Publication
Book
平岡裕章，タンパク質構造とトポロジー: パーシステントホモロジー群入門，共立出版（2013）．
Paper
Yasuaki Hiraoka, Yusuke Imoto, Shu Kanazawa, Enhao Liu. Curse of Dimensionality on Persistence Diagrams. http://arxiv.org/abs/2404.18194.
Yasuaki Hiraoka, Ken Nakashima, Ippei Obayashi, Chenguang Xu. Refinement of Interval Approximations for Fully Commutative Quivers. https://arxiv.org/abs/2310.03649
Toshiaki Yachimura, Hanbo Wang, Yusuke Imoto, Momoko Yoshida, Sohei Tasaki, Yoji Kojima, Yukihiro Yabuta, Mitinori Saitou, Yasuaki Hiraoka. scEGOT: Single-cell trajectory inference framework based on entropic Gaussian mixture optimal transport. bioRxiv https://doi.org/10.1101/2023.09.11.557102
Yasuaki Hiraoka, Yusuke Imoto, Killian Meehan, Théo Lacombe, Toshiaki Yachimura. Topological Node2vec: Enhanced Graph Embedding via Persistent Homology. Journal of Machine Learning Research 25 (2024) 1-26.
Yasuaki Hiraoka, Tomoyuki Shirai. Torsion-weighted spanning acycle entropy in cubical lattices and Mahler measures. J Appl. and Comput. Topology (2024). https://doi.org/10.1007/s41468-024-00163-y
Yuta Shuseki, Shinji Kohara, Tomoaki Kaneko, Keitaro Sodeyama, Yohei Onodera, Chihiro Koyama, Atsunobu Masuno, Shunta Sasaki, Shohei Hatano, Motoki Shiga, Ippei Obayashi, Yasuaki Hiraoka, Junpei T. Okada, Akitoshi Mizuno, Yuki Watanabe, Yui Nakata, Koji Ohara, Motohiko Murakami, Matthew G. Tucker, Marshall T. McDonnell, Hirohisa Oda, and Takehiko Ishikawa. Atomic and Electronic Structure in MgO–SiO2. J. Phys. Chem. A., 2024. https://doi.org/10.1021/acs.jpca.3c05561
Yasuaki Hiraoka, Shu Kanazawa, Jun Miyanaga, Kenkichi Tsunoda. Large deviation principle for persistence diagrams of random cubical filtrations. Journal of Applied and Computational Topology (2024). https://doi.org/10.1007/s41468-023-00161-6
Emerson G. Escolar, Yasuaki Hiraoka, Mitsuru Igami, Yasin Ozcan. Mapping Firms' Locations in Technological Space: A Topological Analysis of Patent Statistics. Research Policy. Vol. 52 (8), 2023. https://doi.org/10.1016/j.respol.2023.104821
Y Asao, Y Hiraoka, S Kanazawa. Girth, magnitude homology and phase transition of diagonality. Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 2024;154(1):221-247. doi:10.1017/prm.2023.7
Y Imoto, Y Hiraoka. V-Mapper: topological data analysis for high-dimensional data with velocity. Nonlinear Theory and Its Applications (NOLTA), Vol. 14 (2), pp. 92-105, 2023.
Yusuke Imoto, Tomonori Nakamura, Emerson G Escolar, Michio Yoshiwaki, Yoji Kojima, Yukihiro Yabuta, Yoshitaka Katou, Takuya Yamamoto, Yasuaki Hiraoka, Mitinori Saitou. Resolution of the curse of dimensionality in single-cell RNA sequencing data analysis. Life Science Alliance 5(12) e202201591-e202201591. 2022.
Ippei Obayashi, Takenobu Nakamura, Yasuaki Hiraoka. Persistent Homology Analysis for Materials Research and Persistent Homology Software: HomCloud. Journal of the Physical Society of Japan 91(9) 2022. https://journals.jps.jp/doi/pdf/10.7566/JPSJ.91.091013
Y. Hiraoka, Yuichi Ike, and M. Yoshiwaki. Algebraic stability theorem for derived categories of zigzag persistence modules. Journal of Topology and Analysis (2022). https://doi.org/10.1142/S1793525322500091
M. Nagano, B. Hu, S. Yokobayashi, A. Yamamura, F. Umemura, M. Coradin, H. Ohta, Y. Yabuta, Y. Ishikura, I. Okamoto, H. Ikeda, N. Kawahira, Y. Nosaka, S. Shimizu, Y. Kojima, K. Mizuta, T. Kasahara, Y. Imoto, K. Meehan, R. Stocsits, G. Wutz, Y. Hiraoka, Y. Murakawa, T. Yamamoto, K. Tachibana, J. Peters, L. Mirny, B. Garcia, J. Majewski, M. Saitou. Nucleome programming is required for the foundation of totipotency in mammalian germline development. The EMBO Journal (2022)e110600. https://doi.org/10.15252/embj.2022110600
Anna Suzuki, Miyuki Miyazawa, James M. Minto, Takeshi Tsuji, Ippei Obayashi, Yasuaki Hiraoka, Takatoshi Ito. Flow estimation solely from image data through persistent homology analysis. Scientific Reports 11, 17948 (2021). https://doi.org/10.1038/s41598-021-97222-6.
A. Hirata, T. Wada, I. Obayashi, and Y. Hiraoka. Structural changes during glass formation extracted by computational homology with machine learning. Commun Mater 1, 98 (2020). https://doi.org/10.1038/s43246-020-00100-3
Philip Salmon, Yohei Onodera, Shinji Kohara, Akihiko Hirata, Norimasa Nishiyama, Suguru Kitani, Anita Zeidler, Motoki Shiga, Atsunobu Masuno, Hiroyuki Inoue, Shuta Tahara, Annalisa Polidori, Henry Fischer, Tatsuya Mori, Seiji Kojima, Hitoshi Kawaji, Alexander Kolesnikov, Matthew Stone, Matthew Tucker, Marshall McDonnell, Alex Hannon, Yasuaki Hiraoka, Ippei Obayashi, Takenobu Nakamura, Jaakko Akola, Yasuhiro Fujii, Koji Ohara, Takashi Taniguchi, and Osami Sakata. Structure and properties of densified silica glass: Characterizing the order within disorder. NPG Asia Mater 12, 85 (2020). https://doi.org/10.1038/s41427-020-00262-z
A. Suzuki, M. Miyazawa, A. Okamoto, H. Shimizu, I. Obayashi, Y. Hiraoka, T. Tsuji, P. K. Kang, T. Ito. Inferring fracture forming processes by characterizing fracture network patterns with persistent homology. Computers and Geosciences. Volume 143, October 2020, 104550. https://doi.org/10.1016/j.cageo.2020.104550
Y. Hiraoka Y and T. Mikami. Percolation on Homology Generators in Codimension One. In: Baas N., Carlsson G., Quick G., Szymik M., Thaule M. (eds) Topological Data Analysis. Abel Symposia, vol 15. Springer (2020). https://doi.org/10.1007/978-3-030-43408-3_12
T. Ichinomiya, I. Obayashi, and Y. Hiraoka. Protein folding analysis using features obtained by persistent homology. Biophysical Journal 118 (2020), 2926-2937. https://doi.org/10.1016/j.bpj.2020.04.032
Y. Hiraoka, H. Ochiai, T. Shirai. Zeta functions of periodic cubical lattices and cyclotomic-like polynomials. Advanced Studies in Pure Mathematics 84 (2020), 93-121.
C. Koyama, S. Kohara, Y. Onodera, T. Ishikawa, A. Masuno, A. Mizuno, Y. Watanabe, Y. Nakata, K. Ohara, H. Tamaru, H. Oda, I. Obayashi, Y. Hiraoka, S. Tahara, J. Okada, O. Sakata, D. René Småbråten, S. Magnus Selbach, and J. Akola. Very sharp diffraction peak in non-glass forming liquid with the formation of distorted tetraclusters. NPG Asia Mater 12, 43 (2020). https://doi.org/10.1038/s41427-020-0220-0
小原真司, 小野寺陽平, 大林一平, 志賀元紀, 平田秋彦, 平岡裕章, 坂田修身. ガラスの二体相関に隠れたトポロジーの抽出. NEW GLASS 35, 24-30 (2020).
小原真司, 坂田修身, 小野寺陽平, 大林一平, 志賀元紀, 平田秋彦, 平岡裕章. パーシステントホモロジーを用いた非晶質物質の回折パターンの理解と二体相関に潜んだトポロジーの抽出. 日本結晶学会誌 62，43-50 (2020).
S. Kohara, Y. Onodera, Y. Takimoto, H. Hijiya, T. Taniguchi, S. Urata, S. Inaba, S. Fujita, I. Obayashi, and Y. Hiraoka. Origin of the mixed alkali effect in the silicate glass. NPG Asia Materials. Vol. 11, Article number: 75 (2019).
Y. Onodera, S. Kohara, S. Tahara, A. Masuno, H. Inoue, M. Shiga, A Hirata, K. Tsuchiya, Y. Hiraoka, I. Obayashi, K. Ohara, A. Mizuno, and O. Sakata. Understanding diffraction patterns of glassy, liquid and amorphous materials via persistent homology analyses. Journal of the Ceramic Society of Japan. 127 (2019), 853-863.
A. Oyama, Y. Hiraoka, I. Obayashi, Y. Saikawa, S. Furui, K. Shiraishi, S. Kumagai, T. Hayashi, and J. Kotoku. Hepatic tumor classification using texture and topology analysis of non-contrast-enhanced three-dimensional T1-weighted MR images with a radiomics approach. Scientific Reports 9, Article number: 8764 (2019).
平岡裕章、大林一平、赤木和人．パーシステントホモロジーと材料構造解析．人工知能34巻3号，330-338，2019．
山田拓洋，鈴木雄太，三俣千春，小野寛太，上野哲朗，大林一平，平岡裕章，小嗣真人．パーシステントホモロジーを用いた迷路状磁区構造におけるトポロジカル欠陥の可視化．表面と真空 Vol. 62, No. 3, pp. 153–160, 2019．
M. Murakami, S. Kohara, N. Kitamura, J. Akola, H. Inoue, A. Hirata, Y. Hiraoka, Y. Onodera, I. Obayashi, J. Kalikka, N. Hirao, T. Musso, A. S. Foster, Y. Idemoto, O. Sakata, and Y. Ohishi. Ultrahigh-pressure form of SiO2 glass with dense pyrite-type crystalline homology. PHYSICAL REVIEW B 99, 045153 (2019).
平岡裕章、大林一平．パーシステントホモロジーの基礎と材料工学への適用例．日本金属学会会報「まてりあ」58巻1号 (2019), 17-22.
H. Asashiba, E. G. Escolar, Y. Hiraoka, H. Takeuchi. Matrix Method for Persistence Modules on Commutative Ladders of Finite Type. Japan J. Indust. Appl. Math. 36 (2019), 97-130. https://doi.org/10.1007/s13160-018-0331-y
Y. Hiraoka, T. Shirai, and K. D. Trinh. Limit theorems for persistence diagrams. Ann. Appl. Probab. Vol 28, Number 5 (2018), 2740-2780.
G. Kusano, K. Fukumizu, and Y. Hiraoka. Kernel method for persistence diagrams via kernel embedding and weight factor. Journal of Machine Learning Research 18 (2018) 1-41.
I. Obayashi, Y. Hiraoka, M. Kimura. Persistence Diagrams with Linear Machine Learning Models. J. Appl. and Comput. Topology (2018), 1, 421–449. https://doi.org/10.1007/s41468-018-0013-5.
Y. Hiraoka and K. Tsunoda. Limit theorems for random cubical homology. Discrete Comput Geom, 60 (3), 665-687 (2018). https://doi.org/10.1007/s00454-018-0007-z.
M. Kimura, I. Obayashi, Y. Takeichi, R. Murao and Y. Hiraoka. Non-empirical identification of trigger sites in heterogeneous processes using persistent homology. Scientific Reports 8, Article number: 3553 (2018) doi:10.1038/s41598-018-21867-z
M. Buchet, Y. Hiraoka, and I. Obayashi. Persistent homology and materials informatics. In: Tanaka I. (eds) Nanoinformatics. pp 75-95. Springer (2018)
M. Kimura, Y. Takeichi, R. Murao, I. Obayashi, Y. Hiraoka, Y. Liu. Chemical state mapping of heterogeneous reduction of iron ore sinter. Journal of Physics: Conf. Series 849 (2017) 012015.
Inatsu, M., H. Kato, Y. Katsuyama, Y. Hiraoka, and I. Obayashi, 2017: A cyclone identification algorithm with persistent homology and merge-tree, Scientific Online Letters on the Atmosphere, 13, 214-218, doi:10.2151/sola.2017-039.
平岡裕章，西浦廉政．ランダムの中に見る秩序ーパーシステントホモロジーとその応用ー．日本物理学会誌「交流」．Vol. 72, No. 9, 632-640 (2017).
Mohammad Saadatfar, Hiroshi Takeuchi, Nicolas Francois, Vanessa Robins, and Yasuaki Hiraoka. Pore configuration landscape of granular crystallisation. Nature Communications. 8:15082 (2017), DOI: 10.1038/ncomms15082.
T. Ichinomiya, I. Obayashi, and Y. Hiraoka. Persistent homology analysis of craze formation. Physical Review E 95 (1), 012504 (2017).
Y. Hiraoka and T. Shirai. Minimum spanning acycle and lifetime of persistent homology in the Linial-Meshulam process. Random Struct. Alg., 51 (2017), 315-340.
Y. Hiraoka and T. Shirai. Tutte polynomials and random-cluster models in Bernoulli cell complexes. RIMS Kôkyûroku Bessatsu B59 (2016), 289-304.
Y. Hiraoka, T. Nakamura, A. Hirata, E. G. Escolar, K. Matsue, and Y. Nishiura. Hierarchical structures of amorphous solids characterized by persistent homology. Proceedings of the National Academy of Sciences of the United States of America 113 (2016), 7035-7040. doi: 10.1073/pnas.1520877113.
http://www.pnas.org/content/early/2016/06/07/1520877113.abstract
G. Kusano, K. Fukumizu, and Y. Hiraoka. Persistence weighted Gaussian kernel for topological data analysis. Proceedings of the 33rd International Conference on Machine Learning, New York, NY, USA, 2016. JMLR: W&CP volume 48. pp.2004–2013. (arXiv:1601.01741).
Y. Hiraoka. Topological Data Analysis. The Brain & Neural Networks. 23 (2), 55--59 (2016) (Japanese).
Y. Hiraoka and G. Kusano. Relative interleavings and applications to sensor networks. Japan J. Indust. Appl. Math., 33 (2016), 99-120.
M. Gameiro, Y. Hiraoka, I. Obayashi. Continuation of Point Clouds via Persistence Diagrams. Physica D: Nonlinear Phenomena, 334 (2016), 118-132 (doi:10.1016/j.physd.2015.11.011)
E. Escolar and Y. Hiraoka. Persistence Modules on Commutative Ladders of Finite Type. Discrete & Computational Geometry, 55 (2016), 100-157.
E. Escolar and Y. Hiraoka. Persistence of Common Topological Structures by a Commutative Triple Ladder Quiver. Mathematical Challenge in a New Phase of Materials Science, Springer Proceedings in Mathematics and Statistics, 69--82 (2016).
平岡裕章．位相的データ解析とパーシステントホモロジー．日本数学会『数学』68, 361--380 (2016)．
T. Nakamura, Y. Hiraoka, A. Hirata, E. G. Escolar, and Y. Nishiura. Persistent Homology and Many-Body Atomic Structure for Medium-Range Order in the Glass. Nanotechnology 26 (2015) 304001.
Emerson G. Escolar and Yasuaki Hiraoka. Optimal Cycles for Persistent Homology via Linear Programming. Optimization in the Real World --Towards Solving Real-World Optimization Problems--. Mathematics for Industry, Springer (2015), 79-96.
M. Gameiro, Y. Hiraoka, S. Izumi, M. Kramar, K. Mischaikow, and V. Nanda. A topological measurement of protein compressibility, Japan J. Indust. Appl. Math., Vol. 32 (2015), 1-17.
E. Escolar and Y. Hiraoka. Computing Persistence Modules on Commutative Ladders of Finite Type. Lecture Notes in Computer Science 8592 (2014), 144-151.
E. Escolar and Y. Hiraoka. Morse Reduction for Zigzag Complexes. J. Indones. Math. Soc., Vol. 20 (2014), 47- 75, 2014.
E. Escolar and Y. Hiraoka. Computing Optimal Cycles of Homology Groups. A Mathematical Approach to Research Problems of Science and Technology - Theoretical Basis and Developments in Mathematical Modeling, 101--118, Springer, 2014.
平岡裕章，パーシステントホモロジー群 --離散データのトポロジカル解析--，COE Lecture Note Vol. 46: Kyushu University, 63-73，2013．
平岡裕章，不変式環と近似最尤推定復号の設計，COE Lecture Note Vol. 44: Kyushu University, 20-27, 2013.
Y. Hiraoka, Algebraic Structures in Rational Maps of Maximum Likelihood Decodings, IEICE Technical Report IT2012-42 (2012-09), 65-68, 2012.
K. Hayashi and Y. Hiraoka, Rational Maps and Maximum Likelihood Decodings. Japan J. Indust. Appl. Math., Vol. 29 (2012), 37-62.
R. Ghrist and Y. Hiraoka, Network Codings and Sheaf Cohomology, NOLTA 2011, 266-269.
Z. Arai, K. Hayashi, and Y. Hiraoka, Mayer-Vietoris sequences and coverage problems in sensor networks, Japan J. Indust. Appl. Math., Vol. 28 (2011), 237-250.
Y. Hiraoka and Y. Kodama, Normal form and solitons, Lecture Notes in Physics 767, Springer, 175-214, 2009.
Y. Hiraoka, Remarks on collision manifolds and nonexistence of non self-similar collision solutions in the 3-vortex problem, RIMS Kôkyûroku Bessatsu B13 (2009),35-43.
Y. Hiraoka, Topological regularizations of the triple collision singularity in the 3-vortex problem, Nonlinearity Vol.21 (2008), 361-379.
Y. Hiraoka, Z. Arai, K. Hayashi, IEICE Technical Report WBS2008-65, pp51-56, 2008.
Y. Hiraoka, Z. Arai, K. Hayashi, IEICE Technical Report NC2008-4, pp17-22, 2008.
Y. Hiraoka, Construction of approximate solutions for rigorous numerics of symmetric homoclinic orbits, RIMS Kôkyûroku Bessatsu B3 (2007), 11-23.
Y. Hiraoka, Rigorous numerics for symmetric homoclinic orbits in reversible dynamical systems, Kybernetika Vol.43 (2007), 797-806.
Y. Hiraoka and T. Ichinomiya, Homotopy reduction of complex networks, Proceedings of the International Symposium on Topological Aspects of Critical Systems and Networks, World Scientific, 18-23, 2007.
Y. Hiraoka and T. Ogawa, An efficient estimate based on FFT in topological verification method, J. Comput. Appl. Math., Vol.199 (2007), 238—244.
平岡裕章, 小川知之, 無限次元力学系における大域分岐検証, 応用数理(小特集・力学系の位相計算理論) Vol. 15 No.2 (2005), 32-43.
Y. Hiraoka and T. Ogawa, Rigorous numerics for localized patterns to the quintic Swift-Hohenberg equation, Japan J. Indust. Appl. Math., Vol. 22 (2005), 57-75.
S. Day, Y. Hiraoka, K. Mischaikow, and T. Ogawa, Rigorous Numerics for Global Dynamics: A Study of the Swift-Hohenberg Equation, SIAM J. Appl. Dynm. Sys., Vol. 4 (2005), 1-31.
Y. Hiraoka, Conley index and numerical verification, Proceedings of Czech-Japanese Seminar in Applied Mathematics 2004, 47-56.
平岡裕章，小川知之，K. Mischaikow, Swift-Hohenberg方程式の定常解大域分岐のConley指数を用いた検証, Trans. Japan. Soc. Ind. Appl. Math. Vol. 13 (2003), 191-211.
京都大学数理解析研究所講究録（RIMS Kôkyûroku）
R. Ghrist and Y. Hiraoka，Applications of Sheaf Cohomology and Exact Sequences to Network Coding，京都大学数理解析研究所講究録1752（諸分野との協働による数理科学のフロンティア）, 31-40，2011．
林和則，平岡裕章，A dynamical system approach to coding theory: Rational map and maximum likelihood decodings，京都大学数理解析研究所講究録1742（力学系 ー理論から応用へ、応用から理論へー）, 158-164，2011．
荒井迅，林和則，平岡裕章，Mayer-Vietoris 完全系列のセンサーネットワーク被覆問題への応用，京都大学数理解析研究所講究録1616（生命現象と関連した非線形問題の数理）, 41-58，2008．
平岡裕章，リバーシブル系に現れる対称ホモクリニック軌道の計算機援用証明，京都大学数理解析研究所講究録1552（力学系理論の最近の発展）, 12-21，2007．
平岡裕章，5次Swift-Hohenberg方程式における局在パターン解，京都大学数理解析研究所講究録1505（計算科学の基盤技術とその発展）, 80-87，2006．
Y. Hiraoka， Localized patterns in space reversible systems，京都大学数理解析研究所講究録1498（反応拡散系に現れる時・空間パターンのメカニズム）, 113-127，2006．
平岡裕章，無限次元力学系における位相検証，京都大学数理解析研究所講究録1485（力学系の研究—トポロジーと計算機による新展開—）, 136-144，2006．
総説
平岡裕章，パーシステントホモロジー／データの形を捉える，数学セミナー12月号（2017）．
平岡裕章，データに潜む幾何構造:パーシステントホモロジー，数理科学６月号（2015）．
平岡裕章，最尤推定復号の代数構造，数学セミナー３月号（2013）.
平岡裕章，巡回符号からBCH符号へ，数学セミナー８月号（2012）.
平岡裕章，BCH符号の復号，数学セミナー９月号（2012）.
平岡裕章，有理写像と最尤推定復号，数理科学 １１月号（2011）．
平岡裕章，Pawel Pilarczyk，CHomPソフトウェア入門，応用数理 Vol. 18 No. 1(2008), 48-55.
平岡裕章，CHomP入門（基礎編），応用数理サマーセミナー 2007「計算ホモロジーとその応用」講究録，北海道大学数学講究録124．
平岡裕章，コンピューターと数値計算，情報化社会への招待（第９章），学術図書出版社，2007.
書評
T. Kaczynski, K. Mischaikow, and M. Mrozek, Computational Homology, Applied Mathematical Sciences 15, Springer, 数学, 2005
Dissertation @ Osaka University
Topological verifications in infinite dimensional dynamical systems, 2005. 指導教官：小川知之助教授