Refereed Papers

  1. Sho Ozaki, Shizuo Kaji (joint first author), Kanabu Nawa, Toshikazu Imae, Atsushi Aoki, Takahiro Nakamoto, Takeshi Ohta, Yuki Nozawa, Hideomi Yamashita, Akihiro Haga, and Keiichi Nakagawa, Training of deep cross-modality conversion models with a small dataset, and their application in megavoltage CT to kilovoltage CT conversion, Medical Physics (2022),

  2. Tomoki Maetani, Naoya Tanabe, Satoru Terada, Yusuke Shiraishi, Hiroshi Shima, Shizuo Kaji, Ryo Sakamoto, Tsuyoshi Oguma, Susumu Sato, Izuru Masuda, and Toyohiro Hirai, Physiological impacts of computed tomography airway dysanapsis, fractal dimension and branch count in asymptomatic never smokers, J Appl Physiol, (2022)

  3. Hiroshi Shima, Naoya Tanabe, Akira Oguma, Kaoruko Shimizu, Shizuo Kaji, Masaru Suzuki, Susumu Sato, Kunihiko Terada, Tsuyoshi Oguma, Takeshi Kubo, Hironi Makita, Atsuyasu Sato, Masaharu Nishimura, Satoshi Konno, and Toyohiro Hirai, Subtyping emphysematous COPD by respiratory volume change distributions on CT, Thorax (2022),

  4. Hiroaki Bando, Shizuo Kaji, Takaharu Yaguchi, Causal inference for empirical dynamical systems based on persistent homology, JSIAM Letters 14 (2022), 69--72,

  5. Naoya Tanabe, Shizuo Kaji (equal contribution), Hiroshi Shima, Yusuke Shiraishi, Tomoki Maetani, Tsuyoshi Oguma, Susumu Sato, and Toyohiro Hirai, Kernel conversion for robust quantitative measurements of archived chest computed tomography using deep learning-based image-to-image translation, Front. Artif. Intell. 17 (2022), doi: 10.3389/frai.2021.769557

  6. Ho Kyoung Ko, Suyoung Choi, and Shizuo Kaji(corresponding), Who has given up on mathematics? A data analysis, Asia Pacific Education Review 22 (2021), 699--714,

  7. Naoya Tanabe, Shizuo Kaji (equal contribution), Susumu Sato, Tomoo Yokoyama, Tsuyoshi Oguma, Kiminobu Tanizawa, Tomohiro Handa, Takashi Sakajo, and Toyohiro Hirai, A homological approach to a mathematical definition of pulmonary fibrosis and emphysema on computed tomography, J Appl Physiol, vol 131-2, (2021), 601--612, doi:10.1152/japplphysiol.00150.2021

  8. Mohamed A. Abdelwahab, Shizuo Kaji(corresponding), Maiya Hori, Shigeru Takano, Yutaka Arakawa, and Rin-ichiro Taniguchi, Measuring “Nigiwai” from Pedestrian Movement, IEEE Access, vol 9 (2021), 24859--24871,, [Code], the 37 Telecommunications Advancement Foundation Award for Interdisciplinary Research.

  9. Jinichi Mori, Shizuo Kaji, Hiroki Kawai, Satoshi Kida, Masaharu Tsubokura, Masahiko Fukatsu, Kayo Harada, Hideyoshi Noji, Takayuki Ikezoe, Tomoya Maeda, and Akira Matsuda, Assessment of dysplasia in bone marrow smear with convolutional neural networks, Sci Rep 10, 14734 (2020),, [Code]

  10. Tomohiro Hayakawa, Tomoya Kamimura, Shizuo Kaji, Fumitoshi Matsuno, Autonomous distributed system for gait generation for single-legged modular robots connected in various configurations, IEEE Transactions on Robotics Vol. 36-5 (2020), 1491--1510. (presented also at the 2021 IEEE International Conference on Robotics and Automation (ICRA))

  11. Satoshi Kida, Shizuo Kaji (joint first author), Kanabu Nawa, Toshikazu Imae, Takahiro Nakamoto, Sho Ozaki, Takeshi Ohta, Yuki Nozawa, and Keiichi Nakagawa, Visual enhancement of Cone-beam CT by use of CycleGAN, Medical Physics, 47-3 (2020), 998--1010, selected as Editor's Choice, [arXiv:1901.05773] [Code]

  12. Shizuo Kaji, Shintarô Kuroki, Eunjeong Lee, Dong Youp Suh, Flag Bott manifolds of general Lie type and their equivariant cohomology rings, Homology, Homotopy and Applications, Vol. 20, No. 1 (2020), pp 375--390. [arXiv:1905.00303]

  13. Shizuo Kaji and Satoshi Kida (joint first author), 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, Volume 12, Issue 3 (2019), pp 235--248. [arXiv:1905.08603], [Code], Most Citation Award 2021.

  14. S. Kaji, Representing a point and the diagonal as zero loci in flag manifolds, Algebraic & Geometric Topology, Volume 19, Number 4 (2019), 2061--2075, [arXiv:1807.09375]

  15. A. Derouet-Jourdan, S. Kaji(corresponding), and Y. Mizoguchi, A linear algorithm for Brick Wang tiling, Japan Journal of Industrial and Applied Mathematics, Volume 36, Issue 3 (2019), pp 749--761. [arXiv:1603.04292], [Code]

  16. Suyoung Choi, Shizuo Kaji, and Hanchul Park, The cohomology groups of real toric varieties associated to Weyl chambers of type C and D, Proceedings of the Edinburgh Mathematical Society, Volume 62, Issue 3, pp. 861--874, 2019. [arXiv:1705.00275]

  17. Soojin Cho, Suyoung Choi, and Shizuo Kaji, Geometric representations of finite groups on real toric spaces, J. Korean Math. Soc. 56 (2019), No. 5, pp. 1265--1283, [arXiv:1704.08591], The Korean Federation of Science and Technology Societies selected this paper as the best paper in the field of mathematics published in Korea in 2019. [Code]

  18. S. Kaji, T. Maeno, K. Nuida, and Y. Numata, Polynomial expressions of p-ary auction functions, Journal of Mathematical Cryptology, Volume 13, Issue 2, Pages 69–80, 2019. [arXiv:1703.07930]

  19. S. Kaji, and S. Theriault, Suspension splittings and self-maps of flag manifolds, Acta Mathematica Sinica, English Series, Vol. 35, No. 4, pp. 445-–462 (2019), [arXiv:1802.01809] [Code]

  20. A. Fauré and S. Kaji, A circuit-preserving mapping from multilevel to Boolean dynamics, J. Theoretical Biology, Volume 440 (7), pp. 71--79 (2018), [arXiv:1703.08934] [poster] [Code]

  21. N. D. Turgay and S. Kaji, The mod 2 dual Steenrod algebra as a subalgebra of the mod 2 dual Leibniz-Hopf algebra, Journal of Homotopy and Related Structures, Volume 12, Issue 3, pp. 727--739 (2017), doi:10.1007/s40062-016-0163-x [arXiv:1505.05465] [slides] [Code]

  22. 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 (2017), No. 2, 143--151,

  23. Shizuo Kaji, Michihiro Sakai, Stephen Theriault, Counting the number of homotopy associative multiplications on certain H-spaces, Topology and its Applications vol.214, 137--149 (2016).

  24. S. Kaji and H. Ochiai, A concise parametrization of affine transformation, SIAM J. Imaging Sci., 9(3), 1355--1373 (2016), [arXiv:1507.05290], [Code]

  25. Shizuo KAJI, Akihiro Ohsita, and Stephen Theriault, Mod p decompositions of the loop spaces of compact symmetric spaces, Algebraic & Geometric Topology, vol.15, 1771--1811, 2015, DOI: 10.2140/agt.2015.15.1771. [arXiv:1409.7958] [slides]

  26. Shizuo KAJI, Weyl group symmetry on the GKM graph of a GKM manifold with an extended Lie group action, Osaka J. Math. vol.52, no.1, 31--43, 2015.

  27. 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, vol.26, no.2, 169--194, 2015. DOI: 10.1142/s0129054115500100, [arXiv:1206.0069]

    • (Early conference version appears in Proceedings of IWSEC 2011 (International Workshop on Security 2011), Lecture Notes in Computer Science 7038, November 2011, pp.144--160, . DOI: 10.1007/978-3-642-25141-2_10)

  28. Shizuo Kaji and Daisuke Kishimoto, Homotopy nilpotency in $p$-regular loop spaces, Mathematische Zeitschrift, vol.264, no.1, 209--224, 2010. [PDF file] , DOI: 10.1007/s00209-008-0459-6

  29. Hiroaki Hamanaka, Shizuo Kaji, and Akira Kono, Samelson products in $Sp(2)$, Topology and its Applications, vol.155, 1207--1212, 2008. , [PDF file]

  30. Shizuo Kaji, Mod 2 cohomology of 2-compact groups of low rank, Journal of Mathematics of Kyoto University, vol.47, no.2, 441--450, 2007.

    • I am very sorry but I made a lot of serious mistakes in the printed version above. A revised version is available at arXiv:math.AT/0710.5926 with the title "Mod 2 cohomology of 2-local finite groups of low rank". I would like to sincerely apologize for that.

  31. Shizuo Kaji, Low rank cohomology of the classifying spaces of gauge groups over 3-manifolds, Publications of the Research Institute for Mathematical Sciences., vol.42, no. 2, pp.581--587, 2006. [PDF file]

  32. Shizuo Kaji, On the nilpotency of rational $H$-spaces, Journal of the Mathematical Society of Japan, vol.57, no. 4, pp.1153--1165, 2005. [PDF file]

Refereed Book Chapters

  1. 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, pp 356--381, CRC Press, 2019, [arXiv:1903.06360] [Code]

  2. S. Kaji, A. Derouet-Jourdan, and H. Ochiai, Dappled tiling, Mathematical Insights into Advanced Computer Graphics Techniques, pp. 59--72, Springer Singapore, 2019. DOI: 10.1007/978-981-13-2850-3 [Code]

    • (Early conference version appears in the Proceedings of MEIS2016) [arXiv:1607.06138]

  3. S. Kaji, Tetrisation of triangular meshes and its application in shape blending, Mathematical Progress in Expressive Image Synthesis III, pp. 7--19, Springer-Singapore, 2016. DOI: 10.1007/978-981-10-1076-7_2 [arXiv:1601.04816] [Code]

  4. S. Kaji and G. Liu, Probe-type deformers, Mathematical Progress in Expressive Image Synthesis II, pp. 63--77. Springer-Japan, 2015. DOI: 10.1007/978-4-431-55483-7_6 [video] [Code]

  5. G. Matsuda, S. Kaji, and H. Ochiai, Anti-commutative Dual Complex Numbers and 2D Rigid Transformation, Mathematical Progress in Expressive Image Synthesis I, pp. 131--138, Springer-Japan, 2014. DOI: 10.1007/978-4-431-55007-5_17 [arXiv:1601.01754] [Code]

Refereed Conference Proceedings

  1. Kodai Takenaga and Shizuo Kaji, Alexandrov Puzzle, Proceedings of Bridges 2022: Mathematics, Art, Music, Architecture, Culture, Pages 371--374, 2022

  2. Hideki Todo, Kunihiko Kobayashi, Jin Katsuragi, Haruna Shimotahira, Shizuo Kaji, and Yonghao Yue, Stroke Transfer: Example-based Synthesis of Animatable Stroke Styles, Proceedings of ACM SIGGRAPH 2022, Article No.54, pp 1--10,, 2022

  3. Nariaki Tateiwa, Yuji Shinano, Keiichiro Yamamura, Akihiro Yoshida, Shizuo Kaji, Masaya Yasuda, Katsuki Fujisawa, CMAP-LAP: Configurable Massively Parallel Solver for Lattice Problems, Proceedings of the 28th edition of the IEEE International Conference on High Performance Computing, Data, and Analytics (HiPC 2021), [preprint, ZIB-report]

  4. Shizuo Kaji, Akira Horiguchi, Takuro Abe, Yohsuke Watanabe, A Hyper-surface Arrangement Model of Ranking Distributions, KDD '21: Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining, 796--804, 2021,, [code]

  5. Nariaki Tateiwa, Yuji Shinano, Satoshi Nakamura, Akihiro Yoshida, Shizuo Kaji, Masaya Yasuda, Katsuki Fujisawa, Massive Parallelization for Finding Shortest Lattice Vectors Based on Ubiquity Generator Framework, Proceedings of the International Conference for High Performance Computing, Networking, Storage, and Analysis (SC20) (SC20), 2020 Vol. 1, 834--848, DOI: 10.1109/SC41405.2020.00064

  6. Nozomi Hata, Shizuo Kaji (equal contribution), Akihiro Yoshida, and Katsuki Fujisawa, Nested Subspace Arrangement for Representation of Relational Data, Proceedings of the thirty-seventh International Conference on Machine Learning (ICML2020), PMLR vol. 119, 4127--4137, [arXiv:2007.02007] [Code]

  7. 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, pp 36--37, 2019. DOI: 10.1145/3355049.3360518 [Video]

  8. S. Choi, S. Kaji, and S. Theriault, Homotopy decomposition of a suspended real toric space, the special volume of the Boletín de la Sociedad Matemática Mexicana dedicated to Sam Gitler, Volume 23, Issue 1, pp 153--161, April 2017. DOI: 10.1007/s40590-016-0090-1 [arXiv:1503.07788]

  9. 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, National Mathematics Centre Abuja, Nigeria, pp. 37 -- 54, 2015. ISBN: 978-8141-26-9 [arXiv:1504.01091] [Code]

  10. S. Kaji, S. Hirose, S. Sakata, Y. Mizoguchi, and K. Anjyo, Mathematical Analysis on Affine Maps for 2D Shape Interpolation, Proceedings of SCA2012 (ACM SIGGRAPH/Eurographics Symposium on Computer Animation 2012), pp. 71--76. [Video]

  11. S. Kaji, Equivariant Schubert calculus of Coxeter groups, Proceedings of The International Conference "GEOMETRY, TOPOLOGY, ALGEBRA and NUMBER THEORY, APPLICATIONS" dedicated to the 120th anniversary of Boris Delone, Proc. Stekelov. Inst. Math, vol 275, 239--250. 2011. , [PDF file]

  12. S. Kaji, Schubert calculus, seen from torus equivariant topology, Proceedings of KAIST Toric Topology Workshop 2010, Trends in Mathematics - New Series, Volume 12, no.1, 71--89, 2010. [PDF file]

Non-Refereed Articles

  1. S. Kaji, S. Hirose, H. Ochiai, and K. Anjyo, A Lie Theoretic Parameterization of Affine Transformation, Proceedings of MEIS2013 (Mathematical Progress in Expressive Image Synthesis 2013), MI Lecture Notes Vol.50, pp. 134--140.

  2. S. Kaji, A closed linkage mechanism having the shape of a discrete Mobius strip, translated from a Japanese article in the Symposium Proceedings of the 2018 Spring meeting of the Japan Society for Precision Engineering, [arXiv:1909.02885]

Refereed Papers in Japanese

  1. (in Japanese) Toshikazu Imae, Shizuo Kaji, Satoshi Kida, Kanako Matsuda, Shigeharu Takenaka, Atsushi Aoki, Takahiro Nakamoto, Sho Ozaki, Kanabu Nawa, Hideomi Yamashita, Keiichi Nakagawa, and Osamu Abe, Improvement in Image Quality of CBCT during Treatment by Cycle Generative Adversarial Network (サイクル敵対的生成ネットワークを用いた 治療中 CBCT 画像の画質改善), 日本放射線技術学会雑誌, Vol. 76(11), 1173-1184, 2020, DOI: 10.6009/jjrt.2020_JSRT_76.11.1173

Non-Refereed Articles in Japanese

  1. (in Japanese) 鍛冶 静雄, エレガントな解答をもとむ, 日本評論社 数学セミナー, 2021年11月号(出題), 2022年2月号(解答)

  2. (in Japanese) 鍛冶静雄, かたちを算する, 数学セミナー連載, 日本評論社, 2020年4月--2021年3月

  3. (in Japanese) 鍛冶 静雄, 木田 智士, 藤田 広志, 論文紹介: 最近の RPT 誌レビュー論文から, 日本放射線技術学会雑誌, 76(11), 1207--1210, 2020.

  4. (in Japanese) 立岩 斉明, 品野 勇治, 吉田 明広, 鍛冶 静雄, 安田 雅哉, 藤澤 克樹, 最短格子ベクトル問題求解における Ubiquity Generator Framework を用いた大規模 MPI 並列化, 研究報告 ハイパフォーマンスコンピューティング(HPC), 情報処理学会, 2020-HPC-176(1), 1--10, 2020

  5. (in Japanese) 鍛冶静雄, 数理のクロスロード/かたちと動きの数理基盤/(2) デザインの数学, 数学セミナー 2019年7月号, 日本評論社, 2019

    1. 日本評論社のご厚意で、版権のある図版を除き軽微な修正を加えた著者原稿を、上のリンクにて公開しています。

  6. (in Japanese) 鍛冶静雄, 数理のクロスロード/かたちと動きの数理基盤/(1) リンク万華鏡, 数学セミナー 2019年6月号, 日本評論社, 2019

    1. 日本評論社のご厚意で、版権のある図版を除き軽微な修正を加えた著者原稿を、上のリンクにて公開しています。

  7. (in Japanese) 木田智士,鍛冶静雄,今江禄一,名和要武,中川恵一, 芳賀昭弘, 敵対的生成ネットワーク(GAN)の放射線治療への応用, Rad Fan Vol.16 No.12 (放射線治療情報BOOK2018), 2018

  8. (in Japanese) S. Kaji, 同変ループ積について, 日本数学会2018年度秋季総合分科会予稿集 (トポロジー分科会 特別講演), 2018

  9. (in Japanese) Tomohiro Hayakawa, Shizuo Kaij, Fumitoshi Matsuno, Autonomous distributed for gait generation of single-leg modular robots connecting into various leg , 第62回システム制御情報学会研究発表講演会(SCI'18)講演論文集, 2018

  10. (in Japanese) 鍛冶静雄, 曲線の幾何学から生まれた閉リンク機構, 2018年度精密工学会春季大会 シンポジウム資料集, pp. 62--65.

    1. (English translation) A closed linkage mechanism having the shape of a discrete Mobius strip, [arXiv:1909.02885]

  11. (in Japanese) 縫田 光司, 阿部 拓郎, 鍛冶 静雄, 沼田 泰英, 前野 俊昭, パラメータ固定ハッシュ関数の理論的安全性評価に関する一考察 -- 関数の近似可能性の観点から --, コンピュータセキュリティシンポジウム2011(CSS2011)予稿集, 情報処理学会 (CD-ROM), 2011

  12. (in Japanese) S. Kaji, リー群のトポロジーから見るシューベルトカリキュラス, 第56回トポロジーシンポジウム予稿集, 2009

  13. (in Japanese) S. Kaji, T.Matsuoka, and S.Oguni, Twisted K-Theory and projective representations, 城崎新人セミナー報告集2008

  14. (in Japanese) M. Honda, S. Kaji, S. Oguni, and A. Tanida, Probabilistic proof of the Atiyah-Singer's index theorem, 城崎新人セミナー報告集2007

  15. (in Japanese) S. Kaji, Cohomology of the homotopy pullbacks, 城崎新人セミナー報告集2006

  16. (in Japanese) S. Kaji, Homotopy types of certain mapping spaces, 城崎新人セミナー報告集2005

  17. (in Japanese) S. Kaji, Introduction to rational homotopy theory, 城崎新人セミナー報告集2004


  1. Yoshiaki Uchida, Shizuo Kaji, and Naoto Nakano (all three have equally contributed), Chemical-Data-Driven Validation of Physical Theories of Liquid Crystals,

  2. Shizuo Kaji and Jingyao Zhang, Free-form Design of Discrete Architectural Surfaces by use of Circle Packing, arXiv:2103.07584 [Code]

  3. Ryo Okada, Sho Sugawara, Tze Mun Loo, Kenichi Miyata, Kaoru Katoh, Shizuo Kaji, Yoshiro Maezawa, Koutaro Yokote, Mizuho Nakayama, Masanobu Oshima, Koji Nagao, Chikashi Obuse, Satoshi Nagayama, Keiyo Takubo, Glen Barber, Akira Nakanishi, Masato Kanemaki, Eiji Hara, and Akiko Takahashi, RNaseH2A Downregulation Drives Chromosomal DNA Fragmentation and Accumulation of RNA-DNA Hybrids in Senescent Cells, SSRN,

  4. Shizuo Kaji, Takeki Sudo, and Kazushi Ahara, Cubical Ripser: Software for computing persistent homology of image and volume data, arXiv:2005.12692 [Code]

  5. S. Kaji, T. Maeno, K. Nuida, and Y. Numata, Polynomial Expressions of Carries in p-ary Arithmetics, arXiv:1506.02742

  6. S. Kaji and H. Tene, Products in Equivariant Homology, arXiv:1506.00441

  7. S. Kaji and P. Pragacz, On diagonals of flag bundles, arXiv:1503.03217

  8. S. Kaji and M. Nakagawa, The Chow rings of the algebraic groups $E_6, E_7$ and $E_8$, arXiv:math.AT/0709.3702, [Code]

  9. S. Kaji, Mod 2 cohomology of 2-local finite groups of low rank, arXiv:math.AT/0710.5926This is a heavily revised version of the paper "Mod 2 cohomology of 2-compact groups of low rank".

  10. S. Kaji and A. Kono, Mod 2 cohomology of BLPSp(2m + 1)


  1. Shizuo Kaji, Johannes Schoenke, Eliot Fried, Michael Grunwald, Moebius Kaleidocycle, 特願2018-033395(Japan), PCT/JP2019/007314(PCT), 特願2020-503522(PCT=>JP), WO 2019167941(Publication Number), 27 Feb. 2018. The contents of the patent are also published in

    • Johannes Schönke and Eliot Fried, Single degree of freedom everting ring linkages with nonorientable topology, PNAS 116 (1) 90--95, 2019.

  2. Shizuo Kaji, Mohamed A. Abdelwahab, Maiya Hori, Shigeru Takano, Yutaka Arakawa, 特許第7050356号, 31 Mar. 2022, (特願2020-204436, 9 Dec. 2020). The contents of the patent are also published in

  3. Shizuo Kaji, Hyeongki Park, Maiya Hori, and Shigeru Takano, "歩行者の行動評価装置、歩行者の行動評価方法、及び、歩行者の行動評価プログラム", 特許第7099771号, 4 Jul. 2022, (特願2021-200374, 9 Dec. 2021)


  1. Osamu Saeki, Ho Tu Bao, Shizuo Kaji, Kenji Kajiwara, Nguyen Ha Nam, Ta Hai Tung, Melanie Roberts, Masato Wakayama, Le Minh Ha, and Philip Broadbridge, Proceedings of Forum “Math-for-Industry” 2021 -Mathematics for Digital Economy-, 2022

  2. Yoshinori Dobashi, Shizuo Kaji, Kei Iwasaki, Mathematical Insights into Advanced Computer Graphics Techniques, Springer Singapore, 2019. DOI: 10.1007/978-981-13-2850-3

  3. Ken Anjyo, Hiroyuki Ochiai, Yoshinori Dobashi, Yoshihiro Mizoguchi, Shizuo Kaji, Symposium MEIS2013: Mathematical Progress in Expressive Image Synthesis, MI Lecture Notes 2013 Vol.50


I occasionally write for Mathematical Reviews (MathSciNet, subscription required). 19 review articles as of 2021.