Makoto Matsumoto

Last Updated :2021/04/06

Affiliations, Positions
Graduate School of Advanced Science and Engineering, Professor
E-mail
mmathiroshima-u.ac.jp
Other Contact Details
1-3-1,Kagamiyama,Higashi-Hiroshima, Japan
TEL : (+81)82-424-7348 FAX : (+81)82-424-0710
Self-introduction
Pure math and its practical applications. In many fields, "random numbers" are core in the algorithm. We designed "Mersenne Twister", which is an algorithm generating almost random numbers quickly. Its design is based on pure algebra. The algorithm is now used world wide.

Basic Information

Academic Degrees

  • Ph.D., Kyoto University
  • Master of Science, The University of Tokyo
  • Doctor of Engineering, The University of Tokyo

Educational Activity

  • 【Bachelor Degree Program】School of Science : Mathematics
  • 【Master's Program】Graduate School of Advanced Science and Engineering : Division of Advanced Science and Engineering : Mathematics Program
  • 【Doctoral Program】Graduate School of Advanced Science and Engineering : Division of Advanced Science and Engineering : Mathematics Program

In Charge of Primary Major Programs

  • Mathematics

Research Fields

  • Mathematical and physical sciences;Mathematics;Foundations of mathematics / Applied mathematics

Research Keywords

  • random numbers
  • fundamental group

Affiliated Academic Societies

  • Japan Mathematical Society, 1987

Educational Activity

Course in Charge

  1. 2021, Undergraduate Education, 3Term, AlgebraII
  2. 2021, Undergraduate Education, 3Term, Exercises in Algebra II
  3. 2021, Undergraduate Education, First Semester, Special Study of Mathematics and Informatics for Graduation
  4. 2021, Undergraduate Education, Second Semester, Special Study of Mathematics and Informatics for Graduation
  5. 2021, Undergraduate Education, 4Term, Network and Algebra
  6. 2021, Graduate Education (Master's Program) , First Semester, Seminar in Mathematics
  7. 2021, Graduate Education (Master's Program) , Second Semester, Seminar in Mathematics
  8. 2021, Graduate Education (Master's Program) , First Semester, Exercises in Mathematics
  9. 2021, Graduate Education (Master's Program) , Second Semester, Exercises in Mathematics
  10. 2021, Graduate Education (Master's Program) , First Semester, Seminar of Algebra II
  11. 2021, Graduate Education (Master's Program) , Second Semester, Seminar of Algebra II
  12. 2021, Graduate Education (Doctoral Program) , First Semester, Seminar in Mathematics
  13. 2021, Graduate Education (Doctoral Program) , Second Semester, Seminar in Mathematics
  14. 2021, Graduate Education (Master's Program) , Academic Year, Algebra Seminar II
  15. 2021, Graduate Education (Master's Program) , Academic Year, Algebra Seminar II
  16. 2021, Graduate Education (Master's Program) , 4Term, Topics in Algebra B
  17. 2021, Graduate Education (Master's Program) , Academic Year, Exercises in Mathematics
  18. 2021, Graduate Education (Master's Program) , First Semester, Exercises in Mathematics A
  19. 2021, Graduate Education (Master's Program) , Second Semester, Exercises in Mathematics B
  20. 2021, Graduate Education (Master's Program) , Academic Year, Seminar in Mathematics
  21. 2021, Graduate Education (Doctoral Program) , Academic Year, Seminar in Mathematics

Research Activities

Academic Papers

  1. Walsh Figure of Merit for Digital Nets: An Easy Measure for Higher Order Convergent QMC, Monte Carlo and Quasi-Monte Carlo Methods, Volume 163 of the series Springer Proceedings in Mathematics, 163, 143-160, 2016
  2. A COMPUTABLE FIGURE OF MERIT FOR QUASI-MONTE CARLO POINT SETS, MATHEMATICS OF COMPUTATION, 83(287), 1233-1250, 201405
  3. ON THE FAST COMPUTATION OF THE WEIGHT ENUMERATOR POLYNOMIAL AND THE t VALUE OF DIGITAL NETS OVER FINITE ABELIAN GROUPS, SIAM JOURNAL ON DISCRETE MATHEMATICS, 27(3), 1335-1359, 2013
  4. A PRNG Specialized in Double Precision Floating Number Using an Affine Transition, Monte Carlo and Quasi-Monte Carlo Methods 2008, 589, 20091201
  5. Relative pro-l completions of mapping class groups, JOURNAL OF ALGEBRA, 321(11), 3335-3374, 20090601
  6. SIMD-oriented Fast Mersenne Twister: a 128-bit Pseudorandom Number Generator, Monte Carlo and Quasi-Monte Carlo Methods 2006, 607-622, 20080101
  7. Error correcting sequence and projective de Bruijn graph, GRAPHS AND COMBINATORICS, 24(3), 185-194, 200806
  8. Efficient jump ahead for F(2)-linear random number generators, INFORMS JOURNAL ON COMPUTING, 20(3), 385-390, 2008
  9. Weight discrepancy tests on M-sequences, Bulltin of Yamagata University (Natural Science), Vol. 16, No.3, 2007, 105--112., 20070401
  10. Computing conditional probabilities for F2-linear pseudorandom bit generator by splitting Mac-Williams identity, International Journal of Pure and Applied Mathematics, Vol.38 No.1, 2007, 20070401
  11. Common Defects in Initialization of Pseudorandom Number Generators, 20070401
  12. SIMD-oriented Fast Mersenne Twister: A 128-bit Pseudorandom Number Generator, Monte Carlo and Quasi-monte Carlo Methods 2006, pp. 617--632, Springer-Verlag, 2007., 20070401
  13. A Fast Stream Cipher with Huge State Space and Quasigroup Filter for Software, 20070401
  14. A Fast Stream Cipher with Huge State Space and Quasigroup Filter for Software, Selected Areas in Cryptography 2007, 246-263, 20071201
  15. Common defects in initialization of pseudorandom number generators, ACM TRANSACTIONS ON MODELING AND COMPUTER SIMULATION, 17(4), 2007
  16. Improved Long-Period Generators Based on Linear Reccurences Modulo 2, ACM Transactions on Mathematical Software, 32, 1-16, 20060301
  17. Pseudorandom Number Generation: Impossibility and Compromise, Journal of Universal Computer Science, 12(6), 672-690, 20060401
  18. Improved long-period generators based on linear recurrences modulo 2, ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 32(1), 1-16, 200603
  19. Pseudorandom number generation: Impossibility and compromise, JOURNAL OF UNIVERSAL COMPUTER SCIENCE, 12(6), 672-690, 2006
  20. Galois actions on fundamental groups of curves and the cycle C-C', Journal of the Inst. Math. Jussieu, 4, 363-403, 20050401
  21. Galois actions on fundamental groups of curves and the cycle C-C-, JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU, 4(3), 363-403, 200507
  22. Sum-discrepancy test on pseudorandom number generators, Mathematics and Computers in Simulation, 62, 431-442, 20030401
  23. Weighted completion of Galois groups and Galois actions on the fundamental group of $P^1-\{0,1,\infty\}$, Compositio Mathematica, 139(2), 119-167, 20030401
  24. Tannakian fundamental groups associated to Galois groups, MSRI Publications, 41, 183-216, 20030401
  25. Sum-discrepancy test on pseudorandom number generators, MATHEMATICS AND COMPUTERS IN SIMULATION, 62(3-6), 431-442, 20030303
  26. Weighted completion of Galois groups and Galois actions on the fundamental group of P-1-{0, 1, infinity}, COMPOSITIO MATHEMATICA, 139(2), 119-167, 200311
  27. A Nonempirical Test on the Weight of Pseudorandom Number Generators, Monte Carlo and Quasi-Monte Carlo Methods, 381-395, 20020401
  28. Mapping-Class-group action versus Galois action on profinite, American Journal of Mathematics, 122, 1017-1026, 20000401
  29. A presentation of mapping class groups in terms of Artin groups and geometric monodromy of singularities, Mathematische Annalen, 316(0), 401-418, 20000101
  30. An Application of Finite Projective Space to Replicated Data Management, 15, 87-91, 20000401
  31. Dynamic Creation of Pseudorandom number generator, Monte Carlo and Quasi-Monte Carlo Methods, 56-69, 20000401
  32. New primitive $t$-nomials $(t=3,5)$ over $GF(2)$ whose degree is a Mersenne exponent, Mathematics of Computation, 69, 811-814, 19990401
  33. Combinatorial Dehn Twists, Advances in Mathematical Sciences and Applications, Special, 137-198, 19990401
  34. Getting Rid of Correlations among Pseudorandom Number, ACM Transactions on Modeling and Computer Simulations, 9, 282-294, 19990401
  35. Getting Rid of Correlations among Pseudorandom Numbers; Discarding versus Tempering, ACM Transactions on Modeling and Computer Simulations, 9, 282-294, 19990401
  36. Association schemes related with type II matrices and spin models, Journal of Algebraic Combinatorics, 8, 39-72, 19980401
  37. Simple cellular automata as pseudorandom $m$-sequence, ACM Transactions on Modeling and Computer Simulations, 8, 31-42, 19980401
  38. Is there a circle that passes through a given number of lattice points?, European Journal of Combinatorics, 19, 591-592, 19980401
  39. A note on difference sets, Journal of Combinatorial Theory Ser.A, 84, 133-144, 19980401
  40. Mersenne Twister; a 623-dimensionally equidistributed uniform pseudorandom number generator, ACM Transactions on Modeling and Computer Simulations, 8, 3-30, 19980401
  41. Galois group $\mbox {\rm G}_{\bf Q}$, Singularity $E_7$, and Moduli ${\cal M}_3$, London Mathematical Society Lecture Note Series, 2;;;;43, 179-218, 19970401
  42. Galois representations on profinite braid groups on curves, Journal f\, 474(0), 169-219, 19960101
  43. Strong Deviations from Randomness in $m$-sequences based on Trinomials, ACM Transactions on Modeling and Computer Simulations, 6, 99-106, 19960401
  44. Local monodromy on the fundamental groups of algebraic curves along a degenerate stable curve, Journal of Pure and Applied Algebra, 103, 235-283, 19950401
  45. On the Galois image in the derivation algebra of $\pi_1$ of the projective line minus three points, Contemporary Mathematics, 186, 201-213, 19950401
  46. On Galois actions on profinite completion of braid groups, Contemporary Mathematics, 186, 173-200, 19950401
  47. Minimum shadows in uniform hypergraphs and a generalization of the Takagi function, Journal of Combinatorial Theory Ser.A, 68, 125-148, 19940401
  48. Twisted GFSR Generators II, ACM Transactions on Modeling and Computer Simulations, 4, 254-266, 19940401
  49. Twisted GFSR Generators, ACM Transactions on Modeling and Computer Simulations, 2, 179-194, 19920401
  50. `Primitive $t$-nomial ($t=3,5$) over GF(2) whose degree is a Mersenne exponent, Applied Mathematics and Computation, 56, 817-821, 19910401
  51. Bounds for the vertex linear arboricity, Journal of Graph Theory, 14, 117-126, 19900401
  52. A generalization of the Katona Theorem for cross $t$-intersecting, Graphs and Combinatorics, 5, 159-171, 19890401
  53. The line digraph of a regular and pancircular digraph is also regular and pancircular, Graphs and Combinatorics, 4(3), 235-239, 19880401
  54. Approximation of Quasi-Monte Carlo worst case error in weighted spaces of infinitely times smooth functions, JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 330, 155-164, 20180301
  55. Characterization of matrices B such that (I, B, B-2) generates a digital net with t-value zero, FINITE FIELDS AND THEIR APPLICATIONS, 52, 289-300, 201807
  56. A Method to Compute an Appropriate Sample Size of the Two-Level Test for NIST Test Suite, Monte Carlo and Quasi-Monte Carlo Methods 2016, 283-294, 2018
  57. Universal mixed elliptic motives, Journal of the Institute of Mathematics of Jussieu, 1-104, 20180430
  58. Checking the quality of approximation of p-values in statistical tests for random number generators by using a three-level test, MATHEMATICS AND COMPUTERS IN SIMULATION, 161, 66-75, 201907

Invited Lecture, Oral Presentation, Poster Presentation

  1. Experimental Comparison of Higher-Order Digital Nets for QMC, Makoto Matsumoto, Makoto Matsumoto, Shinsuke Mori, Mutsuo Saito, 13th International Conference in Monte Carlo & Quasi-Monte Carlo Methods in Scientific Computing,, 2018/07/06, Without Invitation, English, MCQMC organizing committee, Renne, France

Awards

  1. 1999/03, Kirkman Medal, Institute of Combinatorics and Its Applications, Combinatorics

Patented

  1. Patent, JP4682320, 2011/02/18
  2. Patent, JP4724835, 2011/04/22
  3. Patent, JP4774509, 2011/07/08
  4. Patent, JP5207153, 2013/03/01
  5. Patent, JP5268010, 2013/05/17
  6. Patent, JP5268011, 2013/05/17
  7. Patent, US:8553880, 2013/10/08
  8. Patent, JP5403507, 2013/11/08

External Funds

Acceptance Results of Competitive Funds

  1. KAKENHI(Grant-in-Aid for Scientific Research (C)), 2018, 2022

Social Activities

History as Peer Reviews of Academic Papers

  1. 2020, Hiroshima Mathematical Journal, Chief editor, 20
  2. 2017, ACM Transaction on Modeling and Computer Simulation, Editor, Associate Editor, 3
  3. 2016, ACM Transactions on Modeling and Computer Simulation, Editor, Associate Editor, 3
  4. 2016, Hiroshima Mathematical Journal, Editor, Editor, 2
  5. 2017, Hiroshima Mathematical Journal, Editor, Editor, 2
  6. 2017, Hiroshima Mathematical Journal, Editor, 2
  7. 2018, Hiroshima Mathematical Journal, Editor, 3
  8. 2018, ACM Transaction on Modeling and Computer Simulation, Editor, 3