publisher: American mathematical society

  14. Review of "Yang, Jed Rectangular. tileability and complementary tileability are undecidable. European J. Combin. 41 (2014), 20–34.''

    Yohji Akama

    Mathematical Review　2014

    Publisher: American mathematical society

  15. Review of "Zappa, Emilio; Dykeman, Eric C.; Twarock, Reidun. On the subgroup structure of the hyperoctahedral group in six dimensions. Acta Crystallogr. Sect. A 70 (2014), no. 5, 417–428.''

    Yohji Akama

    Mathematical Review　2014

  16. Review of " Kuske, Dietrich Isomorphisms of scattered automatic linear orders. Theoret. Comput. Sci. 533 (2014)"

    AKAMA Yohji

    Mathematical Review　2014

  17. Review of " Kane. The average sensitivity of an intersection of half spaces. Res. Math. Sci. 1 (2014)"

    AKAMA Yohji

    Mathematical Review　2014

  18. Spherical tilings by congruent quadrangles over pseudo-double wheels (III) - the essential uniqueness in case of convex tiles

    Yohji Akama, Yudai Sakano

    2013/12/11

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    In [B.Gruenbaum, G.C. Shephard, Spherical tilings with transitivity properties, in: The geometric vein, Springer, New York, 1981, pp. 65-98], they proved "for every spherical normal tiling by congruent tiles, if it is isohedral, then the graph is a Platonic solid, an Archimedean dual, an n-gonal bipyramid (n>2), or an n-gonal trapezohedron (i.e., the pseudo-double wheel of 2n faces)". In the classification of spherical monohedral tilings, one naturally asks an "inverse problem" of their result: For a spherical monohedral tiling of the above mentioned topologies, when is the tiling isohedral? We prove that for any spherical monohedral quadrangular tiling being topologically a trapezohedron, if the number of faces is 6, or 8, if the tile is a kite, a dart or a rhombi, or if the tile is convex, then the tiling is isohedral.

  19. Review: "Borgström, Johannes; Gordon, Andrew D.; Greenberg, Michael; Margetson, James; Van Gael, Jurgen Measure transformer semantics for Bayesian machine learning"

    Yohji Akama

    Mathematical review　2013

    Publisher: American mathematical society

  20. Review of "Senechal, Marjorie; Taylor, Jean E., Quasicrystals: the view from Stockholm. Math. Intelligencer 35 (2013), no. 2, 1--9."

    Yohji Akama

    Mathematical Review　2013

    Publisher: American mathematical society

  21. Review of ``Li, Xingjie Helen, Luskin, Mitchell and Ortner, Christoph, Positive definiteness of the blended force-based quasicontinuum method, Multiscale Model. Simul. 10 (2012), no. 3, 1023--1045''

    Yohji Akama

    Mathematical Review　2013

    Publisher: American mathematical society

  22. Review of "REVIEW: AOSHIMA AND YATA. STATISTICAL INFERENCE IN HIGH-DIMENSION LOW SAMPLE-SIZE SETTINGS, SUUGAKU EXPOSITION, VOL. 65, NO. 3, 2013.''

    Yohji Akama

    Mathematical Review　2013

    Publisher: American mathematical society

  23. Review of "Borgstro"m, Johannes; Gordon, Andrew D.; Greenberg, Michael; Margetson, James; Van Gael, Jurgen. Measure transformer semantics for Bayesian machine learning. Log. Methods Comput. Sci. 9 (2013). no.3, 3:11, 39pp.''

    Yohji Akama

    Mathematical Review　2013

    Publisher: American mathematical society

  24. VC dimension of ellipsoids

    Yohji Akama, Kei Irie

    2011/09/20

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    We will establish that the VC dimension of the class of d-dimensional ellipsoids is (d^2+3d)/2, and that maximum likelihood estimate with N-component d-dimensional Gaussian mixture models induces a geometric class having VC dimension at least N(d^2+3d)/2. Keywords: VC dimension; finite dimensional ellipsoid; Gaussian mixture model

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Presentations 70

  1. A dichotomous behavior of Guttman-Kaiser criterion from equi-correlated normal population

    Atina Husnaqilati, Yohji Akama

    2022/09/15

  2. Shrinkage of eigenvalue distributions of sample correlation matrix formed from equi-correlated normal population

    Yohji Akama

    Annual meeting of Mathematical Society of Japan　2022/09/15

  3. Graphs on surfaces with positive Forman curvature or corner curvature and spherical tilings

    2021/12/14

  4. A dichotomous behavior of Guttman-Kaiser rule from equi-correlated normal population and the limiting spectral distributions of random matrices

    Atina Husnaqilati, Yohji Akama

    2021/11/13

  5. Component retention to microarray datasets and Mar\v{c}henko-Pastur setting

    Atina Husnaqilati, Yohji Akama

    2020/09/04

  6. Proving SN & CR of Extensional lambda-calculus with Terminal Types by Relativizing Goguen's Typed Operational Semantics

    AKAMA Yohji

    CSCAT　2018/03/19

  7. Transformations of Functional Programs and Relativized Typed Operational Semantics of Type Theories, IPL Workshop on Programming and Beyond International-presentation

    AKAMA Yohji

    IPL Workshop on Programming and Beyond　2018/03/01

  8. SN+CR Proof of Etensional lambda-calculus with Unit Types by a Relativized Typed Operational Semantics International-presentation

    AKAMA Yohji

    48th TRS meeting　2018/02/25

  9. Deza's last problem International-presentation Invited

    AKAMA Yohji

    2017/12/04

  10. The confluent terminating context-free substitutive rewriting system for the lambda-calculus with surjective pairing and terminal type International-presentation

    AKAMA Yohji

    Foundational Structures for Computation and Deduction　2017/10/03

  11. The confluent terminating context-free substitutive rewriting system for the lambda-calculus with surjective pairing and terminal type International-presentation

    Second International Conference on Formal Structures for Computation and Deduction　2017/09/03

  12. The confluent terminating context-free substitutive rewriting system for the lambda-calculus with surjective pairing and terminal type

    CSCAT 2017（理論計算機科学と圏論ワークショップ）　2017/03/21

  13. Exact VC dimension of ellipsoids and consistency of maximum log-likelihood estimator for multivariate Gaussian mixtures

    科 研費シンポジウム統計的モデリングと計算アルゴリズムの数理と 展開.　2017/02/18

  14. spherical tilings by congruent 4-gons on Archimedean dual skeletons International-presentation

    12th annual meeting of the international academy of mathematical chemistry and 2016 international conference on mathematical chemistry　2016/07/04

  15. Spherical tilings by congruent 4-gons on Archimedean dual skeletons International-presentation

    The 12th Annual Meeting of the International Academy of Mathematical Chemistry (IAMC) and the 2016 International Conference on Mathematical Chemistry (ICMC 2016)　2016/06/06

  16. (An)isohedrality and skeleton of spherical monohedral polygonal tilings International-presentation

    Japan Conference on Discrete and Computational Geometry and Graphs　2015/09/14

  17. The rigidity, deformation and tile-transitivity of spherical tilings International-presentation

    Japan Conference on Graph Theory and Combinatorics　2014/05/17

  18. Solution to spherical Hilbert eighteenth problem and the deformation of spherical tilings International-presentation

    Canberra-Japan Meeting, “Pattern Formation: Mathematics and Materials”　2014/04/29

  19. SPHERICAL TILINGS BY CONGRUENT POLYGONS International-presentation

    THE HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY, Department of Mathematics, Student-Faculty Colloquium　2014/03/14

  20. 球面的ヒルベルトの第１８問題の解決と球面タイリングの変形

    直観幾何学　2014/02/10

  21. A predictive survival time for COVID-19 by stacked method

    2012/11/13

  22. A NEW ORDER THEORY OF SET SYSTEMS, WQO AND BQO International-presentation

    SigTheory/Algs, Department of Computer and Information Sciences, University of Delaware　2012/03/07

  23. Classification of spherical tilings by congruent quadrangles International-presentation

    Department of applied mathemtics and computer science seminar　2012/02/14

  24. . CLASSIFICATION OF SPHERICAL TILINGS BY CONGRUENT QUADRANGLES International-presentation

    Seminar at Department of Applied Mathematics and Computer Science　2012/02/09

  25. A new order theory of set systems, WQO and BQO

    Verification Seminar　2012/01/31

  26. 合同な四角形による球面タイリングの分類

    アルゴリズムと計算理論の新展開 （RIMS 研究集会）　2012/01/30

  27. Epsilon-duals of model sets and diffraction measure of randomized model sets International-presentation

    Shinji Iizuka

    Workshop on Dynamical Systems and Aperiodic Order　2011/03/10

  28. VC dimension, measure concentration, and consistency of eigenvalues of sample covariance matrix

    Yasutaka Uwano

    東北大学数学教室談話会　2010/12/20

  29. Consistency of eigenvalues for principal component analysis International-presentation

    Yasutaka Uwano

    Statistics and Operations Research Seminars　2010/05/07

  30. 主成分分析の固有値の一致性について

    第12回データマイニングと統計数理研究会　2010/03/30

  31. Randomized Model Sets and Diffraction International-presentation

    The First CREST-SBM International Conference on Random Media　2010/01/28

  32. 可換シャッフルクローズド正規言語、ネーター性、および極限学習

    人工知能学会第74回基本問題研究会　2009/09/14

  33. Gaussian Mixtgure Models and VC Dimensions

    The Fourth International Workshop on Data-Mining and Statistical Science　2009/06/08

  34. Randomized Model Sets and Diffraction International-presentation

    The 5th Asian International Workshop on Quasicrystals　2009/06/01

  35. Commutative Regular Shuffle Closed Languages, Noetherian Property, and Learning Theory International-presentation

    The 3rd international conference on language and automata theory and application　2009/04/02

  36. 準周期構造と数値積分との関連について

    CREST「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

  37. 主成分分析のVC次元

    応用数理学会大会　2008/09

  38. 不思議な対称性と双対性：準結晶とタイル張りから

    応用数学連携フォーラム　2008/03/14

  39. Diffie-Hellman exponentiationを持つプロトコルの安全性の決定可能性

    日本応用数理学会2007年春の研究部会　2008/03/04

  40. 整数結晶構造の学習理論

    応用数理学会大会　2007/09/15

  41. Multiclass Multisurface Proximity Support Vector Machines International-presentation

    Taufik Sutanto

    Fiftth Workshop onLearning with Logics and Logics for Learning　2007/06/18

  42. Omega-Rules and Learnability International-presentation

    Computability in Europe　2007/06/18

  43. 切断射影集合の数理

    飯塚新司

    「準周期タイリングとその周辺」RIMS 共同研究　2007/03/19

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    研究代表者：伊藤俊次 金沢大学自然科学 研究科教授

  44. Hierarchies of Delayed Consistency Learnings: Some Problems

    2nd Type Theory Workshop　2007/03/07

  45. Diffie-Hellman exponentiation を持つプロトコルの安全性の決定可能性

    日本応用数理学会 (JSIAM)「数理的技法による情報セキュリティ」研究部会 (FAIS)日本応用数理学会2007年春の研究部会連合発表会　2007/03/04

  46. ポスターセッション

    情報論的学習理論ワークショップ　2006/11/01

  47. Cut-and-project Sets and Their Epsilon-duals International-presentation

    Shinji Iizuka

    Aperiodic '06　2006/09/17

  48. Consistency Conditions of Inductive Inference of Functions International-presentation

    Fourth Workshop on Learning with Logics and Logics for Learning　2006/06/05

  49. Consistency Conditions of Inductive Inference of Functions International-presentation

    Workshop on Learning with Logics and Logics for Learning　2006/06/05

  50. Consistent Learning of Virus Signatures from the Behaviour International-presentation

    Type Theory Workshop　2006/01/23

  51. 切断射影集合とそれに関するタイル張りの対称性

    九州大学数理学研究院談話解　2005/12/14

  52. Intrusion Detection System の Case-Smith階層

    人工知能学会基本問題研究会　2005/11/25

  53. ラムダ計算のための計算論的学習理論とその応用 International-presentation

    「代数学と計算」(AC2005)　2005/11/16

  54. Hierarchies of Delayed Consistency Learnings

    人工知能学会基本問題研究会　2005/10/30

  55. 関数の極限ラムダ計算による学習

    日本ソフトウェア科学会全国大会　2005/09

  56. Computability and feasibility of real numbers via beta-adic representation International-presentation

    Workshop on Beta-numeration, generalized substituions and tilings　2004/03/08

  57. Finite-type Arithmetic with 0i-oracle - Hierarchy Theorems of Constructive Arithmetics

    日本数学会秋季大会　2003/09

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    基礎論および歴史分科会

  58. Systems of Typed Limiting Computations

    ALGI　2002/12/16

  59. 構成的算術の階層

    日本数学会秋季大会　2002/09

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    数学基礎論および歴史分科会

  60. Fine metric and Walsh functions associated to beta-expansions

    竹内大輔

    日本数学会秋季大会　2002/09

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    統計数学分科会

  61. Typed Limiting Computation Systems and Categories International-presentation

    Workshop on Type, Lambda, Logic and Automated Provers　2002/03/09

  62. Limit Computations with Type-free and Typed Systems

    日本数学会秋季大会　2001/10/03

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    数学基礎論および歴史分科会

  63. Limiting Partial Combinatory Algebras Towards Infinitary Lambda-Calculi and Classical Logic International-presentation

    15th International Workshop on Computer Science Logic 2001　2001/09/10

  64. 型付き極限計算系と圏論

    林晋

    日本ソフトウェア科学会全国大会　2001/09

  65. Limiting partial combinatory algebras

    第3回プログラミングおよびプログラミング言語ワークショップ　2001/03/21

  66. A Study of Abramsky's Linear Chemical Abstract Machine International-presentation

    4th International Conference on Typed Lambda Calculi and Applications　1999/04/07

  67. SN Combinators and Partial Combinatory Algebras International-presentation

    9th International Conference on Rewriting Techniques and Applications　1998/03/30

  68. A Lambda-to-CL Translations for Strong Normalization International-presentation

    3rd International Conference on Typed Lambda Calculi and Applications　1997/04/02

  69. Conservative Extensions of Polymorphic PCF International-presentation

    Fuji International Workshop on Functional and Logic Programming　1995/06/17

  70. On Mints' Reduction for ccc-Calculus International-presentation

    International Conference on Typed Lambda Calculi and Applications　1993/03/16

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Research Projects 17

  1. 離散幾何 Competitive

    System: Grant-in-Aid for Scientific Research

    2006/04 - Present

  2. Machine Learning Competitive

    System: Grant-in-Aid for Scientific Research

    2004/04 - Present

  3. Tiling Competitive

    2003/10 - Present

  4. Symmetry and deformation of spherical tiling

    Akama Yohji

    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

    2016/04/01 - 2022/03/31

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    By Euler's law, the spherical tilings by congruent polygons are only by triangles, quadrangles, and pentagons. In particular, a spherical tiling by congruent equilateral pentagons is exactly a pentagonal subdivision of a tiling, an earthmap tiling or a flip modification of an earthmap tiling. Moreover, we introduce a new technique similar to Cauchy's arm lemma for polyhedra. Because the area of the sphere is finite and lines on the sphere necessarily intersect, the research on the classification of the spherical tilings by congruent polygons is of recent, and combinatorially hard. As an abstract approach to this problem, we find out not only the symmetry of the tilings, but also the combinatorial curvature of graph which corresponds to Gauss curvature of surfaces.

  5. 単元型を持つ概外延的な型理論の操作的意味論と型検査アルゴリズム Competitive

    赤間 陽二

    Offer Organization: 栢森情報科学振興財団

    System: 情報科学の研究

    2017/11 - 2019/11

  6. The development of discrete geometric analysis

    Sunada Toshikazu

    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: Meiji University

    2015/04/01 - 2019/03/31

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    In this research, I treated several topics in mathematical crystallography. Especially motivated by the recent development in systematic design of crystal structures, I discussed interesting relationships among seemingly irrelevant subjects; say, standard crystal models, tight frames in the Euclidean space, rational points on Grassmannian, and quadratic Diophantine equations. The central object in this study is what I call crystallographic tight frames, which are considered a generalization of root systems. I also made a remark on the connections with tropical geometry, a relatively new area in mathematics, specifically with combinatorial analogues of the Abel-Jacobi map and Abel's theorem. What is more, I explained how the idea of Riemann sum is linked to other branches of mathematics; for instance, some counting problems in elementary number theory and the theory of quasicrystals, the former having a long history and the latter being an active field still in a state of flux.

  7. Mathematical approach to materials science by using non-commutative geometry

    KOTANI Motoko, AKAMA Yohji, ODA Tadao

    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

    2011/04/28 - 2015/03/31

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    One of the fundamental questions of solid state physics is to understand relations between microscopic structures and macroscopic properties of matter. One can computer properties in principle if the matter assumes periodic structure. It however often happens that periodic structures are broken under various physical environment such as with impieties, magnetic fields, boundaries. In this project we challenge to establish a new mathematical approach to those problems by using non-commutative geometry.

  8. Efficiency for machine to learn discrete geometric objects

    AKAMA Yohji

    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 - 2011

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    By studying evaluation methods of the number of connected components of manifolds, we evaluated the VC dimensions of principal component analysis, as statistical learning. Next, we introduce a new order type of set systems to measure the difficulty to learn. We proved (1)any well quasi-ordering can be represented by a set system having our order type ; and (2)if a set system has our order type, then a continuous image of it by a Cantor monotone function does so. Finally, we developed the theory of our order type of set systems to the theory of better quasi-orderings.

  9. Reverse Mathematics in Constructive Mathematics

    ISHIHARA Hajime, AKAMA Yohji

    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: Japan Advanced Institute of Science and Technology

    2007 - 2009

  10. Knowledge Discovery from Structured Data with Efficient Methods of Searching Lower Sets Based on Frequency

    YAMAMOTO Akihiro, HIRATA Kouichi, DOI Koichiro, TOKUNAGA Hiroo, AKAMA Yohji

    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: Kyoto University

    2007 - 2009

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    This research project aimed at constructing foundations of efficient knowledge discovery from data of large scale and of various data types, stored in databases. We clarified various properties of the lattice structure consisting of various types of structured data, designed machine learning/knowledge discovery algorithms by using efficient search of lower sets in the lattices, and applied some of them to theoretical open problems or to problems in science other than informatics. We found that the property of lower sets as being closed sets is useful for both fundamental theories and applications.

  11. statistical learning theory Competitive

    System: Grant-in-Aid for Scientific Research

    2008/04 -

  12. 近似プログララムの計算論-古典論理の証明のテストにむけて-

    赤間 陽二

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業

    Category: 若手研究(B)

    Institution: 東北大学

    2003 - 2005

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    15年度における近似の計算論に関する研究と、16年度における近似の構成的論理に関する研究を踏まえ、数学・計算機科学における近似の現象を計算の立場から以下の2点に絞って研究した。 (1)実数を近似的に表現するするβ展開や、ユークリッド空間上の点を近似的に表現するPisotタイリングなどでは、各数学的対象は唯一の表現を持つが、これらなどを統合的に扱うために、Graph-directed iterated functions systemに着目し、そのアトラクターの要素をそのGIFSが近似的に表現しているものと考えた。この表現系をGIFS-表現と呼ぶことにするが、各数学的対象の表現が唯一である場合は、アトラクター上の実関数で、GIFS-表現に関して計算可能だが局所一様連続でない関数があることを証明した。一方、タイリングから自然に、準結晶の数理モデルである切断射影集合が現れるが、切断射影集合は概周期関数を近似するのに用いられる離散集合であるが、その対称性と双対性に関する研究を行った (2)近似の計算論を研究していたときに近似の収束の速度に興味を持ったが、まず、関数の学習対象とする計算論的学習理論において、近似の速度に関するCase-Smith階層に着目した。計算論的学習の動機として、コンピュータウィルスの振舞からウィルスのシグナチャの学習や、ネットワークを通して計算機を適応的に管理するというところに動機を求めた場合、学習の条件としてGoldが導入した学習の無矛盾性が重要になることを認識した。Goldの無矛盾性を弱めてもやはりCase-Smithの階層が崩壊することを示した。

  13. Comparative studies on nonstandard methods and constructive methods

    TANAKA Kasuyuki, AKAMA Yohji, TAKEDA Masayoshi, MORITA Yasuo, YAMAZAK Takeshi

    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

    2001 - 2003

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    Second order arithmetic was first introduced by D.Hilbert around 1920's to set a firm foundation of analysis. Among many different formalizations of second order arithmetic, RCA_0 and WKL_0 are particularly important with respect to Hilbert's program. Tanaka and Yamazaki, in cooperation with Simpson, proved that one can eliminate, the compactness argument from proofs for a certain sort of theorems in WKL_0, namely WKL_0 is conservative over RCA_0 for the formulas in a certain form. They also showed that the bounded dependent choice scheme, which is often used in the computation of real numbers, can not be eliminated likewise. Thus, Tanaka and Yamazaki constructed an appropriate truth definition for the real number system via the quantifier elimination method, by which one can manipulate the reals freely in RCA_0. By sophisticating this argument, Tanaka, jointly with Sakamoto, could prove Hilbert's Nullstellensatz within RCA_0. Yamazaki and Sakamoto also studied uniform versions of WKL_0 and other statements within higher order arithmetic. Yamazaki investigated the logical strength of completeness theorems for intuitionistic logic.

  14. Logic of Limit Computing and its Applications

    HAYASHI Susumu, YASUGI Mariko, TAMURA Naoyuki

    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: Kobe University

    2001 - 2003

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    The fundamental theory of Limit Computable Mathematics (LCM) were founded and many new results have been obtained in the project. The followings are the main results among them : 1. Improved realizability interpretations for LCM 2. sublearning hierarchy 3. LCM game 4. the arithmetical hierarchy 5. LCM categories 6. Computability in analysis in the light of LCM. Computability theory of discontinuous functions 7. Models of Delta-0-2 maps by means of concurrent computation Among them, the discovery of sublearning hierarchy is quite important. Below the hierarchy of LEM (the laws of excluded middle), principles corresponding to LLPO of constructive mathematics exist and they are related to WKL (Weak Koenig Lemma). This fact has been conceived by some researchers intuitively. By establishing computational and learning theoretic meanings of this fact, we finally explored the position of WKL in the hierarchy of LCM. We found that the principle represents the limit computational model of Popperian game of non-deterministic computation of refutability by finite numbers of processes. The full arithmetical hierarchy of LCM including this sublearning hierarchy was fully explored. This was done through various techniques of mathematical logic, and it is important also from mathematical point of view. The calibration theory according to this hierarchy has been started by a researcher out of our project. We also found that Coquand's game semantics could be restricted in a very natural way so that it coincides with LCM.

  15. Studies on logical structures of arithmetic and computation

    TANAKA Kazuyuki, KASHIMA Ryo, HORAI Masako, AKAMA Yohji, HASEGAWA Ryu, TATSUTA 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

    1997 - 1999

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    K. Tanaka studied along the program of reverse mathematics how much of set theory is needed to prove a theorem of ordinary mathematics. By observing properties of countable models of WKL_0, he proved (jointly with T. Yamazaki and S. Simpson) new conservation results of WKL_0 over RCA_0. Y. Akama introduced an intersection typing system for combinatory logic, and showed that it is sound and complete for the class of partial combinatory algebras. M. Horai has shown that the Curry-Howard isomorphism between higher-order intuitionistic logic and calculus of constructions can be better formulated when a modified version of higher-order type theory is introduced. She also studied the lambda-representability of functions over free structures with respect to the simple type system, as well as the notion of recursive functions over free-structures. M. Tatsuta investigated realizability interpretations of monotone coinductive definition. He proved, among others, that full monotone coinductive definitions are not sound while restricted ones are. R. Hasegawa studied applications of analytic functions to theoretical computer science. R. Kashima obtained several important results on relevant logic.

  16. 変換系と翻訳の理論と応用

    赤間 陽二

    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: 東京大学

    1997 - 1998

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    BerryとBoudolが導入したCHAMは並行計算を記述するための項の書き換え系で、並行計算を化学反応になぞらえて得られた論点は以下の2点である。 1. 計算論的な抽象的な資源の移り変わり。 項(“分子")を資源として扱うために項の多重集合(“溶液")もまた項とされ、多重集合のなかの各項に書き換え(“化学反応")が独立に起きる。 2. カプセル化された計算。 書き換えの及ぶ範囲が定められているため、や、ネットワークの動的な変化が記述できる。Girardの線形論理は、推論過程における論理的な資源の移り変わりを記述できるのだが、線形論理により、CHAMの上記1点目のことが記述できる考える。また、線形論理の証明図の表現の一つであるGirardのproof netは、boxと呼ばれる入れ子構造を持つのだが、対応してCHAMでは複数の計算主体が単一のものとみなされることがある。 私は、CHAMの一種でAbramskyが導入したlinear chemical abstract machine(LCHAM)をまず取り扱い、そこにおける計算資源の移り変わりが機械的に推論するできること(主型定理)を証明した。また、関数型プログラミング言語の中間言語の一つである線形λ計算からLCHAMへの翻訳を導入した。線形λ計算の項のその翻訳による結果は、入出力ポートが原始的であるような計算単位となる。また、この翻訳により、線形λ計算における1ステップの計算はLCHAMにおける1ステップの計算に対応することが明らかになった。

  17. ゲーム理論とプログラム言語の意味論

    赤間 陽二

    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: 東京大学

    1996 - 1996

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    本年度は得られた成果は次の題の論文としてまとめられている."A Lambda-to-CL Translation for Strong Normalization"では,λ計算と組合せ論理(combinatory logic)という簡約系の項の強正規化性という性質に着目し,λ計算の項(λ項と呼ぶ)から組合せ論理の項(CL項と呼ぶ)への新しい対応を定義し、それを使ってλ項の強正規性を適当なCL項の強正規性に還元する新しい方法を示した。ここで、項tが強正規化性を満たすとは,tを無限回、簡約し続けることができないということである。 λ計算は、その重要な要素として関数抽象の機構を持っているため、いろいろな関数を容易に表現することができるが、その反面、1階述語論理の枠組でλ計算の項をそのまま扱うことはできない。これに対して、技術的により扱いやすい1階述語論理の項の形で、関数抽象の機能を巧みに代用できるよう工夫された変換系として、Schoenfinkelが組合せ論理を1930年台に考案している。従来までの研究により、λ計算・組合せ論理に特有な符号を保存・反映するような、λ計算の項から組合せ論理の項への対等が知られていた。 本研究で新しく得られた対応は、加えて、新たに、項の強正正規化をも保存・反映する。この結果は、λ項にεoまでの順序数を対応させることによってその強正規性導くHowardの議論を子細に検討した結果得られたもので、これによってλ項、CL項、及び順序数の間に、これまでより見通しの良い関係が確立されたことになる。また、強正規な組合せ論理の項全体から導かれる部分組合せ代数と、強正規なλ項全体から導かれる部分組合せ代数との関係を調べた。後者は、表現力が極めて豊かな型理論の無矛盾性を証明するのに使われるものであり、われわれの結果により、前者もその目的に使えることが言える。

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Social Activities 7

  1. 国際科学技術財団 日本国際賞推薦人

    2010/04 - Present

  2. 仙台数学セミナー(川井数理科学財団)

    2015/08/16 - 2015/08/18

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    「球面と多面体 – オイラーの多面体定理を中心に」の講演

  3. 宮城野高校 特別講座「学問の世界」講師

    2018/05 -

  4. Mapleセミナー

    2015/05/29 -

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    Cybernetから講師を招聘して、講義および 端末室で実習を行った。

  5. Mathematica のセミナー

    2015/05/15 -

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    ウルフラムリサーチアジアリミティッドの丸山耕司氏にMathematica 10 の紹介していただきます。

  6. 東北大学１００周年記念サイエンスカフェ

    2012/03/15 -

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    数式で解く模様の対称と非対称

  7. 宮城野高校

    2002/06/01 -

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    「学問の世界」の数学講師

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Academic Activities 1

  1. 九州大学マス・フォア・インダストリ研究所 研究集会「学習理論における組合せ論」

    2012/09/18 - 2012/09/21

Other 4

  1. chemical graphのなかのpolycycleの球面幾何的研究

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    chemical graphのなかのpolycycleの球面幾何的研究

  2. 合同な５角形による球面タイリングの分類

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    タイリングの研究

  3. 「コンピュータのための数学」

  4. コンピュータサイエンス入門