Computer Programs
- DeltaViewer, 3-dimensional
image processing program for biology, medicine and physiology.
- OPTi visualizes quasi-conformal
deformations of the once-punctured-torus groups. It interactively
shows the isometric circles, the Ford region, the limit set, etc.
Papers
- H. Akiyama, M. Wada, M. Nakayama, A. Kato, H. Sunahara, Minimizing Information Loss in Anonymization Algorithms (in Japanese), IPSJ Journal 57 (2016), 2675-2681.
- N. Katagiri, Y. Katagiri, M. Wada, D. Okano, Y. Shigematsu, T. Yoshioka,
Three-dimensional reconstruction of the axon extending from the dermal
photoreceptor cell in the extraocular photoreception system of a marine
gastropod, Onchidium, Zoological Science 31(12) (2014) 810-819.
- T. Kitano, M. Suzuki, M. Wada, Erratum to the article Twisted Alexander
polynomials and surjectivity of a group homomorphism, Algebraic & Geometric
Topology 11 (2011) 2937-2939.
- S. Yamada, H. Itoh, C. Uwabe, S. Fujihara, C. Nishibori, M. Wada,
S. Fujii, K. Shiota, Computerized three-dimensional analysis of the
heart and great vessels in normal and holoprosencephalic human embryos,
Anatomical Record, 290(3) (2007), 259-267.
- M. Wada, OPTi's Algorithm for Discreteness Determination, Experimental
Mathematics, Vol.15 (2006), 61-66.
- Y. Komori, T. Sugawa, M. Wada, Y. Yamashita, Drawing Bers Embeddings
of the Teichmuller Space of Once-Punctured Tori, Experimental Mathematics,
Vol. 15 (2006), 51-60.
- T. Kitano, M. Suzuki, M. Wada, Twisted Alexander polynomials and
surjectivity of a group homomorphism, Algebraic & Geometric Topology,
Vol. 5 (2005), 1315-1324.
- N. Katagiri, Y. Shigematsu, A. Horii, M. Wada, Y. Katagiri, Three-dimensional
Reconstruction from Serial Sections of a Unique Lymnaea Eye
using DeltaViewer, Proceedings of the 8th Asia-Pacific Conference on
Electron Microscopy, Kanazawa (2004), 865-866.
- M. Wada: OPTi's Algorithm for Drawing the Limit Set, Interdisciplinary
Information Sciences, Vol. 9 (2003), 183-187.
- H. Akiyoshi, M. Sakuma, M. Wada and Y. Yamashita: Jorgensen's picture
of punctured torus groups and its refinement, Kleinian Groups and Hyperbolic
3-Manifolds, Lond. Math. Soc. Lec. Notes 299, Cambridge Univ. Press,
2003, pp. 247-273.
- H. Akiyoshi, M. Sakuma, M. Wada and Y. Yamashita: A way from punctured
torus groups to two-bridge knot groups, Geometry and Topology, Proceeding
of Workshop in Pure Mathematics, Vol. 19, Pure Mathematics Research
Association, The Korean Academic Council, 2000, pp. 145-173.
- O. Kobayashi and M. Wada: Circular geometry and the Schwarzian,
Far East J. Math. Sci., Special Volume (2000), Part III (Geometry and
Topology), 335-363.
- M. Wada and O. Kobayashi: The Schwarzian and Möbius transformations
in higher dimensions, Clifford Algebras and their Applications in Mathematical
Physics, Vol. 2 "Clifford Analysis", 2000, pp. 239-246.
- M. Wada: A generalization of the Schwarzian via Clifford numbers,
Ann. Acad. Sci. Fenn., Vol. 23 (1998) 453-460.
- M. Wada: Parabolic representations of the groups of mutant knots,
J. Knot Theory and its Ramifications, Vol. 6 (1997) No. 6, 895-905.
- M. Wada, Y. Yamashita and H. Yoshida: An inequality for polyhedra
and ideal triangulations of cusped hyperbolic 3-mainfolds, Proc. A.
M. S., Vol. 124 (1996) No. 12, 3905-3911.
- M. Wada: Twisted Alexander polynomial for finitely presentable groups,
Topology, Vol. 33 (1994) No. 2, 241-256.
- C. Hayashi and M. Wada: Constructing links by plumbing flat annuli,
J. Knot Theory and its Ramifications, Vol. 2 (1993) No. 4, 427-429.
- M. Wada: Coding link diagrams, J. Knot Theory and its Ramifications,
Vol. 2 (1993) No. 2, 233-237.
- M. Wada: Group invariants of links, Topology, Vol. 31 (1992) No.
2, 399-406.
- M. Wada: Conjugacy invariants of Möbius transformations, Complex
Variables, Vol. 15 (1990), 125-133.
- M. Wada: Closed orbits of non-singular Morse-Smale flows on S3,
J. Math. Soc. Japan, Vol. 41 (1989) No. 3, 405-413.
- Ph. D. thesis: Conjugacy invariants and normal forms of isometries
of hyperbolic space, Columbia University (1986), partly appeared as "Conjugacy
invariants of Möbius transformations".
- Master thesis: Links which consist of the closed orbits of non-singular
Morse-Smale flows on 3-spheres, Osaka University (1983), appeared as "Closed
orbits of non-singular Morse-Smale flows on S3".
Books
- M. Wada: Fundamentals of Linear Algebra (in Japanese), Asakura (2009).
- H. Akiyoshi, M. Sakuma, M. Wada, Y. Yamashita: Punctured Torus Groups
and 2-Bridge Knot Groups I, Lec. Notes in Math. 1909, Springer (2007).
- Japanese translation (Ch. 1) of W. Thurston "Three-Dimensional Geometry
and Topology", Baifukan (1999).
Preprints
- M. Wada: Stable cuts for weighted graphs.
- K. Shimomura, M. Wada: An upper bound for the Hausdorff dimension of parabolic Cantor sets.
- M. Wada: From once-punctured torus to twice-punctured torus, 2004.
- M. Wada: Lifting projective linear representations of knot groups
to linear representations, 1993.
- M. Wada: Another group invariant of links, 1991.
- M. Wada: Spin representations of the braid groups and the value
of the Jones polynomial at the square root of -1, 1990.
- M. Wada: Polynomial representations of the braid groups and algebraic
variety invariants for links, 1990.
- M. Wada: Arctangent formulas for pi, 1989.
Other
- M. Wada: Chaotic itinerancy between two Lorenz attractors (Japanese) 2012.
- M. Wada: Cone deformation, RIMS Kokyuroku 1777 "Geometric and analytic approaches to representations of a group and representation spaces" (2012), 113-4.
- M. Wada: Twisted Alexander polynomial revisited, RIMS Kokyuroku 1747 "Twisted topological invariants and topology of low-dimensional manifolds" (2011), 140-144.
- M. Wada: Program for visualizing punctured torus groups – OPTi (Japanese),
Sugaku Seminar Vol. 49 no. 9 (2010) 20-23.
- M. Wada: 3D reconstruction from serial sections using DeltaViewer
(technical notes in Japanese), Comparative Physiology and Biochemistry
Vol. 24, No. 4 (2007), 160-165.
- M. Wada: Stereo reconstruction using DeltaViewer (Japanese), J. of
Japanese Assoc. of Med. Photography Vol. 43, No. 1 (2005), 4-6.
- M. Wada: Stereo reconstruction using DeltaViewer (Japanese), Proc.
of Symposium for Mathematics, Physics, Information and Computer Sciences,
Nara Women's University (2005) 61-70.
- M. Wada: Concerning OPTi a research aid for Kleinnian groups and
hyperbolic geometry (Japanese), Sugaku 55 (2003) 101-107.
- M. Wada: OPTi's algorithm for discreteness determination (Japanese),
RIMS Kokyuroku 1270 "Hyperbolic Spaces and Discrete Groups II" (2002),
67-76.
- Y. Komori, T. Sugawa, M. Wada and Y. Yamashita: Drawing Bers embeddings
of the Teichmuller space of once punctured tori, RIMS Kokyuroku 1163 "Hyperbolic
Spaces and Related Topics II" (2000), 9-17.
- H. Akiyoshi, M. Sakuma, M. Wada and Y. Yamashita: Ford domains of
punctured torus groups and two-bridge knot groups, RIMS Kokyuroku 1163 "Hyperbolic
Spaces and Related Topics II" (1998), 67-77.
- M. Wada: The Schwarzian and univalency of mappings (Japanese), RIMS
Kokyuroku 1065 "Analysis and Geometry of Hyperbolic Spaces" (1998),
44-50.
- H. Akiyoshi, M. Sakuma, M. Wada and Y. Yamashita: Punctured torus
groups and two-parabolic groups, RIMS Kokyuroku 1065 "Analysis
and Geometry of Hyperbolic Spaces" (1998), 61-73.
- M. Wada: Nervous system and the evolution (Japanese), JST Forum "Information,
from the Viewpoints of Physics, Biology, Engeneering, Cultural and
Social Sciences", 1998.
- M. Wada: Simulating the evolution of the central nervous system
(Japanese), Proceedings of the 8th Annual Conference of JNNS (1997),
166-167.
- M. Wada: A generalization of the Schwarzian via Clifford numbers
(Japanese translation), RIMS Kokyuroku 1022 "Analysis of Discrete
Groups II"
(1997), 123-130.
- M. Wada: A generalization of power series to real several dimensions,
RIMS Kokyuroku 967 "Analysis of Discrete Groups" (1996),
196-210.
- M. Wada: Representations of knot groups (Japanese), Sugaku Seminar
(1994), No. 1.
- M. Wada: On parallel information processing (Japanese), Proceeding
of Nara Women's University Information Processing Center, No. 5 (1993).
- M. Wada: He Baihe's theorem on the normal closure (Japanese), Tsuda
Topology symposium "Knot Theory and Topology of Low Dimensional
Manifolds"
(1993).
- M. Wada: Representations of knot groups (Japanese), Abstracts of
the 40th Topology symposium (1993).
- M. Wada: Twisted Alexander polynomial (Japanese), "Topological
Invariants related to Gauge Theory" (1993).
- M. Wada: Coding knot diagrams (Japanese), "Diverse Structures
of Knots and Related Topics" (1992).
Awards
- Bioimaging
Society of Japan, the Best Image Hiruma Prize 2004
"Three-dimensional reconstruction from MRI data using DeltaViewer" by
M. Wada, N. Katagiri, Y. Shigematsu, S. Fujihara, C. Nishibori, C. Takeuchi,
S. Hashimoto, A. Horii, Y. Katagiri
- Bioimaging
Society of Japan, the Best Image Hiruma Prize 2003
"Reconstruction from serial sections using DeltaViewer" by
N. Katagiri, M. Wada, Y. Shigematsu, S. Fujihara, I. Yokoyama, Y. Katagiri
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