Details of the Researcher

PHOTO

Dahan Xavier Gilles Messaoud
Section
Institute for Excellence in Higher Education
Job title
Associate Professor
Degree

  • 博士（情報科学）（エコール･ポリテクニーク）

  • 修士（情報科学）（パリ第六大学）

  • 修士（数学）（パリ第六大学）

Profile
Since November 2008, I joined the Global COE project "Maths for Industry" of the Maths department of Kyushu university.

My research area lies in between Mathematics and Computer Science.
"Computer algebra" or "Symbolic Computation" aims at studying with algortihms and computers the equations arising in algebraic theories,
like polynomial equations and differential/finite-difference equations.

Particularly I am working around "Polynomial System Solving". Usually,
the Groebner bases are used, but "triangular decomposition" is another promising method, in which I am contributing in term of complexity and comparision with lexicographical Groebner bases.

I also have interests in other topics lying at the frontier of Algebra
anc Computer Science, like cryptography and error-correcting codes,
but also algebraic graph theory. I plan to contribute soon in Algrbaic Graph Theory, with the construction of so-called "expander graphs", that have many important applications.

Research History 6

  • 2019/09 - Present
    Tohoku University　Institute for Excellence in Higher Education Global Learning Center　Associate Professor

  • 2014/10 - 2019/08
    Ochanomizu University　Department of Educational Research　Project Associate Professor

  • 2014/04 - 2014/09
    ISIT　Information Security Lab.　Researcher

  • 2013/04 - 2014/03
    Kyushu University (Information and System Science Department)　Computer Science　Assistant Professor

  • 2008/11 - 2013/03
    Kyushu University (Math Dept)　Global COE "Math-for-Industry" research and education center　Assistant Professor

  • 2006/11 - 2008/10
    JSPS　Rikkyo University　Post-Doc

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Education 4

  • Ecole Polytechnique　Doctoral Course　Laboratory of Computer Science LIX

    2003/09 - 2006/11

  • Ecole Polytechnique　Graduate Course (Computer Science)　Laboratory of Computer Science LIX

    2001/10 - 2003/07

  • Universite de Paris 6　Graduate Course　Graduate School of Mathematics (Algebraic Methods)

    2000/09 - 2001/09

  • Universite de Versailles　Faculty of Science　Mathematics

    1996/09 - 2000/07

Professional Memberships 2

  • JAPAN SOCIETY FOR SYMBOLIC AND ALGEBRAIC COMPUTATION

  • ACM SIGSAM

Research Interests 6

  • Symbolic Computation

  • コンピュータ代数

  • 代数的グラフ理論

  • Graph

  • Groebner bases

  • Computer Algebra

Research Areas 1

  • Natural sciences / Applied mathematics and statistics / Computer Algebra

Awards 2

  1. ISSAC 2005 best student author award

    2005/07　ACM　(Lifting techniques for triangular sets)

  2. ISSAC 2004 distinguished paper award

    2004/06　ACM　(Sharp estimates for triangular sets)

Papers 17

  1. Chinese Remainder Theorem for bivariate lexicographic Groebner bases International-journal Peer-reviewed

    Xavier Dahan

    Proceedings of the 48th International Symposium on Symbolic and Algebraic Computation, ISSAC 2023　2023/07

    Publisher: ASSOC COMPUTING MACHINERY

  2. Lexicographic Gröbner bases of bivariate polynomials modulo a univariate one International-journal Peer-reviewed

    Xavier Dahan

    Journal of Symbolic Computation　(110)　24-65　2022/05

    Publisher: ELSEVIER

    DOI： 10.1016/j.jsc.2021.10.001 　

  3. Regular graphs of large girth and arbitrary degree International-journal International-coauthorship Peer-reviewed

    Xavier Dahan

    COMBINATORICA　34　(4)　407-426　2014/08

    DOI： 10.1007/s00493-014-2897-6 　

    ISSN： 0209-9683

    eISSN： 1439-6912

  4. Bit-size estimates for triangular sets in positive dimension International-journal International-coauthorship Peer-reviewed

    Xavier Dahan, Abdulilah Kadri, Eric Schost

    JOURNAL OF COMPLEXITY　28　(1)　109-135　2012/02

    DOI： 10.1016/j.jco.2011.05.001 　

    ISSN： 0885-064X

  5. Lifting techniques for triangular decompositions International-journal International-coauthorship Peer-reviewed

    Xavier Dahan, Marc Moreno Maza, Eric Schost, Wenyuan Wu, Yuzhen Xie

    Proceedings of the 30th International Symposium on Symbolic and Algebraic Computation, ISSAC 2005　108-115　2005/07

    Publisher: ASSOC COMPUTING MACHINERY

  6. Sharp estimates for triangular sets International-journal International-coauthorship Peer-reviewed

    Xavier Dahan, Eric Schost

    Proceedings of the 29th International Symposium on Symbolic and Algebraic Computation, ISSAC 2004　103-110　2004/07

    Publisher: ASSOC COMPUTING MACHINERY

  7. The effects of coating culture dishes with collagen on fibroblast cell shape and swirling pattern formation International-journal International-coauthorship Peer-reviewed

    Kei Hashimoto, Kimiko Yamashita, Kanako Enoyoshi, Xavier Dahan, Tatsu Takeuchi, Hiroshi Kori, Mari Gotoh

    Journal of Biological Physics　46　(46)　351-369　2020/08

    Publisher: SPRINGER

    DOI： 10.1007/s10867-020-09556-3 　

    ISSN： 0092-0606

    eISSN： 1573-0689

    More details Close

    <title>Abstract</title>Motile human-skin fibroblasts form macroscopic swirling patterns when grown to confluence on a culture dish. In this paper, we investigate the effect of coating the culture-dish surface with collagen on the resulting pattern, using human-skin fibroblast NB1RGB cells as the model system. The presence of the collagen coating is expected to enhance the adherence of the fibroblasts to the dish surface, and thereby also enhance the traction that the fibroblasts have as they move. We find that, contrary to our initial expectation, the coating does not significantly affect the motility of the fibroblasts. Their eventual number density at confluence is also unaffected. However, the coherence length of cell orientation in the swirling pattern is diminished. We also find that the fibroblasts cultured in collagen-coated dishes are rounder in shape and shorter in perimeter, compared with those cultured in uncoated polystyrene or glass culture dishes. We hypothesise that the rounder cell-shape which weakens the cell–cell nematic contact interaction is responsible for the change in coherence length. A simple mathematical model of the migrating fibroblasts is constructed, which demonstrates that constant motility with weaker nematic interaction strength does indeed lead to the shortening of the coherence length.

  8. On a non-Archmidean Broyden method International-journal International-coauthorship Peer-reviewed

    Xavier Dahan, Tristan Vacon

    Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation, ISSAC 2020　2020　114-121　2020/07

    Publisher: ASSOC COMPUTING MACHINERY

    DOI： 10.145/3373207.3404045 　

    More details Close

    Newton’s method is an ubiquitous tool to solve eqs, both in the archimedean and non-archimedean settings — for which it does not really differ. Broyden was the instigator of what is called “quasi- Newton methods”. These methods use an iteration step where one does not need to compute a complete Jacobian matrix nor its inverse. We provide an adaptation of Broyden’s method in a general non- archimedean setting, compatible with the lack of inner product, and study its Q and R convergence. We prove that our adapted method converges at least Q-linearly and R-superlinearly with R-order 2^(1/2𝑚) in dimension 𝑚. Numerical data are provided.

  9. On the bit-size of non-radical triangular sets International-journal Peer-reviewed

    Xavier Dahan

    Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)　10693　(10693)　264-269　2017/11

    Publisher: Springer Verlag

    DOI： 10.1007/978-3-319-72453-9_19 　

    ISSN： 1611-3349 0302-9743

  10. Gcd modulo a primary triangular set of dimension zero International-journal Peer-reviewed

    Xavier Dahan

    Proceedings of the 42th International Symposium on Symbolic and Algebraic Computation, ISSAC 2017　42　109-116　2017/07

    Publisher: ASSOC COMPUTING MACHINERY

    DOI： 10.1145/3087604.3087612 　

  11. Bit-size reduction of triangular sets in two and three variables. International-journal Peer-reviewed

    Tetsuro Yamashita, Xavier Dahan

    7th International Symposium on Symbolic Computation in Software Science, SCSS 2016, Tokyo, Japan, March 28-31, 2016　7　169-182　2016/03

    Publisher: EasyChair

  12. Computation of eigenvalues of Cayley graphs and application International-journal Peer-reviewed

    Dahan Xavier

    Proceedings of WAAC'2013　97-103　2013

  13. Evaluation properties of invariant polynomials International-journal International-coauthorship Peer-reviewed

    Xavier Dahan, Eric Schost, Jie Wu

    JOURNAL OF SYMBOLIC COMPUTATION　44　(11)　1592-1604　2009/11

    DOI： 10.1016/j.jsc.2008.12.002test 　

    ISSN： 0747-7171

  14. Size of Coefficients of Lexicographical Grobner Bases [The zero-dimensional, radical and bivariate case] International-journal Peer-reviewed

    Xavier Dahan

    PROCEEDINGS OF THE 34th INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION, ISSAC 2009　34　119-126　2009/07

    DOI： 10.1145/1576702.1576721 　

  15. Change of order for regular chains in positive dimension International-journal International-coauthorship Peer-reviewed

    Xavier Dahan, Xin Jin, Marc Moreno Maza, Eric Schost

    THEORETICAL COMPUTER SCIENCE　392　(1-3)　37-65　2008/02

    DOI： 10.1016/j.tcs.2007.10.003 　

    ISSN： 0304-3975

    eISSN： 1879-2294

  16. Complexity of polynomial systems representations: triangulation, modular methods, dynamic evaluation. International-journal

    Xavier Dahan

    Ecole Polytechnique, France　2006/11

  17. On the complexity of the D5 principle. International-journal International-coauthorship

    Xavier Dahan, Éric Schost, Marc Moreno Maza, Wenyuan Wu, Yuzhen Xie

    ACM SIGSAM Bulletin　39　(3)　97-98　2006/04

    Publisher: ASSOC COMPUTING MACHINERY

    DOI： 10.1016/j.jsc.2008.12.002 　

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Misc. 5

  1. A multivariate quadratic challenge toward post-quantum generation cryptography

    Takanori Yasuda, Xavier Dahan, Yun-Ju Huang, Tsuyoshi Takagi, Kouichi Sakurai

    ACM Communications in Computer Algebra　49　(3)　105-107　2015/09/01

    Publisher: Association for Computing Machinery

    DOI： 10.1145/2850449.2850462 　

    ISSN： 1932-2240 1932-2232

  2. Characterizing NTRU-Variants Using Group Ring and Evaluating their Lattice Security.

    Takanori Yasuda, Xavier Dahan, Kouichi Sakurai

    IACR Cryptology ePrint Archive　1170　2015

  3. MQ Challenge: Hardness Evaluation of Solving Multivariate Quadratic Problems.

    Takanori Yasuda, Xavier Dahan, Yun-Ju Huang, Tsuyoshi Takagi, Kouichi Sakurai

    IACR Cryptology ePrint Archive　2015　275　2015

  4. New constructions of graphs with large girth obtained from "classical" ones (Research into Finite Groups and their Representations, Vertex Operator Algebras, and Combinatorics)

    Dahan Xavier

    RIMS Kokyuroku　1811　130-134　2012/10

    Publisher: Kyoto University

    ISSN： 1880-2818

  5. On bit-size estimates of triangular systems (Developments in Computer Algebra Research)

    Dahan Xavier

    RIMS Kokyuroku　1759　26-42　2011/09

    Publisher: Kyoto University

    ISSN： 1880-2818

Presentations 6

  1. Lexicographic Groebner bases of bivariate polynomials modulo a univariate one Invited

    Computer Algebra seminar of Limoges University (online)　2021/12/09

  2. On a non-Archimedean Broyden Method

    International Symposium On Symbolic and Algebraic Computations 2022　2020/07/21

  3. Size of coefficients of lexicographical Groebner bases International-presentation

    Xavier Dahan

    ISSAC 2009　2009/07

  4. On the complexity of the D5 principle International-presentation

    Xavier Dahan, Marc Moreno Maza, Eric Schost, Yuzhen Xie

    Trangressive Computing 2006　2006/04

  5. Lifting techniques for triangular decompositions International-presentation

    Xavier Dahan, Marc Moreno Maza, Eric Schost, Wenyuan Wu, Yuzhen Xie

    ISSAC 2005　2005/07

  6. Sharp estimates for triangular sets International-presentation

    Xavier Dahan, Eric Schost

    ISSAC 2004　2004/07

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Teaching Experience 33

  1. Basics of Information Science B　Tohoku University Undergraduate (specialized)

  2. Foundations of Calculus　Tohoku University Undergraduate (specialized)

  3. Calculus C　Tohoku University Undergraduate (specialized)

  4. Calculus A　Tohoku University Undergraduate (specialized)

  5. Basics of Information Science B　Tohoku University Undergraduate (specialized)

  6. Calculus B　Tohoku University Undergraduate (specialized)

  7. Foundations of Calculus　Tohoku University Undergraduate (specialized)

  8. Calculus C　Tohoku University Undergraduate (specialized)

  9. Calculus A　Tohoku University Undergraduate (specialized)

  10. Calculus B　Tohoku University Undergraduate (specialized)

  11. Foundations of Calculus　Tohoku University Undergraduate (specialized)

  12. Calculus A　Tohoku University Undergraduate (specialized)

  13. Calculus C　Tohoku University Undergraduate (specialized)

  14. Introduction to Statistics　Ochanomizu Women’s University Graduate (liberal arts)

  15. Introduction to Numercal Methods with Python　Ochanomizu Women’s University Undergraduate (specialized)

  16. Introduction to Statistics　Ochanomizu Women’s University Graduate (liberal arts)

  17. Introduction to Numercal Methods　Ochanomizu Women’s University Undergraduate (specialized)

  18. Introduction to Statistics　Ochanomizu Women’s University Graduate (liberal arts)

  19. Essential Calculus II　Ochanomizu Women’s University Graduate (liberal arts)

  20. Essential Calculus II　Ochanomizu Women’s University Graduate (liberal arts)

  21. Introduction to Statistics　Ochanomizu Women’s University Graduate (liberal arts)

  22. Essential Calculus I　Ochanomizu Women’s University Graduate (liberal arts)

  23. Information Security and Cryptography (co-teacher)　Kyushu University Graduate (liberal arts)

  24. Essential Calculus I　Ochanomizu Women’s University Graduate (liberal arts)

  25. Information Security and Cryptography (co-teacher)　Kyushu University Graduate (liberal arts)

  26. Algebra III, Exercises　Kyushu University Undergraduate (specialized)

  27. Comp. Math.　Kyushu University Graduate (liberal arts)

  28. Comp. Math.　Kyushu University Graduate (liberal arts)

  29. Algorithms and Programming (Practice Classes)　Ecole Polytechnique Undergraduate (specialized)

  30. Fundamentals of Computer Science (Practice Classes)　Ecole Polytechnique Undergraduate (specialized)

  31. Introduction to Computer Science (Practice Classes)　Ecole Polytechnique Undergraduate (specialized)

  32. Algorithms and Programming (Practice Classes)　Ecole Polytechnique Undergraduate (specialized)

  33. Introduction to Computer Science (Practice Classes)　Ecole Polytechnique Undergraduate (specialized)

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