Makoto Matsumoto
Last Updated :2023/01/05
- Affiliations, Positions
- Graduate School of Advanced Science and Engineering, Professor
- E-mail
- mmat
hiroshima-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 : 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
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
- 2022, Undergraduate Education, 1Term, Algebra C
- 2022, Undergraduate Education, First Semester, Special Study of Mathematics and Informatics for Graduation
- 2022, Undergraduate Education, Second Semester, Special Study of Mathematics and Informatics for Graduation
- 2022, Graduate Education (Master's Program) , 2Term, Mathematical Omnibus
- 2022, Graduate Education (Master's Program) , Academic Year, Algebra Seminar II
- 2022, Graduate Education (Master's Program) , Academic Year, Algebra Seminar II
- 2022, Graduate Education (Master's Program) , 1Term, Algebra A
- 2022, Graduate Education (Master's Program) , Academic Year, Exercises in Mathematics
- 2022, Graduate Education (Master's Program) , First Semester, Exercises in Mathematics A
- 2022, Graduate Education (Master's Program) , Second Semester, Exercises in Mathematics B
- 2022, Graduate Education (Master's Program) , Academic Year, Seminar in Mathematics
- 2022, Graduate Education (Doctoral Program) , Academic Year, Seminar in Mathematics
Research Activities
Academic Papers
- The line digraph of a regular and pancircular digraph is also regular and pancircular, Graphs and Combinatorics, 4(3), 235-239, 19880401
- Mapping-Class-group action versus Galois action on profinite, American Journal of Mathematics, 122, 1017-1026, 20000401
- Galois representations on profinite braid groups on curves, Journal f\, 474(0), 169-219, 19960101
- A presentation of mapping class groups in terms of Artin groups and geometric monodromy of singularities, Mathematische Annalen, 316(0), 401-418, 20000101
- A generalization of the Katona Theorem for cross $t$-intersecting, Graphs and Combinatorics, 5, 159-171, 19890401
- Bounds for the vertex linear arboricity, Journal of Graph Theory, 14, 117-126, 19900401
- `Primitive $t$-nomial ($t=3,5$) over GF(2) whose degree is a Mersenne exponent, Applied Mathematics and Computation, 56, 817-821, 19910401
- Twisted GFSR Generators, ACM Transactions on Modeling and Computer Simulations, 2, 179-194, 19920401
- Local monodromy on the fundamental groups of algebraic curves along a degenerate stable curve, Journal of Pure and Applied Algebra, 103, 235-283, 19950401
- Minimum shadows in uniform hypergraphs and a generalization of the Takagi function, Journal of Combinatorial Theory Ser.A, 68, 125-148, 19940401
- Twisted GFSR Generators II, ACM Transactions on Modeling and Computer Simulations, 4, 254-266, 19940401
- On the Galois image in the derivation algebra of $\pi_1$ of the projective line minus three points, Contemporary Mathematics, 186, 201-213, 19950401
- On Galois actions on profinite completion of braid groups, Contemporary Mathematics, 186, 173-200, 19950401
- Association schemes related with type II matrices and spin models, Journal of Algebraic Combinatorics, 8, 39-72, 19980401
- Strong Deviations from Randomness in $m$-sequences based on Trinomials, ACM Transactions on Modeling and Computer Simulations, 6, 99-106, 19960401
- 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
- An Application of Finite Projective Space to Replicated Data Management, 15, 87-91, 20000401
- Simple cellular automata as pseudorandom $m$-sequence, ACM Transactions on Modeling and Computer Simulations, 8, 31-42, 19980401
- Is there a circle that passes through a given number of lattice points?, European Journal of Combinatorics, 19, 591-592, 19980401
- A note on difference sets, Journal of Combinatorial Theory Ser.A, 84, 133-144, 19980401
- New primitive $t$-nomials $(t=3,5)$ over $GF(2)$ whose degree is a Mersenne exponent, Mathematics of Computation, 69, 811-814, 19990401
- Combinatorial Dehn Twists, Advances in Mathematical Sciences and Applications, Special, 137-198, 19990401
- Dynamic Creation of Pseudorandom number generator, Monte Carlo and Quasi-Monte Carlo Methods, 56-69, 20000401
- Getting Rid of Correlations among Pseudorandom Number, ACM Transactions on Modeling and Computer Simulations, 9, 282-294, 19990401
- A Nonempirical Test on the Weight of Pseudorandom Number Generators, Monte Carlo and Quasi-Monte Carlo Methods, 381-395, 20020401
- Sum-discrepancy test on pseudorandom number generators, Mathematics and Computers in Simulation, 62, 431-442, 20030401
- Mersenne Twister; a 623-dimensionally equidistributed uniform pseudorandom number generator, ACM Transactions on Modeling and Computer Simulations, 8, 3-30, 19980401
- Getting Rid of Correlations among Pseudorandom Numbers; Discarding versus Tempering, ACM Transactions on Modeling and Computer Simulations, 9, 282-294, 19990401
- 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
- Tannakian fundamental groups associated to Galois groups, MSRI Publications, 41, 183-216, 20030401
- Weight discrepancy tests on M-sequences, Bulltin of Yamagata University (Natural Science), Vol. 16, No.3, 2007, 105--112., 20070401
- 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
- Common Defects in Initialization of Pseudorandom Number Generators, 20070401
- 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
- A Fast Stream Cipher with Huge State Space and Quasigroup Filter for Software, 20070401
- Improved Long-Period Generators Based on Linear Reccurences Modulo 2, ACM Transactions on Mathematical Software, 32, 1-16, 20060301
- SIMD-oriented Fast Mersenne Twister: a 128-bit Pseudorandom Number Generator, Monte Carlo and Quasi-Monte Carlo Methods 2006, 607-622, 20080101
- A PRNG Specialized in Double Precision Floating Number Using an Affine Transition, Monte Carlo and Quasi-Monte Carlo Methods 2008, 589, 20091201
- Sum-discrepancy test on pseudorandom number generators, MATHEMATICS AND COMPUTERS IN SIMULATION, 62(3-6), 431-442, 20030303
- 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
- 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
- Improved long-period generators based on linear recurrences modulo 2, ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 32(1), 1-16, 200603
- Pseudorandom number generation: Impossibility and compromise, JOURNAL OF UNIVERSAL COMPUTER SCIENCE, 12(6), 672-690, 2006
- Common defects in initialization of pseudorandom number generators, ACM TRANSACTIONS ON MODELING AND COMPUTER SIMULATION, 17(4), 2007
- Error correcting sequence and projective de Bruijn graph, GRAPHS AND COMBINATORICS, 24(3), 185-194, 200806
- Efficient jump ahead for F(2)-linear random number generators, INFORMS JOURNAL ON COMPUTING, 20(3), 385-390, 2008
- Relative pro-l completions of mapping class groups, JOURNAL OF ALGEBRA, 321(11), 3335-3374, 20090601
- 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
- A COMPUTABLE FIGURE OF MERIT FOR QUASI-MONTE CARLO POINT SETS, MATHEMATICS OF COMPUTATION, 83(287), 1233-1250, 201405
- 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
- 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
- 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
- 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
- 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
- UNIVERSAL MIXED ELLIPTIC MOTIVES, JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU, 19(3), 663-766, 202005
- Non-existence and construction of pre-difference sets, and equi-distributed subsets in association schemes, Graphs and Combinatorics
- A Generator of H^1(M^1_g;H^1(?_g;Z)) and a Reflection Representation of the Mapping Class Groups via Iwahori-Hecke Algebras, Progress of theoretical physics. Supplement, 141-144, 20020329
- Unveiling patterns in xorshift128+pseudorandom number generators, JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 402, 20220301
Invited Lecture, Oral Presentation, Poster Presentation
- 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
- 1999/03, Kirkman Medal, Institute of Combinatorics and Its Applications, Combinatorics
Patented
- Patent, JP4682320, 2011/02/18
- Patent, JP4724835, 2011/04/22
- Patent, JP4774509, 2011/07/08
- Patent, JP5207153, 2013/03/01
- Patent, JP5268010, 2013/05/17
- Patent, JP5268011, 2013/05/17
- Patent, US:8553880, 2013/10/08
- Patent, JP5403507, 2013/11/08
External Funds
Acceptance Results of Competitive Funds
- KAKENHI(Grant-in-Aid for Scientific Research (C)), 2018, 2022
Social Activities
History as Peer Reviews of Academic Papers
- 2020, Hiroshima Mathematical Journal, Chief editor, 20
- 2017, ACM Transaction on Modeling and Computer Simulation, Editor, Associate Editor, 3
- 2016, ACM Transactions on Modeling and Computer Simulation, Editor, Associate Editor, 3
- 2016, Hiroshima Mathematical Journal, Editor, Editor, 2
- 2017, Hiroshima Mathematical Journal, Editor, Editor, 2
- 2017, Hiroshima Mathematical Journal, Editor, 2
- 2018, Hiroshima Mathematical Journal, Editor, 3
- 2018, ACM Transaction on Modeling and Computer Simulation, Editor, 3