九州大学 研究者情報
論文一覧
鍛冶 静雄(かじ しずお) データ更新日:2020.01.27

准教授 /  マス・フォア・インダストリ研究所 数理計算インテリジェント社会実装推進部門


原著論文
1. Shizuo Kaji, Weyl group symmetry on the gkm graph of a gkm manifold with an extended lie group action, Osaka Journal of Mathematics, 52, 1, 31-41, 2015.01.
2. S. Kaji, Three presentations of torus equivariant cohomology of flag manifolds, Perspectives and Developments in Mathematics, Proceedings of the International Mathematics Conference in honour of the 70th Birthday of Professor S. A. Ilori, 37-54, 2015.05.
3. Neşet Deniz Turgay, Shizuo Kaji, The mod 2 dual Steenrod algebra as a subalgebra of the mod 2 dual Leibniz-Hopf algebra, Journal of Homotopy and Related Structures, 10.1007/s40062-016-0163-x, 12, 3, 727-739, 2017.09, [URL].
4. Suyoung Choi, Shizuo Kaji, Hanchul Park, The Cohomology Groups of Real Toric Varieties Associated with Weyl Chambers of Types C and D, Proceedings of the Edinburgh Mathematical Society, 10.1017/S001309151800086X, 62, 3, 861-874, 2019.08, [URL], Given a root system, the Weyl chambers in the co-weight lattice give rise to a real toric variety, called the real toric variety associated with the Weyl chambers. We compute the integral cohomology groups of real toric varieties associated with the Weyl chambers of type Cn and Dn, completing the computation for all classical types..
5. S. Kaji, Tetrisation of triangular meshes and its application in shape blending, Mathematical Progress in Expressive Image Synthesis III, 10.1007/978-981-10-1076-7_2, 7-19, 2016.05.
6. Shizuo Kaji, Stephen Theriault, Suspension Splittings and Self-maps of Flag Manifolds, Acta Mathematica Sinica, English Series, 10.1007/s10114-019-8051-z, 35, 4, 445-462, 2019.04, [URL], If G is a compact connected Lie group and T is a maximal torus, we give a wedge decomposition of ΣG/T by identifying families of idempotents in cohomology. This is used to give new information on the self-maps of G/T..
7. S. Kaji, Schubert calculus, seen from torus equivariant topology, Trends in Mathematics - New Series, 12, 1, 71-89, 2010.05.
8. Hiroaki Hamanaka, Shizuo Kaji, Akira Kono, Samelson products in Sp (2), Topology and its Applications, 10.1016/j.topol.2008.02.008, 155, 11, 1207-1212, 2008.06, [URL], We calculate certain Samelson products of Sp (2). Using the result, we classify the homotopy types of the gauge groups of principal Sp (2) bundles over S8 and we also derive the homotopy commutativity of Sp (2) localized at 3..
9. Shizuo Kaji, Representing a point and the diagonal as zero loci in flag manifolds, Algebraic and Geometric Topology, 10.2140/agt.2019.19.2061, 19, 4, 2061-2075, 2019.01, [URL], The zero locus of a generic section of a vector bundle over a manifold defines a submanifold. A classical problem in geometry asks to realise a specified submanifold in this way. We study two cases: a point in a generalised flag manifold and the diagonal in the direct product of two copies of a generalised flag manifold. These cases are particularly interesting since they are related to ordinary and equivariant Schubert polynomials, respectively..
10. S. Kaji and G. Liu, Probe-type deformers, Mathematical Progress in Expressive Image Synthesis I, 10.1007/978-4-431-55483-7_6, 63-77, 2015.05.
11. K. Matsumoto, N. Ogawa, H. Inou, S. Kaji, Y. Ishii, and M. Hirose, Polyvision: 4D Space Manipulation through Multiple Projections, SIGGRAPH Asia 2019 Emerging Technologies, DOI: 10.1145/3355049.3360518, 2019.11.
12. Shizuo Kaji, Toshiaki Maeno, Koji Nuida, Yasuhide Numata, Polynomial expressions of p-ary auction functions, Journal of Mathematical Cryptology, 10.1515/jmc-2018-0016, 13, 2, 69-80, 2019.06, [URL], One of the common ways to design secure multi-party computation is twofold: To realize secure fundamental operations and to decompose a target function to be securely computed into them. In the setting of fully homomorphic encryption, as well as some kinds of secret sharing, the fundamental operations are additions and multiplications in the base field such as the field F2 with two elements. Then the second decomposition part, which we study in this paper, is (in theory) equivalent to expressing the target function as a polynomial. It is known that any function over the finite prime field Fp has a unique polynomial expression of degree at most p-1 with respect to each input variable; however, there has been little study done concerning such minimal-degree polynomial expressions for practical functions. This paper aims at triggering intensive studies on this subject, by focusing on polynomial expressions of some auction-related functions such as the maximum/minimum and the index of the maximum/minimum value among input values..
13. Shizuo Kaji, Satoshi Kida, Overview of image-to-image translation by use of deep neural networks
denoising, super-resolution, modality conversion, and reconstruction in medical imaging, Radiological physics and technology, 10.1007/s12194-019-00520-y, 12, 3, 235-248, 2019.09, [URL], Since the advent of deep convolutional neural networks (DNNs), computer vision has seen an extremely rapid progress that has led to huge advances in medical imaging. Every year, many new methods are reported at conferences such as the International Conference on Medical Image Computing and Computer-Assisted Intervention and Machine Learning for Medical Image Reconstruction, or published online at the preprint server arXiv. There is a plethora of surveys on applications of neural networks in medical imaging (see [1] for a relatively recent comprehensive survey). This article does not aim to cover all aspects of the field, but focuses on a particular topic, image-to-image translation. Although the topic may not sound familiar, it turns out that many seemingly irrelevant applications can be understood as instances of image-to-image translation. Such applications include (1) noise reduction, (2) super-resolution, (3) image synthesis, and (4) reconstruction. The same underlying principles and algorithms work for various tasks. Our aim is to introduce some of the key ideas on this topic from a uniform viewpoint. We introduce core ideas and jargon that are specific to image processing by use of DNNs. Having an intuitive grasp of the core ideas of applications of neural networks in medical imaging and a knowledge of technical terms would be of great help to the reader for understanding the existing and future applications. Most of the recent applications which build on image-to-image translation are based on one of two fundamental architectures, called pix2pix and CycleGAN, depending on whether the available training data are paired or unpaired (see Sect. 1.3). We provide codes ([2, 3]) which implement these two architectures with various enhancements. Our codes are available online with use of the very permissive MIT license. We provide a hands-on tutorial for training a model for denoising based on our codes (see Sect. 6). We hope that this article, together with the codes, will provide both an overview and the details of the key algorithms and that it will serve as a basis for the development of new applications..
14. Shizuo Kaji, On the nilpotency of rational H-spaces, Journal of the Mathematical Society of Japan, 10.2969/jmsj/1150287307, 57, 4, 1153-1165, 2005.10, [URL], In [BG], it is proved that the Whitehead length of a space Z is less than or equal to the nilpotency of ΩZ. As for rational spaces, those two invariants are equal. We show this for a 1-connected rational space Z by giving a way to calculate those invariants from a minimal model for Z. This also gives a way to calculate the nilpotency of an homotopy associative rational H-space..
15. Shizuo Kaji, Akihiro Ohsita, Stephen Theriault, Mod p decompositions of the loop spaces of compact symmetric spaces, Algebraic and Geometric Topology, 10.2140/agt.2015.15.1771, 15, 3, 1771-1811, 2015.06, [URL].
16. Shizuo Kaji, Mod 2 cohomology of 2-compact groups of low rank, Kyoto Journal of Mathematics, 10.1215/kjm/1250281055, 47, 2, 441-450, 2007.01, [URL], We determine the mod 2 cohomology algebra over the Steenrod algebra A 2 of the classifying space of loop groups LG where G = Spin(7), Spin(8), Spin(9), F4 and DI(4). Then we show they are isomorphic as algebras over A2 to the mod 2 cohomology of the 2-compact groups of type G..
17. Shizuo Kaji, S. Hirose, S. Sakata, Yoshihiro Mizoguchi, K. Anjyo, Mathematical analysis on affine maps for 2D shape interpolation, 11th ACM SIGGRAPH / Eurographics Symposium on Computer Animation, SCA 2012
Computer Animation 2012 - ACM SIGGRAPH / Eurographics Symposium Proceedings, SCA 2012
, 71-76, 2012.07.
18. Shizuo Kaji, Low rank cohomology of the classifying spaces of gauge groups over 3-manifolds, Publications of the Research Institute for Mathematical Sciences, 10.2977/prims/1166642116, 42, 2, 581-587, 2006.06, [URL], The purpose of this paper is to calculate the cohomology of the function space Map(M, BG) for degree less than or equal to 3, where G is a simply connected compact Lie group and M is a closed orientable 3-manifold. The calculation enables us to obtain a simple proof and an improvement of the result [4, Theorem 1.2]..
19. Shizuo Kaji, Kenji Kajiwara, Hyeongki Park, Linkage Mechanisms Governed by Integrable Deformations of Discrete Space Curves, Nonlinear Systems and Their Remarkable Mathematical Structures. Volume 2, CRC Press, https://doi.org/10.1201/9780429263743, 2019.12.
20. Shizuo Kaji, Daisuke Kishimoto, Homotopy nilpotency in p-regular loop spaces, Mathematische Zeitschrift, 10.1007/s00209-008-0459-6, 264, 1, 209-224, 2010.01, [URL], We consider the problem how far from being homotopy commutative is a loop space having the homotopy type of the p-completion of a product of finite numbers of spheres. We determine the homotopy nilpotency of those loop spaces as an answer to this problem..
21. Suyoung Choi, Shizuo Kaji, Stephen Theriault, Homotopy decomposition of a suspended real toric space, Boletin de la Sociedad Matematica Mexicana, 10.1007/s40590-016-0090-1, 23, 1, 153-161, 2017.04, [URL].
22. Soojin Cho, Suyoung Choi, Shizuo Kaji, Geometric representations of finite groups on real toric spaces, Journal of the Korean Mathematical Society, 10.4134/JKMS.j180646, 56, 5, 1265-1283, 2019.01, [URL], We develop a framework to construct geometric representations of finite groups G through the correspondence between real toric spaces XR and simplicial complexes with characteristic matrices. We give a combinatorial description of the G-module structure of the homology of XR. As applications, we make explicit computations of the Weyl group representations on the homology of real toric varieties associated to the Weyl chambers of type A and B, which show an interesting connection to the topology of posets. We also realize a certain kind of Foulkes representation geometrically as the homology of real toric varieties..
23. Shizuo Kaji, Equivariant Schubert calculus of Coxeter groups, Proceedings of the Steklov Institute of Mathematics, 10.1134/S0081543811080177, 275, 1, 239-250, 2011.12, [URL], We consider an equivariant extension for Hiller's Schubert calculus on the coinvariant ring of a finite Coxeter group..
24. Ho Kyoung Ko, Hyung Won Kim, Shizuo Kaji, Suyoung Choi, Elementary school students who give up on learning mathematics: Correlations with non-cognitive learner characteristics, J. Korea Soc. Math. Ed. Ser. C, 20, 2, 143-151, 2017.04.
25. S. Kaji, A. Derouet-Jourdan, H. Ochiai, Dappled tiling, Mathematical Insights into Advanced Computer Graphics Techniques, 10.1007/978-981-13-2850-3, 59-72, 2019.03.
26. Shizuo Kaji, Michihiro Sakai, Stephen Theriault, Counting the number of homotopy associative multiplications on certain H-spaces, Topology and its Applications, 10.1016/j.topol.2016.10.008, 214, 137-149, 2016.12, [URL].
27. G. Matsuda, S. Kaji, H. Ochiai, Anti-commutative Dual Complex Numbers and 2D Rigid Transformation, Mathematical Progress in Expressive Image Synthesis I, 10.1007/978-4-431-55007-5_17, 131-138, 2014.05.
28. Koji Nuida, Takuro Abe, Shizuo Kaji, Toshiaki Maeno, Yasuhide Numata, A mathematical problem for security analysis of hash functions and pseudorandom generators, International Journal of Foundations of Computer Science, 10.1142/S0129054115500100, 26, 2, 169-194, 2015.02, [URL].
29. Koji Nuida, Takuro Abe, Shizuo Kaji, Toshiaki Maeno, Yasuhide Numata, A mathematical problem for security analysis of hash functions and pseudorandom generators, 6th International Workshop on Security, IWSEC 2011
Advances in Information and Computer Security - 6th International Workshop, IWSEC 2011, Proceedings
, 10.1007/978-3-642-25141-2_10, 144-160, 2011.11, [URL], The aim of this paper is to emphasize the significance of a certain mathematical problem in research on information security. We point out that the mathematical problem, which we refer to as "Function Density Problem," has connections to the following two major cryptographic topics; security analysis of hash functions in the real world (like SHA-1), and construction of pseudorandom generators with some enhanced security property. We also provide a first example to show how a study of Function Density Problem can contribute to the progress of the above-mentioned two topics. Other potential applications of Function Density Problem to information security are also discussed..
30. Alexandre Derouet-Jourdan, Shizuo Kaji, Yoshihiro Mizoguchi, A linear algorithm for Brick Wang tiling, Japan Journal of Industrial and Applied Mathematics, 10.1007/s13160-019-00369-z, 36, 3, 749-761, 2019.09, [URL], The Wang tiling is a classical problem in combinatorics. A major theoretical question is to find a (small) set of tiles which tiles the plane only aperiodically. In this case, resulting tilings are rather restrictive. On the other hand, Wang tiles are used as a tool to generate textures and patterns in computer graphics. In these applications, a set of tiles is normally chosen so that it tiles the plane or its sub-regions easily in many different ways. With computer graphics applications in mind, we introduce a class of such tileset, which we call sequentially permissive tilesets, and consider tiling problems with constrained boundary. We apply our methodology to a special set of Wang tiles, called Brick Wang tiles, introduced by Derouet-Jourdan et al. in 2016 to model wall patterns. We generalise their result by providing a linear algorithm to decide and solve the tiling problem for arbitrary planar regions with holes..
31. Shizuo Kaji, Hiroyuki Ochiai, A concise parametrization of affine transformation, SIAM Journal on Imaging Sciences, 10.1137/16M1056936, 9, 3, 1355-1373, 2016.09, [URL].
32. Adrien Fauré, Shizuo Kaji, A circuit-preserving mapping from multilevel to Boolean dynamics, Journal of Theoretical Biology, 10.1016/j.jtbi.2017.12.013, 440, 71-79, 2018.03, [URL].

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