## 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

- 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

- 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