MACHIDA Manabu

Researcher Information

Degree

• PhD（The University of Tokyo）

URL

https://jglobal.jst.go.jp/detail?JGLOBAL_ID=201801003790737439

Research funding number

• 40396916

ORCID ID

•  https://orcid.org/0000-0002-1830-0760

J-Global ID

• 201801003790737439

Research Interests

• optical tomography   inverse problems   radiative transfer   

Research Areas

• Informatics / Computational science
• Natural sciences / Applied mathematics and statistics
• Natural sciences / Mathematical physics and basic theory

Academic & Professional Experience

• 2023 - Today  Kindai University工学部情報学科准教授
• 2020 - Today  Japan Science and Technology AgencyPRESTO Researcher
• 2017 - 2023  Hamamatsu University School of MedicinePreeminent Medical Photonics Education & Research CenterLecturer

Association Memberships

• AMS   SIAM   THE PHYSICAL SOCIETY OF JAPAN   THE JAPAN SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS   

Published Papers

• Coarse-graining of perplexity for the spatial distribution of molecules

  Lili Xu; Chi Zhang; Soho Oyama; Manabu Machida; Tomoaki Kahyo; Mitsutoshi Setou

  Physical Review E American Physical Society (APS) 109 (1) 2470-0045 2024/01
• The inverse Rytov series for diffuse optical tomography

  Machida M

  Inverse Problems IOP Publishing 39 (10) 105012  0266-5611 2023/09 [Refereed]
   

  Abstract The Rytov approximation is known in near-infrared spectroscopy including diffuse optical tomography. In diffuse optical tomography, the Rytov approximation often gives better reconstructed images than the Born approximation. Although related inverse problems are nonlinear, the Rytov approximation is almost always accompanied by the linearization of nonlinear inverse problems. In this paper, we will develop nonlinear reconstruction with the inverse Rytov series. By this, linearization is not necessary and higher order terms in the Rytov series can be used for reconstruction. The convergence and stability are discussed. We find that the inverse Rytov series has a recursive structure similar to the inverse Born series.
• Homogenization and inverse problems for fractional diffusion equations

  Kawamoto A; Machida M; Yamamoto M

  Fractional Calculus and Applied Analysis Springer Science and Business Media LLC 26 (5) 2118 - 2165 1311-0454 2023/08 [Refereed]
  
• Expressions of the peak time for time-domain boundary measurements of diffuse light

  Eom J Y; Machida M; Nakamura G; Nishimura G; Sun C L

  Journal of Mathematical Physics AIP Publishing 64 083504  0022-2488 2023/08 [Refereed]
   

  Light propagation through diffusive media can be described by the diffusion equation in a space–time domain. Furthermore, fluorescence can be described by a system of coupled diffusion equations. This paper analyzes time-domain measurements. In particular, the temporal point-spread function is measured at the boundary of a diffusive medium. Moreover, the temporal profile of fluorescence is considered. In both cases, we refer to the maximum temporal position of measured light as the peak time. In this paper, we provide proofs of the existence and uniqueness of the peak time and give explicit expressions of the peak time. The relationship between the peak time and the object position in a medium is clarified.
• Spatial distribution of the Shannon entropy for mass spectrometry imaging

  Xu L; Kikushima K; Sato S; Islam A; Sato T; Aramaki S; Zhang C; Sakamoto T; Eto F; Takahashi Y; Yao I; Machida M; Kahyo T; Setou M

  PLOS ONE Public Library of Science (PLoS) 18 (4) e0283966  2023/04 [Refereed]
   

  Mass spectrometry imaging (MSI) allows us to visualize the spatial distribution of molecular components in a sample. A large amount of mass spectrometry data comprehensively provides molecular distributions. In this study, we focus on the information in the obtained data and use the Shannon entropy as a quantity to analyze MSI data. By calculating the Shannon entropy at each pixel on a sample, the spatial distribution of the Shannon entropy is obtained from MSI data. We found that low-entropy pixels in entropy heat maps for kidneys of mice had different structures between two ages (3 months and 31 months). Such changes cannot be visualized by conventional imaging techniques. We further propose a method to find informative molecules. As a demonstration of the proposed scheme, we identified two molecules by setting a region of interest which contained low-entropy pixels and by exploring changes of peaks in the region.
• Changes of Mass Spectra Patterns on a Brain Tissue Section Revealed by Deep Learning with Imaging Mass Spectrometry Data

  Yamada H; Xu L; Eto F; Takeichi R; Islam A; Mamun M A; Zhang C; Yao I; Sakamoto T; Aramaki S; Kikushima K; Sato T; Takahashi Y; Machida M; Kahyo T; Setou M

  Journal of the American Society for Mass Spectrometry American Chemical Society (ACS) 33 (9) 1607 - 1614 1044-0305 2022/09 [Refereed]
  
• On fluorescence imaging: The diffusion equation model and recovery of the absorption coefficient of fluorophores

  Liu J J; Machida M; Nakamura G; Nishimura G; Sun C L

  Science China Mathematics Springer Science and Business Media LLC 65 (6) 1179 - 1198 1674-7283 2022/06 [Refereed]
  
• Linear Transport in Porous Media

  Amagai K; Hatano Y; Machida M

  Journal of Computational and Theoretical Transport Informa UK Limited 50 (5) 377 - 389 2332-4309 2021/09 [Refereed]
  
• Diffuse optical tomography by simulated annealing via a spin Hamiltonian

  Jiang Y; Machida M; Todoroki N

  Journal of the Optical Society of America A Optica Publishing Group 38 (7) 1032 - 1040 1084-7529 2021/06 [Refereed]
   

  Diffuse optical tomography (DOT) is an imaging modality that uses near-infrared light. Although iterative numerical schemes are commonly used for its inverse problem, correct solutions are not obtained unless good initial guesses are chosen. We propose a numerical scheme of DOT, which works even when good initial guesses of optical parameters are not available. We use simulated annealing (SA), which is a method of the Markov-chain Monte Carlo. To implement SA for DOT, a spin Hamiltonian is introduced in the cost function, and the Metropolis algorithm or single-component Metropolis–Hastings algorithm is used. By numerical experiments, it is shown that an initial random spin configuration is brought to a converged configuration by SA, and targets in the medium are reconstructed. The proposed numerical method solves the inverse problem for DOT by finding the ground state of a spin Hamiltonian with SA.
• Experimental tests of indicators for the degree of validness of the diffusion approximation

  Capart A; Ikegaya S; Okada E; Machida M; Hoshi Y

  Journal of Physics Communications IOP Publishing 5 (2) 025012  2021/02 [Refereed]
   

  Abstract The diffusion approximation has been one of the central topics in near-infrared spectroscopy (NIRS). When NIRS measurements are analyzed by the diffusion theory, the measurements must be performed in the diffusive regime. However, since most of past researches have focused on theoretical or qualitative nature of the diffusion approximation, it is not easy to know if each measurement is designed in the diffusive regime. In this paper, we consider the diffusion approximation quantitatively and propose indicators that quantify the degree of validness of the diffusion approximation. The difference between the measurement and diffusion theory can be evaluated with the χ² value, ℓ¹ and ℓ² norms, and Kullback-Leibler divergence. We conduct a liquid phantom experiment to test the proposed χ² value. Moreover, the χ² value is further investigated by Monte Carlo simulations. We find the χ² value becomes significantly large when measurements are performed in the nondiffusive or transport regime. The proposed indicators similarly work. In particular, the χ² value is shown to work as an indicator which evaluates the degree of validness of the diffusion approximation. These indicators are general and can be used for different numerical, experimental, and clinical measurements in NIRS.
• Global Lipschitz stability for a fractional inverse transport problem by Carleman estimates

  Kawamoto A; Machida M

  Applicable Analysis Informa UK Limited 100 (4) 752 - 771 0003-6811 2021/02 [Refereed]
  
• Decay behavior and optical parameter identification for spatial-frequency domain imaging by the radiative transport equation

  Machida M; Hoshi Y; Kagawa K; Takada K

  Journal of the Optical Society of America A Optica Publishing Group 37 (12) 2020 - 2031 1084-7529 2020/11 [Refereed]
   

  The decay behavior of specific intensity is studied for spatial-frequency domain imaging (SFDI). It is shown using the radiative transport equation that the decay is given by a superposition of different decay modes, and the decay rates of these modes are determined by spatial frequencies and Case’s eigenvalues. This explains why SFDI can focus on shallow regions. The fact that light with nonzero spatial frequency rapidly decays makes it possible to exclusively extract optical properties of the top layer of a layered medium. We determine optical properties of the top layer of a solid phantom. This measurement is verified with different layered media of numerical phantoms.
• The Linear Boltzmann Equation in Column Experiments of Porous Media

  Amagai K; Yamakawa M; Machida M; Hatano Y

  Transport in Porous Media Springer Science and Business Media LLC 132 (2) 311 - 331 0169-3913 2020/03 [Refereed]
  
• Lipschitz Stability in Inverse Source and Inverse Coefficient Problems for a First- and Half-order Time-fractional Diffusion Equation

  Atsushi Kawamoto; Manabu Machida

  SIAM Journal on Mathematical Analysis Society for Industrial & Applied Mathematics (SIAM) 52 (1) 967 - 1005 0036-1410 2020/02 [Refereed]
  
• Fast and robust reconstruction algorithm for fluorescence diffuse optical tomography assuming a cuboid target

  Sun C L; Nakamura G; Nishimura G; Jiang Y; Liu J J; Machida M

  Journal of the Optical Society of America A Optica Publishing Group 37 (2) 231 - 239 1084-7529 2020/01 [Refereed]
   

  A fast algorithm for fluorescence diffuse optical tomography is proposed. The algorithm is robust against the choice of initial guesses. We estimate the position of a fluorescent target by assuming a cuboid (rectangular parallelepiped) for the fluorophore target. The proposed numerical algorithm is verified by a numerical experiment and an experiment with a meat phantom. The target position is reconstructed with a cuboid from measurements in the time domain. Moreover, the long-time behavior of the emission light is investigated making use of the analytical solution to the diffusion equation.
• Born series for the photon diffusion equation perturbing the Robin boundary condition

  Machida M; Nakamura G

  Journal of Mathematical Physics AIP Publishing 61 (1) 013502  0022-2488 2020/01 [Refereed]
   

  The photon diffusion equation is solved making use of the Born series for the Robin boundary condition. We develop a general theory for arbitrary domains with smooth enough boundaries and explore the convergence. The proposed Born series is validated by numerical calculation in the three-dimensional half space. It is shown that in this case, the Born series converges regardless the value of the impedance term in the Robin boundary condition.
• Numerical algorithms of the radiative transport equation using rotated reference frames for optical tomography with structured illumination

  Machida M

  Journal of Quantitative Spectroscopy and Radiative Transfer Elsevier BV 234 124 - 138 0022-4073 2019/09 [Refereed]
  
• A Hybrid Inversion Scheme Combining Markov Chain Monte Carlo and Iterative Methods for Determining Optical Properties of Random Media

  Jiang Y; Hoshi Y; Machida M; Nakamura G

  Applied Sciences MDPI AG 9 (17) 3500  2019/08 [Refereed]
   

  Near-infrared spectroscopy (NIRS) including diffuse optical tomography is an imaging modality which makes use of diffuse light propagation in random media. When optical properties of a random medium are investigated from boundary measurements of reflected or transmitted light, iterative inversion schemes such as the Levenberg–Marquardt algorithm are known to fail when initial guesses are not close enough to the true value of the coefficient to be reconstructed. In this paper, we investigate how this weakness of iterative schemes is overcome using Markov chain Monte Carlo. Using time-resolved measurements performed against a polyurethane-based phantom, we present a case that the Levenberg–Marquardt algorithm fails to work but the proposed hybrid method works well. Then, with a toy model of diffuse optical tomography we illustrate that the Levenberg–Marquardt method fails when it is trapped by a local minimum but the hybrid method can escape from local minima by using the Metropolis–Hastings Markov chain Monte Carlo algorithm until it reaches the valley of the global minimum. The proposed hybrid scheme can be applied to different inverse problems in NIRS which are solved iteratively. We find that for both numerical and phantom experiments, optical properties such as the absorption and reduced scattering coefficients can be retrieved without being trapped by a local minimum when Monte Carlo simulation is run only about 100 steps before switching to an iterative method. The hybrid method is compared with simulated annealing. Although the Metropolis–Hastings MCMC arrives at the steady state at about 10,000 Monte Carlo steps, in the hybrid method the Monte Carlo simulation can be stopped way before the burn-in time.
• The time-fractional radiative transport equation—Continuous-time random walk, diffusion approximation, and Legendre-polynomial expansion

  Machida M

  Journal of Mathematical Physics AIP Publishing 58 (1) 013301  0022-2488 2017/01 [Refereed]
   

  We consider the radiative transport equation in which the time derivative is replaced by the Caputo derivative. Such fractional-order derivatives are related to anomalous transport and anomalous diffusion. In this paper we describe how the time-fractional radiative transport equation is obtained from continuous-time random walk and see how the equation is related to the time-fractional diffusion equation in the asymptotic limit. Then we solve the equation with Legendre-polynomial expansion.
• How to Construct Three-Dimensional Transport Theory Using Rotated Reference Frames

  Machida M

  Journal of Computational and Theoretical Transport Informa UK Limited 45 (7) 594 - 609 2332-4309 2016/11 [Refereed]
  
• The radiative transport equation in flatland with separation of variables

  Machida M

  Journal of Mathematical Physics AIP Publishing 57 (7) 073301  0022-2488 2016/07 [Refereed]
   

  The linear Boltzmann equation can be solved with separation of variables in one dimension, i.e., in three-dimensional space with planar symmetry. In this method, solutions are given by superpositions of eigenmodes which are sometimes called singular eigenfunctions. In this paper, we explore the singular-eigenfunction approach in flatland or two-dimensional space.
• Polarization oscillations of near-field thermal emission

  Machida M; Narimanov E; Schotland J C

  Journal of the Optical Society of America A The Optical Society 33 (6) 1071 - 1075 1084-7529 2016/06 [Refereed]
  
• The Green's function for the three-dimensional linear Boltzmann equation via Fourier transform

  Machida M

  Journal of Physics A: Mathematical and Theoretical IOP Publishing 49 (17) 175001  1751-8113 2016/03 [Refereed]
  
• Radiative transport and optical tomography with large datasets

  Machida M; Panasyuk G Y; Wang Z-M; Markel V A; Schotland J C

  Journal of the Optical Society of America A The Optical Society 33 (4) 551 - 558 1084-7529 2016/03 [Refereed]
  
• Inverse Born series for the radiative transport equation

  Machida M; Schotland J C

  Inverse Problems IOP Publishing 31 (9) 095009  0266-5611 2015/08 [Refereed]
  
• An FN method for the radiative transport equation in three dimensions

  Machida M

  Journal of Physics A: Mathematical and Theoretical IOP Publishing 48 (32) 325001  1751-8113 2015/07 [Refereed]
  
• Global Lipschitz stability in determining coefficients of the radiative transport equation

  Machida M; Yamamoto M

  Inverse Problems IOP Publishing 30 (3) 035010  0266-5611 2014/02 [Refereed]
  
• Singular eigenfunctions for the three-dimensional radiative transport equation

  Machida M

  Journal of the Optical Society of America A The Optical Society 31 (1) 67 - 74 1084-7529 2013/12 [Refereed]
  
• Diffuse optical tomography in the presence of a chest wall

  Ban H Y; Busch D R; Pathak S; Moscatelli F A; Machida M; Schotland J C; Markel V A; Yodh A G

  Journal of Biomedical Optics SPIE-Intl Soc Optical Eng 18 (2) 026016  1083-3668 2013/02 [Refereed]
  
• ESR intensity and the Dzyaloshinsky-Moriya interaction of the nanoscale molecular magnet V15

  Machida M; Iitaka T; Miyashita S

  Physical Review B American Physical Society (APS) 86 (22) 224412  1098-0121 2012/12 [Refereed]
  
• Survival probability and saturation energy in periodically driven quantum chaotic systems

  Machida M; Miyashita S

  Physics Letters A Elsevier BV 376 (22) 1777 - 1780 0375-9601 2012/04 [Refereed]
  
• The Green's function for the radiative transport equation in the slab geometry

  Machida M; Panasyuk G Y; Schotland J C; Markel V A

  Journal of Physics A: Mathematical and Theoretical IOP Publishing 43 (6) 065402 - 065402 1751-8113 2010/02 [Refereed]
  
• Diffusion approximation revisited

  Machida M; Panasyuk G Y; Schotland J C; Markel V A

  Journal of the Optical Society of America A Optica Publishing Group 26 (5) 1291 - 1300 1084-7529 2009/05 [Refereed]
  
• Transient Oscillation of Currents in Quantum Hall Effect of Bloch Electrons

  Machida M; Goryo J; Hatano N

  Journal of the Physical Society of Japan Physical Society of Japan 77 (2) 024713 - 024713 0031-9015 2008/02 [Refereed]
  
• Temporal Oscillation of Conductances in Quantum Hall Effect of Bloch Electrons

  Machida M; Hatano N; Goryo J

  Journal of the Physical Society of Japan Physical Society of Japan 75 (6) 063704 - 063704 0031-9015 2006/06 [Refereed]
  
• Distribution of the spacing between two adjacent avoided crossings

  Machida M; Saito K

  Physical Review E American Physical Society (APS) 72 (5) 056206  1539-3755 2005/11 [Refereed]
  
• Dzyaloshinskii-Moriya interactions and adiabatic magnetization dynamics in molecular magnets

  De Raedt H; Miyashita S; Michielsen K; Machida M

  Physical Review B American Physical Society (APS) 70 (6) 064401  1098-0121 2004/08 [Refereed]
  
• Frequency Dependence of Quantum Localization in a Periodically Driven System

  Machida M; Saito K; Miyashita S

  Journal of the Physical Society of Japan Physical Society of Japan 71 (10) 2427 - 2433 0031-9015 2002/10 [Refereed]
  

Books etc

• Practical Inverse Problems and Their Prospects

  (ed.) Takiguchi T, Ohe T, Cheng J, Hua C (ContributorSec. 5 Radiative Transport Equation in Optical Tomography)Springer, Singapore 2023/09
• 生体ひかりイメージング基礎と応用

  (編集委員)岡田英史、川口拓之、西條芳文、渡辺英寿 (Contributor第2章第1節 pp.91-96)エヌ・ティー ・エス 2021/12 

  光輸送方程式について

Conference Activities & Talks

• 3次元解析的離散方位法

  町田 学

  日本流体力学会 年会2023  2023/09
• Inverse problems for the Duffing equation in pediatrics  [Invited]

  Machida M

  ICIAM 2023  2023/08
• Nonlinear Rytov Approximation as a Practial Inversion Scheme for Optical Tomography  [Invited]

  Machida M

  BIRS Workshop 2023 Leveraging Model- and Data-Driven Methods in Medical Imaging,  2023/06
• 生体の情報抽出のための 数理の活用法  [Invited]

  町田 学

  JST ACT-X 「生命と化学」 第1回研究者交流会議 「生命と化学と情報科学」  2023/05
• Linear Boltzmann equation for transport phenomena in porous media  [Invited]

  町田 学

  北海道大学 MMCセミナー  2022/11
• 多孔質媒体中の分子の異常拡散

  町田 学

  日本流体力学会 年会2022  2022/09
• 逆級数を用いた偏微分方程式の逆問題解法  [Invited]

  町田 学

  日本応用数理学会 2022年度年会  2022/09
• 医学のための数理科学研究

  町田 学

  第3回浜松医科大学学内研究交流会  2022/06
• 偏微分方程式の逆問題の逆級数による再構成法  [Invited]

  町田 学

  岡山応用数学セミナー  2022/06
• Diffuse optical tomography with a simulated annealing Monte Carlo algorithm  [Invited]

  Machida M

  The 10th International Conference Inverse Problems: Modeling and Simulation  2022/05
• 多孔質媒体中の輸送の支配方程式としての輻射輸送方程式

  町田 学

  日本応用数理学会 第18回研究部会連合発表会  2022/03
• Direct and iterative reconstruction methods in optical tomography  [Invited]

  Machida M

  Practical inverse problems and their prospects  2022/03
• Diffuse optical tomography using simulated annealing  [Invited]

  Machida M

  逆問題における理論と実用  2022/01
• Optical tomography and biophysics  [Invited]

  Machida M

  日本生物物理学会年会  2021/11
• 強散乱下の逆問題:光トモグラフィー  [Invited]

  町田 学

  日本光学会年次学術講演会  2021/10
• 光トモグラフィーを通じた医学と理学の交流  [Invited]

  町田 学

  静岡大学理学部x 浜松医科大学 研究情報交換会  2021/09
• 逆級数を用いた逆問題解法による 光トモグラフィー  [Invited]

  町田 学

  数理情報学談話会  2021/06
• Spatio-temporal frequency domain imaging using time-resolving CMOS image sensor and stripe pattern projection

  Takada K; Osada K; Machida M; Hoshi Y; Yasutomi K; Kawahito S; Kagawa K

  SPIE Photonics West BiOS  2021/03
• 輻射輸送方程式の係数決定逆問題 に対するリプシッツ安定性  [Invited]

  町田 学

  京都大学数学教室 談話会  2020/10
• 多孔質媒体中の分子の線形ボルツマン輸送

  雨谷 健司; 町田 学; 羽田野 祐子

  日本流体力学会年会  2020/09
• The linear Boltzmann equation as a governing equation in porous media  [Invited]

  Machida M

  Summer Intensive Seminar on Inverse Modelling and Computation  2020/08
• A numerical method for inverse transport problems  [Invited]

  Machida M

  偏微分方程式による逆問題解析とその周辺  2020/01
• 輻射輸送方程式の新解法と光トモグラフィー  [Invited]

  町田 学

  日本学術会議 第9回計算力学シンポジウム  2019/12
• The linear transport in porous media

  Machida M

  The 26th International Conference on Transport Theory  2019/09
• ランダム媒質の光学特性値決定

  町田 学

  日本物理学会秋季大会  2019/09
• Near-infrared spectroscopy  [Invited]

  Machida M

  Summer School on Applied Inverse Problems and Related Topics  2019/08
• Optical medical imaging in the radiative transport regime  [Invited]

  Machida M

  International Congress on Industrial and Applied Mathematics (ICIAM)  2019/07
• Time-fractional derivatives in inverse transport problems  [Invited]

  Machida M

  International Congress on Industrial and Applied Mathematics (ICIAM)  2019/07
• Spatial-frequency-domain optical tomography in the nondiffusive regime  [Invited]

  Machida M

  Applied Inverse Problems Conference (AIP)  2019/07
• Lipschitz stability in inverse diffusion problems with first- and half-order derivatives  [Invited]

  Machida M

  Applied Inverse Problems Conference (AIP)  2019/07
• Spatial-frequency-domain optical tomography in the radiative transport regime

  Machida M

  European Conference on Biomedical Optics (ECBO)  2019/06
• Time-domain diffuse optical tomography with lp sparsity regularization for thyroid cancer imaging,

  Okawa S; Mimura T; Fujii H; Kawaguchi H; Tanikawa Y; Machida M; Okada E; Hoshi Y

  European Conference on Biomedical Optics (ECBO)  2019/06
• 解析解に基づく輻射輸送方程式の数値計算

  町田 学

  応用数理学会第15回研究部会連合発表会  2019/03
• Stability analysis of inverse problems for 1+1/2 fractional parabolic equations  [Invited]

  Machida M

  A3 Workshop in Applied Inverse Problems  2019/01
• Nondestructive inspection of biological tissue by optical tomography  [Invited]

  Machida M

  Non-destructive inspection for concrete structures and related topics  2018/10
• 3次元FN法による輻射輸送方程式の高速数値計算

  町田 学

  日本物理学会秋季大会  2018/09
• Radiative transport-based optical tomography with structured illumination  [Invited]

  Machida M

  The 12th International Conference on Complex Medical Engineering (ICME)  2018/09
• Inverse problems in medical imaging: Optical tomography  [Invited]

  Machida M

  若手研究集会「波動・振動・流れ の制御と逆問題-理論と数値計算-」  2018/08
• Stability analysis for homogenized diffusion equations  [Invited]

  Machida M

  The 9th International Conference on Inverse Problems and Related Topics (ICIP)  2018/08
• Spatial-frequency optical tomography in the radiative-transport regime  [Invited]

  Machida M

  Tianyuan Workshop on Mathematical and Computational Challenges of Medical Imaging and Inverse Problems  2018/08
• 光トモグラフィーとは何か

  町田 学

  浜松医科大学第2回学内研究交流会  2018/07
• 光トモグラフィーの数値計算：具体例を交えながら

  町田 学

  計算光バイオイメージング勉強会  2018/07
• 非整数階時間微分による異常輸送現象

  町田 学

  日本物理学会第73回年次大会  2018/03
• Optical tomography with structured illumination based on the radiative transport equation  [Invited]

  Machida M

  Inverse Problems and Medical Imaging  2018/02
• 3次元輻射輸送方程式の新解法 と光トモグラフィー  [Invited]

  町田 学

  輸送理論と生体医用光学  2018/02
• Coefficient inverse problems for the time-fractional linear Boltzmann equation  [Invited]

  Machida M

  A3 Workshop on Applied Inverse Problems and Related Topics  2017/11
• Theoretical tools for optical medical imaging  [Invited]

  Machida M

  The 11th International Conference on Complex Medical Engineering (ICME)  2017/11
• 輻射輸送方程式を用いた光トモグラフィー

  町田 学

  日本物理学会秋季大会  2017/09
• Numerical techniques for optical tomography  [Invited]

  Machida M

  現象数理解析研究会  2017/06
• Optical tomography with structured illumination using the three-dimensional FN method  [Invited]

  Machida M

  Applied Inverse Problems (AIP)  2017/06
• Half-order fractional inverse transport problems by Carleman estimates  [Invited]

  Machida M

  Applied Inverse Problems (AIP)  2017/06
• Optical medical imaging with the radiative transport equation  [Invited]

  Machida M

  東南大学数学科セミナー  2017/05
• Stability analysis for inverse transport problems  [Invited]

  Machida M

  复旦大学数理科学部セミナー  2017/03
• 多次元輻射輸送方程式の解析解

  町田 学

  日本物理学会第72回年次大会  2017/03
• Optical tomography based on the radiative transport equation  [Invited]

  Machida M

  金沢大学数物科学系セミナー  2017/03
• Transport-based optical tomography algorithms by rotated reference frames  [Invited]

  Machida M

  Inverse problems and medical imaging  2017/02
• 輻射輸送方程式の解析解法の歴史と現状  [Invited]

  町田 学

  日本学術振興会第185委員会  2017/01
• Linear Boltzmann transport and optical tomography  [Invited]

  Machida M

  京都大学基礎物理学研究所セミナー  2016/11
• ３次元線形ボルツマン方程式のグリーン関数

  町田 学

  日本物理学会秋季大会  2016/09
• Half-order fractional inverse transport problems by Carleman estimates  [Invited]

  Machida M

  The 8th International Conference on Inverse Problems and Related Topics (ICIP)  2016/06
• Half-order fractional inverse transport problems by Carleman estimates  [Invited]

  Machida M

  NCTS PDE and Analysis Seminar  2016/05
• Transport-based optical tomography  [Invited]

  町田 学

  AMED産学共創基礎基盤プログラム  2016/02
• Transport-based optical tomography

  Machida M

  Winter School in Imaging Science  2016/01
• The FN method in three dimensions

  Machida M

  24th International Conference on Transport Theory  2015/09
• The Green's function by the 3D FN method for inverse transport problems  [Invited]

  Machida M

  American Mathematical Society Spring Southeastern Sectional Meeting  2015/03
• Inverse Born series for the radiative transport equation  [Invited]

  Machida M

  Society for Industrial and Applied Mathematics Annual Meeting  2014/07
• 光の輸送現象とその逆問題  [Invited]

  町田 学

  核物理×物性セミナー  2014/05
• Case's method in three dimensions  [Invited]

  Machida M

  Society for Industrial Applied Mathematics Conference on Analysis of Partial Differential Equations  2013/12
• Global Lipschitz stability for determining coefficients of the radiative transport equation  [Invited]

  Machida M

  Inverse Problems Seminar  2013/10
• Light propagation in random media  [Invited]

  Machida M

  Applied and Interdisciplinary Mathematics Seminar  2013/09
• Case's Method in Three Dimensions with Rotated Reference Frames

  Machida M

  23rd International Conference on Transport Theory  2013/09
• Recursion algorithm for the inverse Born series  [Invited]

  Machida M

  Workshop on Computational Mathematics  2013/05
• Transport in random media and inverse problems  [Invited]

  Machida M

  Applied and Interdisciplinary Mathematics Seminar  2011/09
• Optical tomography  [Invited]

  町田 学

  第1部セミナー  2010/12
• Inverse Problem for the Radiative Transport Equation with the Method of Rotated Reference Frames  [Invited]

  Machida M; Panasyuk G; Schotland JC; Markel VA

  Progress in Electromagnetic Research Symposium (PIERS)  2009/08
• Optical tomography based on the method of rotated reference frames  [Invited]

  Machida M; Panasyuk GY; Wang Z-M; Markel VA; Schotland JC

  Conference on Applied Inverse Problems (AIP)  2009/07
• An efficient numerical method for the radiative transport equation: method of rotated reference frames  [Invited]

  Machida M; Panasyuk GY; Markel VA; Schotland JC

  The 24th Progress in Electromagnetics Research Symposium  2008/07
• Time-Dependent Conductivity in the Quantum Hall Effect

  Machida M; Hatano N; Goryo J

  APS March Meeting Denver  2007/03
• Temporal oscillation of conductivities in quantum Hall effect of Bloch electrons  [Invited]

  町田 学

  古崎物性理論研究室セミナー  2007/01
• A correction term to the Chern number of quantum Hall conductivity  [Invited]

  町田 学

  安藤恒也研究室セミナー  2006/10
• 量子ホール伝導度のチャーン数への補正項

  町田 学; 羽田野 直道; 御領 潤

  日本物理学会秋季大会  2006/09
• Temporal oscillation of conductances in the Hofstadter butterfly

  Machida M; Hatano N; Goryo J

  International Conference on Quantum Mechanics and Chaos  2006/09
• Fluctuation of conductances in quantum Hall effect

  Machida M

  Dynamics and Relaxation in Complex Quantum and Classical Systems and Nanostructures  2006/08
• Quantum Fluctuation of the Hall Conductivity  [Invited]

  Machida M

  Pizza Seminar  2006/06
• Temperature Dependence of ESR Intensity of the Nanomagnet V15  [Invited]

  Machida M

  Quantum Condensed Matter Seminar  2006/05
• Temperature Dependence of ESR Intensity of the Nanomagnet V15  [Invited]

  Machida M

  Condensed Matter Seminar  2006/05
• Nonadiabatic transition in the quantum Hall effect

  Machida M; Hatano N; Goryo J

  American Physical Society March Meeting  2006/03
• Simulational study on the linear response for huge Hamiltonians - Temperature dependence of the ESR of a nanomagnet

  Machida M; Iitaka T; Miyashita S

  19th Annual Workshop Recent Developments in Computer Simulation Studies in Condensed Matter Physics  2006/02
• Nano quantum systems -Distribution of the spacing between two adjacent avoided crossings  [Invited]

  Machida M

  Condensed Matter Seminar  2006/01
• ブロッホ電子系の量子ホール効果 〜非断熱遷移によるチャーン数からの補正項

  町田 学; 羽田野 直道; 御領 潤

  CREST量子情報研究領域ワークショップ  2005/12
• Numerical simulation of the temperature dependence of the ESR intensity of nanomagnet V15  [Invited]

  Machida M

  The 2nd International Workshop on Simulational Physics  2005/12
• 非交差間隔分布  [Invited]

  町田 学

  非線形物理研究室セミナー  2005/10
• 非交差間隔分布

  町田 学; 齊藤 圭司

  日本物理学会秋季大会  2005/09
• 分子磁性体V15におけるESR吸収強度の温度依存性とDM相互作用

  町田 学; 飯高 敏晃; 宮下 精二

  日本物理学会秋季大会  2005/09
• ESR intensity and anisotropy of nanoscale molecular magnet V15

  Machida M; Iitaka T; Miyashita S

  24th International Conference on Low Temperature Physics  2005/08
• Numerical study on ESR of V15

  Machida M; Iitaka T; Miyashita S

  Conference on Single Molecule Magnets and Hybrid Magnetic Nanostructures  2005/06
• Numerical calculation of the Kubo formula for huge Hamiltonian quantum systems at finite temperature

  Machida M; Iitaka T; Miyashita S

  日本物理学会第60回年次大会  2005/03
• Spectral statistics and the Dzyaloshinsky-Moriya interaction of nanomagnet V15

  Machida M; Miyashita S

  First International Symposium on Nanometer-scale Quantum Physics (nanoPHYS'05)  2005/01
• Eigenvalues of nanoscale molecular magnets

  Machida M; Miyashita S

  Chaos and Nonlinear Dynamics in Quantum-Mechanical and Macroscopic Systems  2004/12
• V15のESRにおける吸収強度の温度依存性

  町田 学; 宮下 精二; 飯高 敏晃

  日本物理学会秋季大会  2004/09
• Anisotropy and Dzyaloshinsky-Moriya Interaction in V15

  Machida M; Miyashita S; Iitaka T

  International Conference on Statistical Physics of Quantum Systems  2004/07
• パラメタ−を含む量子カオス系における非交差間隔分布

  町田 学; 齊藤 圭司

  量子力学とカオス：基礎的問題からナノサイエンスまで  2003/11
• ランダム行列における摂動パラメター空間上の反交差間分布II

  町田 学; 齊藤 圭司

  日本物理学会秋季大会  2003/09
• V15のESRにおける異方性とDzyaloshinsky-Moriya相互作用

  町田 学; 宮下 精二

  日本物理学会秋季大会  2003/09
• パラメタ−に依存するランダム行列ハミルトニアンにおける拡散現象の振動数依存性

  町田 学; 齊藤 圭司; 宮下 精二

  日本物理学会第58回年次大会  2003/03
• 周期外場下における量子局在現象の振動数依存性

  町田 学

  基研研究会「量子カオス：理論と実験の現状」  2002/09
• ランダム行列における摂動パラメター空間上の反交差間分布

  町田 学; 齊藤 圭司

  日本物理学会秋季大会  2002/09
• Frequency Dependence of Quantum Localization in a Periodically Driven System

  Machida M; Saito K; Miyashita S

  Microscopic Chaos and Transport in Many-Particle Systems  2002/08
• 周期外場下における量子局在現象の振動数依存性

  町田 学; 齊藤 圭司; 宮下 精二

  日本物理学会第57回年次大会  2002/03
• 周期外場下における量子局在現象の振動数依存性

  町田 学

  ISSP Theory Forum for the 21st Century  2002/03
• 周期外場下における量子局在 現象の振動数依存性  [Invited]

  町田 学

  量子ダイナミクスに関する研究会  2002/01
• Response of systems with complex structure of levels to a varying external field

  Mashida M; Saito K; Miyashita S

  YITP International Workshop on Order, Disorder, and Dynamics in Quantum Spin Systems  2001/11
• Response of systems with complex structure of levels to a varying external field

  Matida M; Saito K; Miyashita S

  International Workshop on Materials Simulation  2001/11
• 複雑な非断熱遷移構造をもつ系の動的外場へのレスポンス

  町田 学; 齊藤 圭司; 宮下 精二

  日本物理学会秋季大会  2001/09
• パラメターの関数として複雑に変化するエネルギー準位の構造  [Invited]

  町田 学

  量子ダイナミクス研究会  2001/02
• The structure of energy levels which change in a complex manner as a function of a parameter  [Invited]

  町田 学

  上田正仁研究室セミナー  2001/02
• 反交差の性質を中心としたパラメターの関数として複雑に変化するエネルギー準位の構造

  町田 学; 清水 明

  日本物理学会第55回年次大会  2000/09
• 量子カオス系の非交差におけるギャップの分布

  町田 学; 清水 明

  第８回非平衡系の統計物理シンポジウム  1999/11
• 量子カオス系の準位のパラメター 依存性と非断熱遷移  [Invited]

  町田 学; 清水 明

  量子ダイナミクス研究会  1999/09

MISC

• 光学と逆問題:光トモグラフィー

  町田学  日本物理学会誌  72-  712  -716  2017/10

Awards & Honors

• 2021/03 Waseda University e-Teaching Grand Award
   

  受賞者: Momoko Hayamizu, Manabu Machida, Kenji Nakamura
• 2019/06 JSIAM Best Talk Award
  

Research Grants & Projects

• Application of the method of fundamental solutions for abnormal diffusion equations in the layered medium

  Japan Society for the Promotion of Science：Grants-in-Aid for Scientific Research

  Date (from‐to) : 2018/04 -2023/03 

  Author : 大江 貴司; 町田 学

   

  令和3年度は、令和2年度に開発した基本解の数値計算法を基に初期値をゼロとした境界値問題の数値解法を実装し、主に誤差の収束特性について数値実験により検討した。その結果、誤差の収束について、以下のことがわかった。(i) 空間変数については電荷点の個数に対し、指数関数的である。なお収束の速度は電荷点と拘束点の距離を大きくとった方が高い、(ii) 時間変数については時間刻み幅に対し、線型オーダーである。この中で、(i)の特性はLaplace方程式に対する代用電荷法が持っている性質と類似のものであり、好ましいものである。一方で、(ii) の特性は不満足ではあるものの、ある程度、予想されたものであった。これらの研究成果は、日本応用数理学会年会（2021年10月）および環瀬戸内応用数理研究部会第27回シンポジウムにおいて口頭発表を行った。 その後、層状領域への拡張を検討していたが、数値実験を進めていくうちに、時間刻み幅を小さくした場合に不安定性が生じることが判明した。線型安定解析に基づく分析を行った結果、電荷点と拘束点の距離を小さくすれば多少改善されるものの、この不安定性は今回用いている手法、すなわち時間方向について単純な線形和を取る手法が本質的に持っている性質であり、そのままの形での解決は困難であるものと考えられた。そのため、時間方向の近似手法を根本から考え直すことが必要となった。 年度末になり、時間依存問題に対する境界要素法の手法について調べた結果、Lubichが開発したConvolution Quadrature Method(CQM) を適用することで解決できるのではないかとの着想を得た。現在、CQMを適用した代用電荷法の数値計算法の開発を行い、予備的数値実験を行っている段階であるが、良好な結果を得つつある。
• 輻射輸送方程式の解析解

  日本学術振興会：科学研究費助成事業

  Date (from‐to) : 2017/04 -2023/03 

  Author : 町田 学

   

  多孔質媒体を水とともに流れる分子の輸送が輻射輸送方程式に支配されることをさらに検証した。以前の研究では半空間について輻射輸送方程式の解を求めたが、今回は実験を反映して両端の境界を考慮した。実験では、砂などを詰めたシリンダー状の容器にターゲット分子をまぜた水を流す。実験状況から、1次元の空間における輸送を扱った。輻射輸送方程式の解は固有モードの重ね合わせとして求める。斉次方程式は解析的に解くことができ、固有モードは数値計算せずに得られる。このとき、輻射輸送方程式の積分項を離散方位法によって離散化しておくと、固有モードに超関数が現れない。時間に依存する輻射輸送方程式を解いたが、ラプラス変換によって時間に依存しない方程式に帰着させた後、逆ラプラス変換で時間に依存する解を得た。逆ラプラス変換には二重指数関数型数値積分公式を利用した。吸収係数・散乱係数の異なる様々な実験の結果と比較したところ、いずれの場合にも輻射輸送方程式の解とよく合うことがわかった。
  光トモグラフィーの逆問題は非線型であり反復法におけるコスト関数は非常に複雑な多谷構造を持つ。反復法にかわる逆問題解法として、シミュレーテッドアニーリングの利用を検討した。この方法では、乱数を用いることで局所解から抜け出すことができる。最初の試みとして、輻射輸送方程式に対する拡散近似を用いた。拡散方程式による光トモグラフィーについてシミュレーテッドアニーリングの方法を試すことにより、この手法が有望であることがわかった。
• Estimation of optical properties in biological tissue using time-resolved spectroscopy with femtosecond laser

  Japan Society for the Promotion of Science：Grants-in-Aid for Scientific Research

  Date (from‐to) : 2017/04 -2020/03 

  Author : Hoshi Yoko

   

  Diffuse optical tomography (DOT), one of the most sophisticated optical imaging techniques for observations through biological tissue, provides functional and anatomical information. DOT image reconstruction algorithm essentially consists of the forward and inverse problems. Tissue optical properties, absorption and reduced scattering coefficients, are crucial for modeling light propagation in biological tissue (the forward problem) and guessing initial values in the inverse problem, whereas these values remain unknown in detail due to difficulties in the experimental determination and significant variations in tissue constitution. The aim of this study was in situ separate estimation of the optical properties of the gray and white matter in the brain tissue. We employed the femtosecond time-resolved spectroscopy system to measure the brain tissues of living rats and a monkey, estimating the optical properties by using a look-up table created by the Monte Carlo method.
• Effects of Interaction and Leads on Electronic Conduction in Mesoscopic Systems

  Japan Society for the Promotion of Science：Grants-in-Aid for Scientific Research

  Date (from‐to) : 2005 -2008 

  Author : HATANO Naomichi; MACHIDA Manabu; SAKAKI Hiroyuki

   

  メゾスコピック系の電気伝導において、メゾスコピック系内の電子間相互作用や、メゾスコピック系に接続されている導線がどのような効果を及ぼすかを議論した。前者が多体の束縛状態を、後者が共鳴状態を生み出すことを明らかにした。

Other link

researchmap

https://researchmap.jp/mmachida