Manabu Machida Lecturer Institute for Medical Photonics Research Hamamatsu University School of Medicine JST PRESTO researcher Address: 1-20-1 Handayama, Higashi-ku, Hamamatsu,      Shizuoka 431-3192, Japan Email:  Physical Applied Mathematics, Scientific Computing, Inverse Problems Erdös Number: 3 Einstein Number: 4 Ph.D., The University of Tokyo

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Teaching

Doctoral course (Cooperative Major in Medical Photonics): Light propagation in biological tissue

Spring 2020

メディカル生体情報処理学 (1st&2nd lectures)

生体内光伝播

Department of Life Science and Medical Bioscience, Waseda University: Calculus

Fall 2020

数学Ｂ１（微分積分）　生医

多変数の微分積分

Department of Mathematics, Kyoto University: Inverse problems for partial differential equations

Fall 2020

数学特別講義（応用数学Ｉ）

偏微分方程式の逆問題

Some past teaching materials including lecture notes can be found below.

• Numerical methods (University of Michigan, Math 471 course page)
• Partial differential equations (University of Michigan, Math 454 course page)
• Linear algebra (University of Michigan, Math 417 course page)
• Lecture note on Case's method in linear transport theory (pdf)
• Lecture note on inverse problems by Carleman estimates (pdf)

Miscellaneous materials.

• Optics and Inverse Problems: Optical Tomography (Japanese), 日本物理学会誌 (membership journal of the Physical Society of Japan) 72:10, 712–716, October 2017.
• note: rotated boiled egg (Japanese), May 2002.

Recent Papers

• T. Mimura, M. Machida, S. Okawa, H. Kawaguchi, Y. Tanikawa, and Y. Hoshi,
  Imaging the human whole thyroid using three-dimensional diffuse optical tomography,
  submitted.

• (arXiv:2009.04277)
  M. Machida and M. Yamamoto,
  Global Lipschitz stability for inverse problems for radiative transport equations,
  submitted.

• A. Capart, S. Ikegaya, E. Okada, M. Machida, Y. Hoshi,
  Experimental test of the χ² indicator for the degree of validness of the diffusion approximation,
  submitted.

• (arXiv:2005.11946)
  K. Amagai, Y. Hatano, and M. Machida,
  Linear transport in porous media,
  to appear in Journal of Computational and Theoretical Transport.
  doi: 10.1080/23324309.2020.1842453

• (arXiv:1304.5207)
  M. Machida,
  Chandrasekhar polynomials - A brief review,
  submitted.

• (arXiv:2005.09937)
  M. Machida, Y. Hoshi, K. Kagawa, and K. Takada
  Decay behavior and optical parameter identification for spatial-frequency domain imaging by the radiative transport equation,
  Journal of the Optical Society of America A 37:12, 2020–2031, November 2020.
  doi: 10.1364/JOSAA.402124

• (arXiv:1912.11375)
  Y. Jiang, M. Machida, and N. Todoroki,
  Diffuse optical tomography by simulated annealing via a spin Hamiltonian,
  submitted.

• J. J. Liu, M. Machida, G. Nakamura, G. Nishimura, C. L. Sun,
  On fluorescence imaging: diffusion equation model and recovery of absorption coefficient of fluorophores,
  to appear in Science China Mathematics.
  doi: 10.1007/s11425-020-1731-y

• M. Machida, A. Kawamoto, Y. Tanikawa, and Y. Hoshi,
  submitted.

• (arXiv:1908.00726)
  K. Amagai, M. Yamakawa, M. Machida, and Y. Hatano,
  The linear Boltzmann equation in column experiments of porous media,
  Transport in Porous Media 132:2, 311–331, March 2020.
  doi: 10.1007/s11242-020-01393-1

• (arXiv:1903.01281)
  C. Sun, G. Nakamura, G. Nishimura, Y. Jiang, J. Liu, and M. Machida,
  Fast and robust reconstruction algorithm for fluorescence diffuse optical tomography assuming a cuboid target,
  Journal of the Optical Society of America A 37:2, 231–239, February 2020.
  doi: 10.1364/JOSAA.37.000231

• (arXiv:1811.06223)
  A. Kawamoto and M. Machida,
  Lipschitz stability in inverse source and inverse coefficient problems for a first- and half-order time-fractional diffusion equation,
  SIAM Journal on Mathematical Analysis 52:1, 967–1005, February 2020.
  doi: 10.1137/18M1235776

• (arXiv:1706.04500)
  M. Machida and G. Nakamura,
  Born series for the Robin boundary condition,
  Journal of Mathematical Physics 61:1, 013502 (17pp), January 2020.
  doi: 10.1063/1.5095179

• (arXiv:1608.07914)
  A. Kawamoto and M. Machida,
  Global Lipschitz stability for a fractional inverse transport problem by Carleman estimates,
  Applicable Analysis, 2021.
  doi: 10.1080/00036811.2019.1620931

Recent Talks

• [invited] Lipschitz stability for the inverse problem of determining coefficients of the radiative transport equation, Colloquium（談話会）, Department of Mathematics, Kyoto University, Kyoto, October 21, 2020 (Zoom).

• 多孔質媒体中の分子の線形ボルツマン輸送, 日本流体力学会（The Japan Society of Fluid Mechanics）年会2020, Yamaguchi University (Zoom), September 18, 2020.

• [invited] The linear Boltzmann equation as a governing equation in porous media, Summer Intensive Seminar on Inverse Modelling and Computation, Zoom Conference (Shanghai University of Finance and Economics, and Fudan University), August 3-6, 2020.

• [invited] Diffuse optical tomography with a simulated annealing Monte Carlo algorithm, The 10th International Conference Inverse Problems: Modeling and Simulation, Malta, May 16-22, 2020. (postponed until May 22-28, 2022)

• [Talk given by N. Todoroki] スピン系を利用した拡散光トモグラフィー (with Y. Jiang and N. Todoroki), The Physical Society of Japan 75th Annual Meeting, Nagoya University, March 16, 2020. (canceled due to COVID-19)

• Robin境界条件におけるBorn級数 (with G. Nakamura), JSIAM 第16回研究部会連合発表会, Chuo University, March 4, 2020. (canceled due to COVID-19)

• [invited] A numerical method for inverse transport problems, 偏微分方程式による逆問題解析とその周辺 (Analysis of Inverse Problems through Partial Differential Equations and Related Topics), RIMS, Kyoto, January 10, 2020.

• [invited] 輻射輸送方程式の新解法と光トモグラフィー, 日本学術会議　第9回計算力学シンポジウム, Tokyo, December 11, 2019.

• Optical tomography: Some mathematical and numerical aspects, Shanghai University of Finance and Economics, Shanghai, November 22, 2019.

• The linear transport in porous media, The 26th International Conference on Transport Theory (ICTT-26), Sorbonne University, Paris, September 26, 2019.

• ランダム媒質の光学特性値決定, 日本物理学会2019年秋季大会, 岐阜大学, Gifu, September 11, 2019.

• [invited] Near-infrared spectroscopy, Summer School on Applied Inverse Problems and Related Topics, Tambara, Gumma, August, 2019.

• [invited] Optical medical imaging in the radiative transport regime, International Congress on Industrial and Applied Mathematics (ICIAM), Universitat de València, Valencia, July 18, 2019.

• [invited] Time-fractional derivatives in inverse transport problems, International Congress on Industrial and Applied Mathematics (ICIAM), Universitat de València, Valencia, July 17, 2019.

• [invited] Lipschitz stability in inverse diffusion problems with first- and half-order derivatives, Applied Inverse Problems Conference (AIP), Université Grenoble Alpes, Grenoble, July 8, 2019.

• [invited] Spatial-frequency-domain optical tomography in the nondiffusive regime, Applied Inverse Problems Conference (AIP), Université Grenoble Alpes, Grenoble, July 8, 2019

• [poster] Spatial-frequency-domain optical tomography in the radiative transport regime, European Conference on Biomedical Optics (ECBO), Munich, June 24, 2019.

• 解析解に基づく輻射輸送方程式の数値計算, JSIAM 第15回研究部会連合発表会, University of Tsukuba, March 4, 2019.

• [invited] Stability analysis of inverse problems for 1+1/2 fractional parabolic equations, A3 Workshop in Applied Inverse Problems, Okinawa, Japan, January 29, 2019.

Java Applet

EZ-RTE is now released!  →  https://sites.google.com/site/ezrte13/

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日本応用数理学会　2019年研究部会連合発表会優秀講演賞
(JSIAM 2019 Best Talk Award)  学会記事

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• Biography
• Publications
• Conferences and Talks

[Hamamatsu, Japan]

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