研究業績

査読付き論文・プロシーディングス

榊原 航也

1. T. Kemmochi, Y. Miyatake, and K. Sakakibara
   Structure-preserving numerical methods for constrained gradient flows of planar curves with explicit tangential velocities
   Japan Journal of Industrial and Applied Mathematics, Published online: 1--29 (DOI: 10.1007/s13160-024-00684-0)

2. Y. Giga, A. Kubo, H. Kuroda, J. Okamoto, K. Sakakibara and M. Uesaka
   Fractional time differential equations as a singular limit of the Kobayashi–Warren–Carter system
   Proceedings of the Royal Society of Edinburgh Section A: Mathematics, Published online 2024: 1--37. (DOI: 10.1017/prm.2024.122)

3. K. Ishii, Y. Kohsaka, N. Miyake, and K. Sakakibara
   A thresholding algorithm for Willmore-type flows via fourth-order linear parabolic equation
   Interfaces and Free Boundaries (2024), published online fast (DOI: 10.4171/IFB/533)

4. Y. Giga, J. Okamoto, K. Sakakibara, and M. Uesaka
   On a singular limit of the Kobayashi−Warren−Carter energy
   Indiana University Mathematics Journal 73 (2024), no. 4, 1453--1491. (DOI: 10.1512/iumj.2024.73.9890)

5. K. Sakakibara and Y. Shimizu
   Numerical analysis of the Plateau problem by the method of fundamental solutions
   Journal of Scientific Computing 100 (2024), article number 2, 20 pp. (DOI: 10.1007/s10915-024-02551-z)

6. M. Kolář, S. Yazaki, and K. Sakakibara
   Image segmentation of flame front of smoldering experiment by gradient flow of curves
   Proceedings of the Conference Algoritmy 2024 (2024), 119--128.

7. M. Nagayama, H. Monobe, K. Sakakibara, K.-I. Nakamura, Y. Kobayashi, and H. Kitahata
   On the reaction-diffusion type modelling of the self-propelled object motion
   Scientific Reports 13 (2023), 12633, 10 pp. (DOI: 10.1038/s41598-023-39395-w)

8. K. Sakakibara, Y. Shimoji, and S. Yazaki
   A simple numerical method for Hele-Shaw type problems by the method of fundamental solutions
   Japan Journal of Industrial and Applied Mathematics 39 (2022), no. 3, 869--887 (Special Issue on Czech-Japanese Seminar in Applied Mathematics 2021 (CJS2021), DOI: 10.1007/s13160-022-00530-1)

9. H. Matano, Y. Mori, M. Nara, and K. Sakakibara
   Asymptotic behavior of fronts and pulses of the bidomain model
   SIAM Journal on Applied Dynamical Systems 21 (2022), no. 1, 616--649. (DOI: 10.1137/21M1416904)

10. K. Sakakibara
    Numerical analysis of constrained total variation flows
    Advanced Studies in Pure Mathematics 85 (2020), 349--358. (DOI: 10.2969/aspm/08510349)

11. K. Sakakibara and Y. Miyatake
    A fully discrete curve-shortening polygonal evolution law for moving boundary problems
    Journal of Computational Physics 424 (2021), 109857, 22 pp. (DOI: 10.1016/j.jcp.2020.109857)

12. Y. Giga, K. Sakakibara, K. Taguchi, and M. Uesaka
    A new numerical scheme for discrete constrained total variation flows and its convergence
    Numerische Mathematik 146 (2020), 181--217. (DOI: 10.1007/s00211-020-01134-y)

13. K. Sakakibara
    Bidirectional numerical conformal mapping based on the dipole simulation method
    Engineering Analysis with Boundary Elements 114 (2020), 45--57. (DOI: 10.1016/j.enganabound.2020.01.009)

14. K. Sakakibara and S. Yazaki
    Structure-preserving numerical scheme for the one-phase Hele-Shaw problems by the method of fundamental solutions
    Computational and Mathematical Methods 1 (2019), no. 6, 25 pp. (DOI: 10.1002/cmm4.1063）

15. K.-I. Nakamura, K. Sakakibara, and S. Yazaki
    Numerical approach to three-dimensional model of cellular electrophysiology by the method of fundamental solutions
    JSIAM Letters 11 (2019), 17--20. (DOI: 10.14495/jsiaml.11.17)

16. K. Sakakibara
    Method of fundamental solutions for biharmonic equation based on Almansi-type decomposition
    Applications of Mathematics 62 (2017), no. 4, 297--317. (DOI: 10.21136/AM.2017.0018-17)

17. K. Sakakibara and S. Yazaki
    Method of fundamental solutions with weighted average condition and dummy points
    JSIAM Letters 9 (2017), 41--44. (DOI: 10.14495/jsiaml.9.41)

18. K. Sakakibara and S. Yazaki
    On invariance of schemes in the method of fundamental solutions
    Applied Mathematics Letters 73 (2017), 16--21. (DOI: 10.1016/j.aml.2017.04.018)

19. K. Sakakibara
    Asymptotic analysis of the conventional and invariant schemes for the method of fundamental solutions applied to potential problems in doubly-connected regions
    Japan Journal of Industrial and Applied Mathematics, 34 (2017), no. 1, 177--228 (DOI: 10.1007/s13160-017-0241-4)

20. K. Sakakibara
    Analysis of the dipole simulation method for two-dimensional Dirichlet problems in Jordan regions with analytic boundaries
    BIT Numerical Mathematics 56 (2016), no. 4, 1369--1400. (DOI: 10.1007/s10543-016-0605-1)

21. K. Sakakibara and M. Katsurada
    A Mathematical Analysis of the Complex Dipole Simulation Method
    Tokyo Journal of Mathematics 38 (2015), no. 2, 309--326 (DOI: 10.3836/tjm/1452806041)

橋本 悠香

22. Y. Hashimoto, S. Sonoda, I. Ishikawa, A. Nitanda, and T. Suzuki
    Koopman-based generalization bound: New aspect for full-rank weights
    Accepted for International Conference on Learning Representations (ICLR) (2024)  (URL: https://openreview.net/forum?id=JN7TcCm9LF)

23. Y. Hashimoto, M. Ikeda, and H. Kadri
    Deep learning with kernels through RKHM and the Perron-Frobenius operator
    Conference on Neural Information Processing Systems (NeurIPS) (2023) (URL: https://openreview.net/forum?id=3ZrGmenVM2)

24. S. Sonoda, Y. Hashimoto, I. Ishikawa, and M. Ikeda
    Deep Ridgelet Transform: Voice with Koopman Operator Proves Universality of Formal Deep Networks
    NeurIPS Workshop on Symmetry and Geometry in Neural Representations (2023) (URL: https://openreview.net/forum?id=2EuaV9an6m)

25. Y. Hashimoto, F. Komura, and M. Ikeda
    Hilbert C*-module for structured data analysis
    Matrix and Operator Equations and Applications (2023) (DOI: 10.1007/16618_2023_58)

26. Y. Hashimoto, M. Ikeda, and H. Kadri
    Learning in RKHM: a C*-algebraic twist for kernel machines
    International Conference on Artificial Intelligence and Statistics (AISTATS) (2023) (URL: https://proceedings.mlr.press/v206/hashimoto23a.html)

27. Y. Hashimoto, Z. Wang, and T. Matsui
    C*-algebra net: a new approach generalizing neural network parameters to C*-algebra
    International Conference on Machine Learning (ICML) (2022) (URL: https://proceedings.mlr.press/v162/hashimoto22a.html)

28. Y. Hashimoto and T. Nodera
    A preconditioning technique for Krylov subspace methods in RKHSs
    Journal of Computational and Applied Mathematics 415 (2022), 114490 (DOI: 10.1016/j.cam.2022.114490)

29. Y. Hashimoto, I. Ishikawa, M. Ikeda, F. Komura, T. Katsura, and Y. Kawahara
    Reproducing kernel Hilbert C*-module and kernel mean embeddings
    Journal of Machine Learning Research 22 (2021), no. 267, 1--56 (URL: https://www.jmlr.org/papers/v22/20-1346.html)

30. Y. Hashimoto and T. Nodera
    Krylov subspace methods for estimating operator-vector multiplications in Hilbert spaces
    Japan Journal of Industrial and Applied Mathematics 38 (2021), 781--803 (DOI: 10.1007/s13160-021-00460-4)

31. Y. Hashimoto and T. Nodera
    Inexact Rational Krylov Method for Evolution Equations
    BIT Numerical Mathematics 61 (2021), 473--502 (DOI: 10.1007/s10543-020-00829-w)

32. Y. Hashimoto, I. Ishikawa, M. Ikeda, Y. Matsuo, and Y. Kawahara
    Krylov Subspace Method for Nonlinear Dynamical Systems with Random Noise
    Journal of Machine Learning Research 21 (2020), no. 172, 1--29 (URL: https://www.jmlr.org/papers/v21/19-993.html)

33. Y. Hashimoto and T. Nodera
    Shift-invert Rational Krylov method for an operator φ-function of an unbounded linear operator
    Japan Journal of Industrial and Applied Mathematics 36 (2019), 421--433 (DOI: 10.1007/s13160-019-00347-5)

34. I. Ishikawa, K. Fujii, M. Ikeda, Y. Hashimoto, and Y. Kawahara
    Metric on Nonlinear Dynamical Systems with Koopman Operators
    Conference on Neural Information Processing Systems (NeurIPS) (2018) (URL: https://papers.nips.cc/paper_files/paper/2018/hash/fa1e9c965314ccd7810fb5ea838303e5-Abstract.html)

35. Y. Hashimoto and T. Nodera
    Double-shift-invert Arnoldi method for computing the matrix exponential
    Japan Journal of Industrial and Applied Mathematics 35 (2018), 727--738 (DOI: 10.1007/s13160-018-0309-9)

36. Y. Hashimoto and T. Nodera
    Shift-invert Rational Krylov Method for Evolution Equation
    Computational Techniques and Applications Conference, ANZIAM Journal 58 (2017), C149--C161 (DOI: 10.21914/anziamj.v58i0.11622)

37. Y. Hashimoto，T. Nodera
    Inexact Shift-invert Arnoldi Method for Evolution Equation
    ANZIAM Journal 58 (2016)，E1--E2 (DOI: 10.21914/anziamj.v58i0.10766)

38. 橋本悠香，野寺隆
    線形発展方程式のための Inexact Shift-invert Arnoldi 法
    情報処理学会論文誌 57 (2016)，no. 10，2250--2259 (URL: http://id.nii.ac.jp/1001/00175021/)

プレプリント

榊原 航也

1. Y. Giga, A. Kubo, H. Kuroda, J. Okamoto, and K. Sakakibara
   Piecewise constant profiles minimizing total variation energies of Kobayashi-Warren-Carter type with fidelity
   arXiv:2408.04228

2. K. Sakakibara
   Well-conditioned dipole-type method of fundamental solutions: derivation and its mathematical analysis
   arXiv:2408.00212

3. K. Morikuni, K. Sakakibara, and A. Takatsu
   Error estimate for regularized optimal transport problems via Bregman divergence
   arXiv:2309.11666

4. 榊原 航也
   基本解近似解法の現状
   日本数学会「数学」

橋本 悠香

5. D. Giannakis, Y. Hashimoto, M. Ikeda, I. Ishikawa, and J. Slawinska
   Koopman spectral analysis of skew-product dynamics on Hilbert C*-modules
   arXiv:2307.08965

6. R. Hataya and Y. Hashimoto
   Noncommutative C*-algebra Net: Learning Neural Networks with Powerful Product Structure in C*-algebra
   arXiv: 2302.01191

1. K. Sakakibara and P. Wang
   TBA

2. S. Kobayashi, K. Sakakibara, and T. Uechi
   TBA

3. Y. Hashimoto, N. Ogawa, and K. Sakakibara
   TBA

1. 小川 尚比古，榊原 航也，"カーネル法のための再生核ヒルベルト空間"（ポスター発表），数学と現象 in 伊香保，ホテルニュー伊香保，2024年8月30日〜9月1日．

2. 上地 泰慧，榊原 航也，"細胞の運動と移動境界問題"（ポスター発表），数学と現象 in 伊香保，ホテルニュー伊香保，2024年8月30日〜9月1日．

3. 上地 泰慧，"細胞運動の移動境界モデル"，数学と現象 in 清里，2025年2月2日〜4日．（榊原との共同研究）

4. Naohiko Ogawa, "Kernel-Based Numerical Scheme for Geometric Flows", Czech–Japanese Seminar in Applied Mathematics 2025, Technical University of Liberec, August 25--29, 2025.（榊原，橋本との共同研究）

5. Taikei Uechi, "Dynamics of the wave-pinning model for cell polarity", Czech–Japanese Seminar in Applied Mathematics 2025, Technical University of Liberec, August 25--29, 2025.（小林俊介氏（宮崎大学），榊原との共同研究）

6. 上地 泰慧，"2次元 wave-pinning モデルにおけるマルチタイムスケールの界面ダイナミクス"，数学と現象 in 岩舟，2025年9月8日〜10日．

7. 小川 尚比古，"カーネル法を用いた曲線短縮流の数値計算"，数学と現象 in 岩舟，2025年9月8日〜10日．

8. 正木 歩，"曲線短縮流と曲線上の拡散方程式のカップリング問題の解析"，数学と現象 in 岩舟，2025年9月8日〜10日．

9. Taikei Uechi, "Dynamics of the wave-pinning model for cell polarity", 2025 International workshop on modeling, analysis and computation with application in Economics and AI, Shanghai University of Finance and Economics, China, October 25--26, 2025.

10. Naohiko Ogawa, "Kernel-based numerical scheme for geometric flows", 2025 International workshop on modeling, analysis and computation with application in Economics and AI, Shanghai University of Finance and Economics, China, October 25--26, 2025.

11. Naohiko Ogawa, "Kernel-based numerical scheme for geometric flows", Czech Academy of Sciences–Kanazawa University Workshop, Shiinoki Cultural Complex, Ishikawa, Japan, November 2--3, 2025