the 9th international conference on inverse problems and ... · [ms6-3] a fully nonlinear...

The 9th International Conference on Inverse Problems and Related Topics

13 – 17 August, 2018

National University of Singapore

Singapore

International Conference on Inverse Problems and Related Topics

The 9th International Conference on Inverse Problems and Related Topics will take place at National University of Singapore in Singapore during 13 -17 Aug. 2018. This series of conferences were previously held in Hong Kong (2002), Shanghai (2004), Hokkaido (2006), Daejeon (2009), Hong Kong (2010), Nanjing (2012), Taipei (2014), and Seoul (2016). This conference features speakers from both theoretical (mathematics) and applied (engineering) aspects of inverse problems. It aims to strengthen the interaction and, most importantly, to nurture collaborations between two groups of scientists. In addition, one of the focuses of the conference is to promote young scholars in inverse problems in the Asia-Pacific region.

Inverse problems arise in many areas of science including mathematics, engineering, medicine, physics, and geophysics. The varieties of their applications are enormous such as medical imaging, oil exploration, radar, sonar and seismology. In the last twenty years the active research carried out in the field of inverse problems has made it become a very promising interdisciplinary topic.

The topics of the conference include, but are not limited to:

Inverse boundary value problems Inverse scattering problems Medical imaging Regularization theory Cloaking and invisibility Coupled physics inverse problems Sparse representation Numerical methods Deep learning for inverse problems

All scientists who are interested in the current research trends in the field of inverse problems are welcome to attend the conference.

Scientific Committee

Gang Bao Department of Mathematics, Zhejiang University Matti Lassas Department of Mathematics and Statistics, University of Helsinki Wen-Wei Lin Department of Applied Mathematics, National Chiao Tung University Gen Nakamura Department of Mathematics, Hokkaido University John C Schotland Department of Mathematics, University of Michigan Jin Keun Seo Computational Science & Engineering, Yonsei University Zuowei Shen Department of Mathematics, National University of Singapore Jun Zou Mathematics Department, Chinese University of Hong Kong

Organizing Committee Xudong Chen Dept. of Electrical and Computer Engineering, National University of Singapore Jin Cheng Department of Mathematics, Fudan University Benny Hon Department of Mathematics, City University of Hong Kong June-Yub Lee Department of Mathematics, Ewha Womens University Jijun Liu Department of Mathematics, Southeast University Jenn-Nan Wang Institute of Applied Mathematics, National Taiwan University Masahiro Yamamoto Department of Mathematical Sciences, University of Tokyo

Local Organizing Committee Xudong Chen Dept. of Electrical and Computer Engineering, National University of Singapore Hui Ji Department of Mathematics, National University of Singapore Zuowei Shen Department of Mathematics, National University of Singapore The staff of the Institute for Mathematical Sciences (IMS), National University of Singapore

JiongWei Young Researcher Award Selection Committee Bernd Hofmann Technische Universität Chemnitz, Germany (Committee Chair) Masahiro Yamamoto University of Tokyo, Japan (Coordinator) Markus Hegland Australian National University, Australia Barbara Kaltenbacher Alpen-Adria University Klagenfurt, Austria Shuai Lu Fudan University, China Andreas Neubauer Johannes Kepler University Linz, Austria Lothar Reichel Kent State University, USA Jun Zou Chinese University of Hong Kong, Hong Kong SAR Jorge Zubelli IMPA, Rio de Janeiro, Brazil

Conference Sponsors

Program at a glance

Aug 13 (M) Aug 14 (Tu) Aug 15 (W) Aug 16 (Th) Aug 17 (F)

9:00-10:00 Registration

Opening Ceremony (9.45am)

Group Photo

KN3 (Hofmann) KN6 (Liu_H)

KN7 (Ammari) KN10 (Zhang)

10:00-10:30 Coffee Break 10:30-11:30 KN1 (Uhlmann) KN4 (Leow) YA1 KN8 (Nara) KN11 (Lee) 11:30-12:30 KN2 (Liu J) KN5 (Park) YA2 KN9 (Tong) KN12 (Lin)

12:30-14:00 Lunch

Free and Easy

afternoon

Lunch Lunch Closing Ceremony

14:00-15:40

MS1 (Fractional-1)

MS2 (Learning-1)

MS3 (Scattering-1)

MS6 (Technological-2)

MS7 (Scattering-3)

CP2

MS10 (Fractional-2)

CP3

15:40-16:10 Coffee Break Coffee Break

16:10-17:50

MS4 (Technological-1)

MS5 (Scattering-2)

CP1

MS8 (Learning-2)

MS9 (EIT)

18:30 Welcome Reception

KN: Keynote talk; YA: Young Researcher Award; MS: Minisymposium; CP: Contributed Paper

All morning talks (KN1-KN12, YA1, YA2), registration, and opening ceremony will be held at LT5. All afternoon talks (MS1-MS10, CP1-CP3) will be placed at seminar rooms:

MS1 (Fractional-1): M. Yamamoto; G. Li; T. Wei; J. Liu [Room: E4-04-02] MS2 (Learning-1): J. K. Choi; J. Yang; C. Bao [Room: E1-06-02] MS3 (Scattering-1): X. Cao; Y. Deng; C. Carstea; H. Diao [Room: E3-06-14] MS4 (Technological-1): M. Yamamoto; Y. Ota; X. Xu; M. Uesaka [Room: E4-04-02] MS5 (Scattering-2): H. Li; Y. Lin; M. Vashisth; X. Liu [Room: E3-06-14] MS6 (Technological-2): T. Saito; V. Krishnan; G. Nakamura [Room: E1-06-06] MS7 (Scattering-3): Y. Wang; X. Ji; E. Blåsten [Room: E3-06-02] MS8 (Learning-2): K. Jiang; T. Pang; Y. Shen; D. Xiang [Room: E1-06-06] MS9 (EIT): M. Li; W. Zhun; D. Liu [Room: E1-06-07] MS10 (Fractional-2): M. Machida; G. Nakamura; L. Ylinen; Z. Zhang [Room: E3-06-02] CP1: T. Furuya; A. Konschi; W.-K. Park; T. Ghosh [Room: E1-06-02] CP2: R. R. Real; D. S. Choi; Y. Jung; J. Kim [Room: E1-06-07] CP3: X. Huang; H. Takase; M.-C. Cheng; J.-C. Croix [Room: E3-06-03]

Keynote Talks & Young-Researcher-Award Lectures

Aug 13 (M), Room: LT5 Chairs: Zuowei Shen and Xudong Chen

Time: 10:30-11:30[KN-01] Inverse Problems in Wave Propagation

Gunther Uhlmann, University of Washington Time: 11:30-12:30 [KN-02] On fluorescence imaging by diffusion process: model and algorithm

Jijun Liu, Southeast University

Aug 14 (Tu), Room: LT5 Chair: Benny Hon Time: 9:00-10:00 [KN-03] The distinguished role of smoothness in variational regularization for the

solution of inverse problems Bernd Hofmann, TU Chemnitz

Time: 10:30-11:30 [KN-04] Accurate Reconstruction of Interpolation

Wee Kheng Leow, National University of SingaporeTime: 11:30-12:30 [KN-05] Metal artifacts in X-ray CT-mathematical analysis and reduction

methods Hyoungsuk Park, Natl. Inst. of Math. Sciences

Aug 15 (W), Room: LT5 Chair: Jenn-Nan Wang

Time: 9:00-10:00[KN-06] Scattering by curvatures, radiationless sources, transmission

eigenfunctions and inverse shape problems Hongyu Liu, Hong Kong Baptist University

Time: 10:30-11:30 [YA-01] Inverse problems for hyperbolic PDEs

Lauri Oksanen, University College London Time: 11:30-12:30 [YA-02] Super-resolution by subwavelength resonators

Hai Zhang, The Hong Kong University of Science and Technology

Aug 16 (Th), Room: LT5 Chairs: Hui Ji and Xudong Chen Time: 9:00-10:00[KN-07] Bio-inspired sensing and imaging

Habib Ammari, ETH ZürichTime: 10:30-11:30 [KN-08] Biomagnetic inverse problems: magnetic resonance electrical property

tomography (MREPT) and magnetoencephalography (MEG) Takaaki Nara, University of Tokyo

Time: 11:30-12:30 [KN-09] Localization for high dimensional Bayesian inverse problems

Xin Tong, National University of Singapore

Aug 17 (F), Room: LT5 Chair: June-Yub Lee Time: 9:00-10:00 [KN-10] Inverse Scattering Problems With Phaseless Data

Bo Zhang, Chinese Academy of Sciences & University of Chinese Academy of Sciences

Time: 10:30-11:30 [KN-11] Wave propagation in bubbly media and metamaterials

Hyundae Lee, Inha University

Time: 11:30-12:30 [KN-12] On the nonlocal inverse problems

Yi-Hsuan Lin, Hong Kong University of Science and Technology

Minisymposia

MS1: Inverse problems for fractional partial differential equations (1)

Time: Aug 13 (M), 14:00-15:40 Chair: Zhiyuan Li and Yikan Liu Room: E4-04-02

[MS1-1] Recent results on inverse problems for fractional differential equations Masahiro Yamamoto, The University of Tokyo

[MS1-2] Simultaneous inversion for diffusion coefficient and source term in the fractional diffusion equations Gongsheng Li, Shandong University of Technology

[MS1-3] Recovering a space-dependent source term in a time-fractional diffusion wave equation Ting Wei, Lanzhou University

[MS1-4] On an inverse problem for distributed time-fractional diffusion system Jijun Liu, Southeast University

MS2: Variational Approaches for Inverse Problems and Machine learning (1)

Time: Aug 13 (M), 14:00-15:40 Chair: Jianbin Yang Room: E1-06-02

[MS2-1] HIRE: Harmonic Incompatibility REmoval Model for Whole Brain Susceptibility Imaging Jae Kyu Choi, Shanghai Jiao Tong University

[MS2-2] Wavelet frame based scattered data reconstruction Jianbin Yang, Hohai University

[MS2-3] A computational approach for phase space tomography Chenglong Bao, Tsinghua University

MS3: Recent Advances in Inverse Scattering and Cloaking (1)

Time: Aug 13 (M), 14:00-15:40 Chair: Hongyu Liu Room: E3-06-14

[MS3-1] Some simultaneous recovery results in nonlocal inverse problem Xinlin Cao, Hong Kong Baptist University

[MS3-2] On identifying magnetized anomalies using geomagnetic monitoring Youjun Deng, Central South University

[MS3-3] An inverse boundary value problem for a nonlinear time harmonic Maxwell system Catalin Carstea, Hong Kong University of Science and Technology

[MS3-4] Inverse elastic surface scattering with far-field data Huaian Diao , Northeast Normal University

MS4: Technological Aspect of Inverse Problems and Related Problems (1)

Time: Aug 13 (M), 16:10-17:50 Chair: Gen Nakamura and Masahiro Yamamoto Room: E4-04-02

[MS4-1] Some inverse problems in industry and environmental engineering Masahiro Yamamoto, The University of Tokyo

[MS4-2] Computing the local volatility and the real trend in financial markets by using Bayesian inference and numerical analysis Yasushi Ota, Okayama University of Science, Okayama

[MS4-3] An inverse random source problem for biharmonic equation Xiang Xu, Zhejiang University

[MS4-4] The time-discretized one-harmonic flow with constraint in Lie group and its numerical simulation Masaaki Uesaka, Hokkaido University


Time: Aug 13 (M), 16:10-17:50 Chair: Xiaodong Liu Room: E3-06-14

[MS5-1] On anomalous resonance and cloaking for the Maxwell equation Hongjie Li, Hong Kong Baptist University

[MS5-2] On localizing and concentrating electromagnetic fields. Yi-Hsuan Lin, Institute for Advanced Study, HKUST

[MS5-3] Inverse Boundary Value Problem for Non-linear Hyperbolic PDEs Manmohan Vashisth, TIFR Centre for Applicable Mathematics, Bangalore, India

[MS5-4] Data recovery: from limited-aperture to full-aperture Xiaodong Liu, Chinese Academy of Sciences


Time: Aug 15 (W), 14:00-15:40 Chair: Gen Nakamura and Masahiro Yamamoto Room: E1-06-06

[MS6-1] Linearized inverse scattering analysis for defect in anisotropic materials T. Saitoh, Gunma University

[MS6-2]

[MS6-3]

A fully nonlinear optimization approach to acousto-electric tomography Venky Krishnan, TIFR Centre for Applicable Mathematics, BangaloreBorn approximation and sequence for hyperbolic equationsGen Nakamura, Hokkaido University


Time: Aug 15 (W), 14:00-15:40 Chair: Youjun Deng Room: E3-06-02

[MS7-1]

[MS7-2]

[MS7-3]

A joint reconstruction scheme for inverse scattering problems with limited aperture data Yuliang Wang, Hong Kong Baptist University Computation of Interior Transmission Eigenvalues for Elastic Waves Xia Ji, Chinese Academy of Sciences Inverse problems with one measurement Eemeli Blåsten, HKUST Jockey Club Institute for Advanced Study


Time: Aug 15 (W), 16:10-17:50 Chair: Jianbin Yang Room: E1-06-06

[MS8-1] A finite element method of self-consistent field theory on a general curved surface Kai Jiang, Xiangtan University

[MS8-2] Data-driven method for image restoration problems Tongyao Pang, National University of Singapore, Singapore

[MS8-3] Stable recovery of analysis based approachesYi Shen, Zhejiang Sci-Tech University

[MS8-4] The Stability of SVMs Daohong Xiang, Zhejiang Normal University

MS9: Efficient Reconstruction Methods for Electrical Impedance Tomography

Time: Aug 15 (W), 16:10-17:50 Chair: Dong Liu and Maokun Li Room: E1-06-07

[MS9-1] Study on the Feasibility of EIT Absolute Imaging for Human Pulmonary Monitoring Ke Zhang1,2, Maokun Li1,2, Fan Yang1,2, Shenheng Xu1,2, and Aria Abubakar3 1State Key Laboratory on Microwave and Digital Communications, (BNRist), 2Tsinghua University, 3Schlumberger, Houston, TX, USA

[MS9-2] New FFT Subspace-Based Optimization Method for Electrical Impedance Tomography Zhun Wei and Chen Xudong, National University of Singapore

[MS9-3] A parametric level set method for imaging multiphase conductivity using electrical impedance tomography Dong Liu and Jiangfeng Du, University of Science and Technology of China


Time: Aug 16 (Th), 14:00-15:40 Chair: Zhiyuan Li and Yikan Liu Room: E3-06-02

[MS10-1] Stability analysis for homogenized diffusion equations Manabu Machida, Hamamatsu University School of Medicine

[MS10-2] Unique continuation property for multi-terms time fractional diffusion Equations Gen Nakamura, Hokkaido University

[MS10-3] Uniqueness of the conductivity in a space-time fractional diffusion equation Lauri Ylinen, University of Helsinki

[MS10-4] An inverse random source problem in a fractional diffusion equation Zhidong Zhang, University of Helsinki

Contributed Papers

CP1 Time: Aug 13 (M), 16:10-17:50 Chair: Won-Kwang Park Room: E1-06-02

[CP1-1]

[CP1-2]

[CP1-3]

A modification of the factorization method for scatterers with different physical properties Takashi Furuya, Nagoya University Application of the Floquet-Transform to the Helmholtz Equation and Maxwell Equations on Locally Perturbed Bi-periodic Structures Alexander Konschin, University of Bremen Real-Time Microwave Imaging of Small Anomalies Without Diagonal Elements of the Scattering Matrix Won-Kwang Park, Kookmin University Inverse problem for fractional-Laplacian operator with lower order non-local perturbationsTuhin Ghosh, Hong Kong University of Science and Technology

CP2 Time: Aug 15 (W), 14:00-15:40 Chair: Mikyoung Lim Room: E1-06-07

[CP2-1] Hanke-Raus Heuristic Rule for Landweber Iteration with General Nonsmooth Convex Penalty Functional Rommel R. Real, The Australian National University

[CP2-2] New geometric factors of the planar inclusion Doo Sung Choi, Johan Helsing, Mikyoung Lim, KAIST

[CP2-3] Series representation of layer potential opreators for the transmission problem Younghoon Jung, Mikyoung Lim, Department of Mathematical Sciences, KAIST

[CP2-4] Electric field concentration between nearly touching boundaries using image line charges Junbeom Kim, Mikyoung Lim, Department of Mathematical Sciences, KAIST

[CP1-4]

CP3 Time: Aug 16 (Th), 14:00-15:40 Chair: Xinchi Huang Room: E3-06-03

[CP3-1] Inverse problems for a magnetohydrodynamic system Xinchi Huang, The University of Tokyo

[CP3-2] Inverse Source Problem related to the Gravitational Wave in General Relativity Hiroshi Takase, The University of Tokyo

[CP3-3] Manufacturer's production plan for products sold with warranty in an imperfect production system under preventive maintenance and trade credits Chun-Tao Chang1, Mei-Chuan Cheng2* 1Tamkang University, 2Hsin-Sheng Junior College of Medical Care and Management

[CP3-4] Bayesian Estimation of Diffusion, Decay and Source in An Evolution Model with Application to Biology J.-C. Croix1, N. Durrande2, M. A. Alvarez3 1GMI, 2PROWLER, 3The University of Sheffield

Abstract

Keynote Talks and Young-Researcher-Award Lectures

KN-01: Inverse Problems in Wave Propagation

Gunther Uhlmann, University of Washington

Time: 10:30-11:30, Aug 13 (M)

Abstract: We will describe a general method to solve inverse problems arising in non-linear wave propagation. In particular this method can be applied to Einstein's equations coupled with matter fields, the Einstein-Maxwell equations and also inverse problems for non-linear elastic materials.

KN-02: On fluorescence imaging by diffusion process: model and algorithm


Time: 11:30-12:30, Aug 13 (M)

Abstract: Fluorescence imaging is a type of wave spectroscopy that extracts the quantitative property of fluorescence from some measurable data of the sample. This process in the randomly inhomogeneous medium is governed by the radiative transfer equation for excitation and emission fields. By introducing the average of angularly reserved wave energy density, we derive an imaging model by a coupled diffusion system for the average fields. This nonlinear inverse problem is linearized with an error estimate on the excitation field indicating the model approximation. Then we give the explicit expression for emission fields, which provide the fundamentals for the efficient realizations for fluorescence imaging by the iterative schemes. Finally, in terms of the representations of the solution to the diffusion equation, the imaging of fluorophore is implemented by solving a linear integral equation of the first kind. The uniqueness and non-uniqueness of this inverse problem are rigorously analyzed for boundary measurement data, which reveals the essence of the imaging model. An iteration algorithm is proposed for recovering the unknown fluorescence density.

KN-03: The distinguished role of smoothness in variational regularization for the solution of

inverse problems

Bernd Hofmann, TU Chemnitz

Time: 9:00-10:00, Aug 14 (Tu)

Abstract: For the successful approximate solution of ill-posed inverse problems, stabilization approaches are required. Our focus in this talk is on variational regularization and on the capability of variational source conditions for obtaining convergence rates of the regularized solutions in Hilbert and Banach spaces.

The first part of the talk presents in a Hilbert space setting different concepts of well-posedness and ill-posedness and their relations for solving non-linear and linear operator equations and discusses moreover cross connections between conditional stability and regularization. We mention also results on over-regularization, where the unknown solution fails to have a finite penalty value.

In the second part, the impact of different varieties of smoothness on variants of variational regularization in Banach spaces is under consideration. In this context, variational source conditions represent a sophisticated tool for expressing the solution smoothness with respect to the character of the forward operator, for non-linear problems even in combination with the occurring structure of non-linearity. Several example situations for applying regularization approaches are presented, including the sparsity-promoting versions of -regularization with p=0 and p=1.

This talk presents joint work with Jin Cheng, Shuai Lu and Wei Wang (Shanghai), Jens Flemming, Daniel Gerth (Chemnitz), Peter Math ́ (Berlin), Robert Plato (Siegen) as well as Stefan Kindermann (Linz) and Otmar Scherzer (Vienna). Research is partially supported by the Deutsche Forschungsgemeinschaft (DFG) under grants HO 1454/10-1 and 12-1.

KN-04: Accurate Reconstruction of Interpolation

Wee Kheng Leow, National University of Singapore

Time: 10:30-11:30, Aug 14 (Tu)

Abstract: Reconstruction of images and 3D models is an important and challenging task. It is particularly challenging when the task needs to reconstruct the missing parts or normal parts to replace defective parts. Typical reconstruction algorithm strives to generate a reconstructed object from the input object by fitting the reconstructed object as closely as possible to the input object. This fitting process incurs reconstruction errors even in the parts of the input object that are not defective. This kind of error is generally regarded as unavoidable.

Careful analysis shows that reconstruction errors of the non-defective part is a result of approximating algorithms. In the general sense, an approximating algorithm generates an output object by minimizing the difference between the output object and selected points on the input object, subject to some constraints. On the other hand, an interpolating algorithm generates an output object that matches selected data points on the input object exactly, subject to some constraints. If many points are selected on the input object, then the output object can practically match the input object exactly everywhere, resulting in a reconstruction that has zero error in the non-defective parts.

Interpolating algorithms are not as easy to apply as approximating algorithms. There are challenges in developing interpolating algorithms, which include automatic selection of data points, convergence and efficiency of optimization process, and other domain-specific difficulties. These challenges are some of the primary reasons why interpolating algorithms are not as widely used as approximating algorithms.

Recently, interpolating approach is applied to the reconstruction of 3D model of normal skull from defective input skull due to injury or birth defects. It is also applied to the reconstruction of unoccluded face image from input occluded face image. Test results show that this approach achieves practically zero error in the non-defective parts of the reconstructed object, and smaller errors in the reconstruction of the defective parts compared to existing the performance of competing approximating algorithms.

KN-05: Metal artifacts in X-ray CT-mathematical analysis and reduction methods

Hyoungsuk Park, Natl. Inst. of Math. Sciences

Time: 11:30-12:30, Aug 14 (Tu)

Abstract: X-ray computed tomography (CT) is the most widely used tomographic imaging technique in the field of dental and medical radiography. Even though CT provides the cross-sectional images with the excellent resolution and contrast, its advantage is partly limited by the metallic object-related artifacts in the images. Metal artifacts, which appear as streaks and shadow, seriously degrade image quality. In this presentation, we provide mathematical analysis of metal artifacts in X-ray CT using the notion of the Wavefront set from microlocal analysis. Based on the mathematical analysis of metal artifacts, we introduce an analytical artifact corrector depending on geometry of the metallic regions, energy-dependent attenuation coefficient, and the energy spectrum of X-ray source. Recently, deep learning techniques show significant performance over existing methods for medical imaging modalities including X-ray CT. In this talk, we introduce how deep learning is utilized to reduce metal artifacts in X-ray CT imaging.

KN-06: Scattering by curvatures, radiationless sources, transmission eigenfunctions and

inverse shape problems

Hongyu Liu, Hong Kong Baptist University

Time: 9:00-10:00, Aug 15 (W)

Abstract: In this talk, I shall discuss our recent results on wave scattering from an active source or an inhomogeneous passive medium, referred to as a scatterer. We derive sharp local geometric behaviours of the corresponding wave fields near high-curvature or singular points on the boundary of the support of the scatterer. This enables us to classify radiationless sources and nonradiating incident waves as well as to derive geometric structures of transmission eigenfunctions. We also consider the application to the inverse scattering problem of determining the shape of a scatterer by a single measurement.

YA-01: Inverse problems for hyperbolic PDEs

Lauri Oksanen, University College London

Time: 10:30-11:30, Aug 15 (W)

Abstract: We review some recent results concerning coefficient determination problems for hyperbolic partial differential equations, both linear and non-linear. Special attention will be payed on the geometric features of the solution methods and the associated geometric assumptions. In the linear case the known results are essentially confined to geometries of cylinder type, whereas some non-linear cases allow for much more general geometries. We will also highlight certain convexity assumptions present in some, but not all, results for linear equations.

YA-02: Super-resolution by subwavelength resonators

Hai Zhang, The Hong Kong University of Science and Technology

Time: 11:30-12:30, Aug 15 (W)

Abstract: We develop a mathematical theory to explain the mechanism of super-resolution in resonant media which consists of sub-wavelength resonators such as Helmholtz resonators and bubbles. For the media consists of small finite number of resonators, we show that super-resolution is due to sub-wavelength propagating modes; for the case of large number of resonators, we derive an effective media theory and show that super-resolution is due to the effective high contrast in the wave speed.

KN-07: Bio-inspired sensing and imaging

Habib Ammari, ETH Zürich

Time: 9:00-10:00, Aug 16 (Th)

Abstract: The aim of this talk is to exhibit the physical mechanisms underlying shape perception for weakly electric fish and bats and to apply them for nano-sensing and bio-medical imaging.

KN-08: Biomagnetic inverse problems: magnetic resonance electrical property tomography

(MREPT) and magnetoencephalography (MEG)

Takaaki Nara, University of Tokyo

Time: 10:30-11:30, Aug 16 (Th)

Abstract: In this talk, novel methods for two topics in biomagnetic inverse problems are shown.

The first one is magnetic resonance electrical property tomography (MREPT), which is the inverse problem to reconstruct the electrical conductivity and permittivity from the magnetic field inside the human body measured by using an MRI scanner. This modality attracts attention since the electrical properties of the cancerous tissues are much different from those

of the normal tissues. We propose a method based on complex analysis [1]. First, a Dbar equation is derived from Faraday’s law, which is solved by the Cauchy-Pompeiu formula for the electric field in terms of the measured magnetic field. Then, from Ampere’s law, an explicit expression of the conductivity and permittivity is obtained in terms of the magnetic field.

The second one is magnetoencephalography (MEG), which is the inverse problem to reconstruct neural current inside the human brain from the measurements of the magnetic field outside the head. This modality is useful to find an epileptic foci. In order to identify source domains on highly-convolved human brain, we propose an optimization-based algorithm by using a mapping from a sphere to a cortical surface.

References

[1] T. Nara, T. Furuichi and M. Fushimi, An explicit reconstruction method for magnetic resonance electrical property tomography based on the generalized Cauchy formula, Inverse Problems, vol. 33, 105005, 2017.

KN-09: Localization for high dimensional Bayesian inverse problems

Xin Tong, National University of Singapore

Time: 11:30-12:30, Aug 16 (Th)

Abstract: Many inverse problems in practice are high dimensional. Classical Bayesian computational methods are not directly applicable to these problems, since they often require a sample size that depends on the dimension exponentially. However, when the underlying physical domain is large, components are often nearly independent if they correspond to far apart locations. The localization technique was designed to exploit this feature to improve sampling accuracy in the ensemble Kalman filter (EnKF), which is a popular algorithm for data assimilation. In this talk, we will first discuss the mathematical mechanism that guarantees a localized EnKF perform well with a small sample size, assuming the dynamical system is linear and preserves local structures. Then we discuss how to generalize the localization technique for non-Gaussian high dimensional sampling problems. Two Markov chain Monte Carlo (MCMC) algorithms will be devised for different settings, where the necessary sample size can be independent of the state dimension.

KN-10: Inverse Scattering Problems With Phaseless Data

Bo Zhang, Chinese Academy of Sciences & University of Chinese Academy of Sciences

Time: 9:00-10:00, Aug 17 (F)

Abstract: In this talk, we give a brief review on uniqueness results and numerical methods for inverse scattering problems with phaseless data, obtained recently in our group. These results include recursive Newton iteration methods for reconstructing acoustic obstacles from multi-frequency phaseless far-field data, direct imaging algorithms with phaseless far-field data at a fixed frequency, recursive Newton iteration and direct imaging methods for locally rough

surfaces from phaseless near-field and far-field data, and unique determination of acoustic obstacles and inhomogeneous media from phaseless far-field data at a fixed frequency. This talk is based on joint works with Xiaoxu Xu and Haiwen Zhang.

References:

[1] B Zhang & H Zhang, Recovering scattering obstacles by multi-frequency phaseless far-field data, J. Comput. Phys. 345 (2017), 58-73. [2] B Zhang & H Zhang, Fast imaging of scattering obstacles from phaseless far-field measurements at a fixed frequency, arXiv:1805.09046v1, 2018. [3] X Xu, B Zhang & H Zhang, Uniqueness in inverse scattering problems with phaseless far-field data at a fixed frequency, SIAM J. Appl. Math. 78(3) (2018), 1737-1753. [4] B. Zhang and H. Zhang, Imaging of locally rough surfaces from intensity-only far-field or near-field data, Inverse Problems 33 (2017) 055001 (28pp). [5] X Xu, B Zhang & H Zhang, Uniqueness in inverse scattering problems with phaseless far-field data at a fixed frequency. II. arXiv:1806.09127v1, 2018.

KN-11: Wave propagation in bubbly media and metamaterials

Hyundae Lee, Inha University

Time: 10:30-11:30, Aug 17 (F)

Abstract: The study of metamaterials has drawn increasing interest nowadays because of their many important applications in fields such as super-resolution, cloaking, and novel optic and phononic devices. The bubbly media, because of the simplicity of the acoustic properties of the air bubbles, becomes a natural model for such study. It is known that a single bubble in the water possesses a quasi-static resonance which is called the Minneart resonance. Our results show that near and below the Minneart resonant frequency, the effective media has high refractive index, which explains the super-focusing phenomenon observed in the experiment while near and above the Minneart resonant frequency, the effective media is dissipative. We also present some works on bubbly meta-surface which is a homogenization theory for a thin layer of periodically arranged bubbles mounted on a perfect reflection surface.

KN-12: On the nonlocal inverse problems

Yi-Hsuan Lin, Hong Kong University of Science and Technology

Time: 11:30-12:30, Aug 17 (F)

Abstract: We demonstrate recent progress in the nonlocal inverse problems, especially for the nonlocal type Calderón problem, where one tries to determine an unknown coefficient in an anisotropic Schrödinger equation from exterior measurements of solutions. This equation enjoys remarkable uniqueness and approximation properties, which turn out to yield strong results in related inverse problems.

Minisymposium 1


Organizer: Zhiyuan Li, Shandong University of Technology

Yikan Liu, The University of Tokyo

Time: 14:00-15:40, Aug 13 (M), Room: E4-04-02

Description: In recent years, partial differential equations with fractional derivatives have gathered increasing popularity among multidisciplinary researchers, owing to their novel features in mathematics and potential feasibility in applied sciences. Especially, many related inverse problems possess practical significance in some environmental issues of common concern. This minisymposium will bring together researchers on inverse problems for fractional-order partial differential equations to share new ideas and present the latest progresses on this topic and related areas, including inverse source problems, coefficient inverse problems, etc.. Also, this minisymposium aims at further strengthening the collaboration in the mathematical and numerical analyses of relevant problems.

MS1-1: Recent results on inverse problems for fractional differential equations

Masahiro Yamamoto, The University of Tokyo

Email: [email protected]

Abstract: Recently inverse problems for fractional differential equations attract greater attention of researchers, because they are demanded from practical points of view and are interesting as mathematical analytical subjects. I will survey recent results and try to propose future research topics.

MS1-2: Simultaneous inversion for diffusion coefficient and source term in the fractional

diffusion equations

Gongsheng Li, Shandong University of Technology


Abstract: In this talk, we give numerical inversions for determining diffusion coefficient and source term simultaneously in two kinds of fractional diffusion equations. The one is to determine the diffusion coefficient and the spatially dependent source term in the space fractional advection-diffusion equation (SFADE in short) using final observations, the other is to determine the space-dependent diffusion coefficient and the source coefficient in the multi-term time fractional diffusion equation (TFDE in short) using measurements at one inner point.

From a view point of optimality, solving the inverse problem is transformed to minimize an error functional with the help of the solution operator from the unknowns to the additional observations. The solution operator is nonlinear but it is of Lipschitz continuity by which existence of a minimum to the error functional can be obtained. The homotopy regularization algorithm is introduced to solve such simultaneous inversion problems based on the minimization problem, and numerical examples with noisy data are presented. The inversion solutions give good approximations to the exact solutions demonstrating that the homotopy regularization algorithm is efficient for the simultaneous inversion problems arising in the fractional diffusion equations. This is a joint work with Xianzheng Jia (Shandong University of Technology) and Chunlong Sun (Hokkaido University).

[1] G. Li, W. Gu and X. Jia, Numerical inversions for space-dependent diffusion coefficientin the time fractional diffusion equation, J. Inverse Ill-Posed Probl., 20, 2012, 339–366

[2] G. Li, D. Zhang, X. Jia and M. Yamamoto, Simultaneous inversion for the spacedependentdiffusion coefficient and the fractional order in the time-fractional diffusion equation, InverseProblems, 29, 2013, 065014.

[3] X. Jia, D. Zhang, G. Li et al., Numerical inversion of the fractional orders in the space-time fractional advection-dispersion equation with variable coefficients (in Chinese), Math.Numer. Sin., 36, 2014, 113–132.

[4] X. Jia, G. Li, C. Sun and D. Du, Simultaneous inversion for a diffusion coefficient and aspatially dependent source term in the SFADE, Inverse Probl. Sci. Eng., 24, 2016, 832–859.

[5] C. Sun, G. Li and X. Jia, Simultaneous inversion for the diffusion and source coefficientsin the multi-term TFDE, Inverse Probl. Sci. Eng., 25, 2017, 1618–1638.

MS1-3: Recovering a space-dependent source term in a time-fractional diffusion wave equation

Ting Wei, Lanzhou University


Abstract: This work is devoted to identify an space-dependent source function in a time-fractional diffusion wave equation from a noisy final data by a variational regularization approach. The regularity of the corresponding direct problem as well as the existence and uniqueness of a weak solution for the adjoint problem are proved. By the Tikhonov regularization method, the inverse source problem is formulated into a variational problem and a conjugate gradient algorithm is proposed to solve it. Two examples in one dimensional case and one example in two dimensional case are provided to illustrate the efficiency and robust of the proposed method. This is a joint work with X. B. Yan.

MS1-4: On an inverse problem for distributed time-fractional diffusion system



Abstract: To describe some ultra-slow diffusion phenomena in many engineering areas such as a particle's motion in a quenched random force field, the initial boundary value problems for a diffusion equation with distributed time-fractional derivative should be considered. We study an inverse problem for this model, with the purpose of recovering the non-negative weight function for the distributed time-fractional derivative using interior measurement data. This new inverse problem can be considered as generalizations of the fractional diffusion process with multiple fractional terms. Since the measurement data can be specified only in finite time interval, there is no uniqueness for this problem in general. So we recast this problem as an optimization problem, for which we establish the theoretical framework for reconstruction together with some iteration schemes.

Minisymposium 2


Organizer: Jianbin Yang, Hohai University, [email protected]

Time: 14:00-15:40, Aug 13 (M), Room: E1-06-02

Description: Classical approaches to analyze and process data often reduce to designing and minimizing empirical objective functions. The challenge is on the one hand to incorporate the structural information that might be available on the problem. On the other hand to develop optimization schemes that can exploit such a structure. In our minisymposium, the main theme is to explore recent development of variational models including modeling, algorithm, asymptotic analysis, and applications in inverse problems and related topics. The goal is to nurture collaborations among the scientists, as well as to promote further developments in the field of inverse problems and machine learning.

MS2-1: HIRE: Harmonic Incompatibility REmoval Model for Whole Brain Susceptibility

Imaging

Jae Kyu Choi, Shanghai Jiao Tong University


Abstract: It is well known that the inverse problem of quantitative susceptibility mapping (QSM) is ill-posed as the integral kernel has the zeros in the frequency domain. While numerous regularization based models have been proposed to overcome this ill-posedness, they show drawbacks as the field data may contain an incompatibility other than the additive noise. In this talk, we propose a new regularization based susceptibility reconstruction model from a given estimated local field data. Following the underlying Maxwell's equation, we characterize that the estimated data contains the incompatibility which is harmonic almost everywhere. This harmonic incompatibility is embedded in our reconstruction model by means of sparse approximation under discrete Laplacian. To solve the proposed reconstruction model, an alternating minimization algorithm is proposed with the guaranteed convergence. Finally, the numerical experiments show that our proposed models achieve better performance over the existing reconstruction methods.

MS2-2:Wavelet frame based scattered data reconstruction

Jianbin Yang, Hohai University


Abstract: In real world applications many signals contain singularities, like edges in images. Recent wavelet frame based approaches were successfully applied to reconstruct scattered data from such functions while preserving these features. In this talk we present a recent

approach which determines the approximant from shift invariant subspaces by minimizing an L1-regularized least squares problem which makes additional use of the wavelet frame transform in order to preserve sharp edges. We give a detailed analysis of this approach, i.e., how the approximation error behaves dependent on data density and noise level. Moreover, a link to wavelet frame based image restoration models is established and the convergence of these models is analyzed. We present some numerical examples, for instance how to apply this approach to handle coarse grained models in molecular dynamics.

MS2-3: A computational approach for phase space tomography

Chenglong Bao, Tsinghua University


Abstract: Phase space tomography is an important tool in the study of light propagation and dynamics. In this talk, we firstly show that traditional measurement methods result in the coherence loss due to ignoring the pixel contents. Besides, we propose a robust model with trace regularization term to overcome the noise effects. Both simulated and experimental results will be reported.

Minisymposium 3


Organizer: Hongyu Liu, Hong Kong Baptist University

Xiaodong Liu, Chinese Academy of Sciences

Youjun Deng, Central South University

Time: 14:00-15:40, Aug 13 (M), Room: E3-06-14

Description: Recently, significant progress has been achieved for inverse problems associated with the wave phenomena. This includes modeling for new applications, and theoretical and computational studies for inverse scattering problems with minimal a priori knowledge, or optimal measurement data, or limited aperture or phaseless data. Another closely related topic of significant interest is the invisibility technology including cloaking and plasmonic resonances. The minisymposium aims at bringing active researchers working in these areas to report their recent research outputs and exchange ideas.

MS3-1: Some simultaneous recovery results in nonlocal inverse problem

Xinlin Cao, Hong Kong Baptist University


Abstract: The study of fractional and nonlocal operators is currently an active research field in mathematics and has plenty of applications in probability theory, physics, finance and biology. Here we will introduce two significant simultaneous recovery results for fractional differential operators. First, consider anisotropic fractional Schrödinger operator. We are concerned with the simultaneous recovery of the potential q and possibly embedded soft or hard obstacles inside q by the exterior Dirichlet-to-Neumann (DtN) map outside a bounded domain associated with the operator. These are surprising findings since in the local case, they are longstanding problems and still remain open in the literature. Next, we will discuss the determination results of a fractional Helmholtz system with unknown source and medium parameter. We establish several general uniqueness results in simultaneously recovering both the medium parameter and the internal source by the corresponding exterior measurements. In sharp contrast, these unique determination results are also unknown in the local case, which would be of significant importance in thermo- and photo-acoustic tomography.

MS3-2: On identifying magnetized anomalies using geomagnetic monitoring



Abstract: We propose and investigate the inverse problem of identifying magnetized anomalies beneath the Earth using the geomagnetic monitoring. Suppose a collection of magnetized anomalies presented in the shell of the Earth. The presence of the anomalies interrupts the magnetic field of the Earth, monitored above the Earth. Using the difference of the magnetic fields before and after the presence of the magnetized anomalies, we show that one can uniquely recover the locations as well as their material parameters of the anomalies. Our study provides a rigorous mathematical theory to the geomagnetic detection technology that has been used in practice.

MS3-3: An inverse boundary value problem for a nonlinear time harmonic Maxwell system

Catalin Carstea, Hong Kong University of Science and Technology


Abstract: In this talk I will consider a class of nonlinear time harmonic Maxwell systems at fixed frequency, with nonlinear terms real analytic in the fields. Such nonlinear terms appear in theoretical models of nonlinear optics. Under certain regularity conditions, it can be shown that boundary measurements of tangent components of the electric and magnetic fields determine the electric permittivity and magnetic permeability functions as well as the form of the nonlinear terms.

MS3-4: Inverse elastic surface scattering with far-field data

Huaian Diao , Northeast Normal University


Abstract: A rigorous mathematical model and an efficient computational method are proposed to solving the inverse elastic surface scattering problem which arises from the near-field imaging of periodic structures. We demonstrate how an enhanced resolution can be achieved by using more easily measurable far-field data. The surface is assumed to be a small and smooth perturbation of an elastically rigid plane. By placing a rectangular slab of a homogeneous and isotropic elastic medium with larger mass density above the surface, more propagating wave mode scan be utilized from the far-field data which contributes to the reconstruction resolution. Requiring only a single illumination, the method begins with the far-to-near (FtN) field data conversion and utilizes the transformed field expansion to derive an analytic solution for the direct problem, which leads to an explicit inversion formula for the inverse problem. Moreover, a nonlinear correction scheme is developed to improve the accuracy of the reconstruction. Results show that the proposed method is capable of stably reconstructing surfaces with resolution controlled by the slab's density. This is the joint work with Peijun Li and Xiaokai Yuan.

Minisymposium 4


Organizer: Gen Nakamura (Hokkaido University, Japan)

Masahiro Yamamoto (Tokyo University, Japan)

Time: 16:10-17:50, Aug 13 (M), Room: E4-04-02

Description: An inverse problem exists wherever there is an acquisition of data. Any inverse problem plays an important part of analyzing the data. Nowadays development of advanced technology is giving more and more demands to study inverse problems. In such demands the technological aspect of inverse problems are becoming very important. During the past 30 years there were rapid growth of studies in inverse problems both theoretical and numerical. As the outcomes of studies there are several important mathematical idea, concepts and their computational schemes. However they are still mathematically idealistic and they cannot be directly applied in practice. There are a lot of works necessary to realize these in practice. To improve this situation, we need to reexamine the outcomes from the technological point of view so that they can be used to some extent. This mini-symposium aim to make an innovative step toward such technological reexamination.

MS4-1: Some inverse problems in industry and environmental engineering

Masahiro Yamamoto, The University of Tokyo


Abstract: As a mathematician, I have worked for inverse problems solving realistic issues in manufacturing industry and environmental engineering. Here I present such case studies on applications of inverse problems.

MS4-2: Computing the local volatility and the real trend in financial markets by using Bayesian

inference and numerical analysis

Yasushi Ota, Okayama University of Science, Okayama


Abstract: One of the most interesting problems discerned when applying the Black--Scholes model to financial derivatives, is reconciling the deviation between expected and observed values. In our recent work, we derived a new model based on the Black--Scholes model and formulated a new mathematical approach to an inverse problem in financial markets. In this talk, we apply microlocal analysis to prove a uniqueness of the solution and propose numerical method to our inverse problem.

First, we explain our model, which is a type of arbitrage model. Financial derivatives are contracts wherein payment is derived from an underlying asset such as a stock, bond,

commodity, interest, or exchange rate. An underlying asset St at time t is modeled by the following stochastic differential equation:

t, dt t, dW ) (1)

where the process W is the Brownian motion. The parameters t, and t, are called the real drift and the local volatility of the underlying asset, respectively.

Black and Sholes first found how to construct a dynamic portfolio Π of the derivative security, and by using Ito’s lemma and the absence of arbitrage opportunities, the stochastic behavior of the derivative security t, is governed by the following partial differential equation:

22 2

2

1 ( , ) ( ) 02

t S S r S r

t SS (2)

where r and the divided rate are the known constants.

Their approach is developed in probability theory, and the hedging and pricing theory of the derivative security is established as mathematical finance. However, as shown in deriving the Black-Scholes model (see [1]), under the no arbitrage property of the financial market, the real drift does not enter equation (2).

Taking this into account, we have derived the following new model, by using instead of :

22 2

2

1 ( , ) ( ) 02

t A A r A r

t AA (3)

Next we illustrate our new mathematical approach, and then for space-dependent local volatility and real drift, we obtain stable linearization and an integral equation. In [2], we used the standard linearization method with an option pricing inverse problem and derived an integral equation.

Moreover, in this talk, by applying microlocal analysis to the integral equation of our inverse problm, we prove our uniqueness of the solution to our new mathematical model in financial markets.

Finally, by using numerical algorithm and MCMC method to our inverse problem, we confirm that using market prices of options with different strike prices enables us to identify the term structure of local volatility and real drift.

[1] Black F and Sholes M. The pricing of options and corporate liabilities. Journal of PoliticalEconomy, 1973, 81, 637-659.

[2] Ota Y and Kaji S. Reconstruction of local volatility for the binary option model 2016, J.Inverse Ill-posed probl. 24 No.6 727-742.

MS4-3: An inverse random source problem for biharmonic equation

Xiang Xu, Zhejiang University


Abstract: The establishment of relevant model and solving an inverse random source problem are one of the main tools for analyzing mechanical properties of elastic materials. In this talk, we will introduce an inverse random source problem for biharmonic equation. Under some regularity assumptions on the structure of random source, the well-posedness of the forward problem is established. Moreover, based on the explicit solution of the forward problem, we can solve the corresponding inverse random source problem via two transformed integral equations. Numerical examples are presented to illustrate the validity and effectiveness of the proposed inversion method.

MS4-4: The time-discretized one-harmonic flow with constraint in Lie group and its numerical

simulation

Masaaki Uesaka, Hokkaido University


Abstract: In this talk, we propose the numerical scheme for calculating the 1-harmonic flow with a constraint in Lie group. A manifold constraint naturally appears in color image processing or crystallography, and the one-harmonic flow in this situation is useful for data processing. Manifold valued constraint often makes it hard to calculate the gradient of an energy. If the manifold has the Lie group structure, however, we can introduce the relaxed functional with easily computable gradient by using its associated Lie algebra. We explain this idea and show the time-discretization scheme of one-harmonic flow together with the rigorous convergence result. Moreover, we show the numerical simulation in one- and two-dimensional regions using Bregman splitting method.

Minisymposium 5





Time: 16:10-17:50, Aug 13 (M), Room: E3-06-14

MS5-1: On anomalous resonance and cloaking for the Maxwell equation

Hongjie Li, Hong Kong Baptist University


Abstract: In this talk, we mainly consider the resonance and cloaking phenomena for the Maxwell equation. We derive the spectral system for the corresponding operator of the Maxwell equation, depending on which we show that if the parameters of the electric permittivity and the magnetic permeability are properly chosen, then the Maxwell system could induce anomalous resonance. What is more, with another proper choice for the parameters inside a domain, the domain is then invisible to the certain incident wave.

MS5-2: On localizing and concentrating electromagnetic fields.

Yi-Hsuan Lin, Institute for Advanced Study, HKUST


Abstract: We consider field localizing and concentration of electromagnetic waves governed by the time-harmonic anisotropic Maxwell system in a bounded domain. It is shown that there always exist certain boundary inputs which can generate electromagnetic fields with energy localized/concentrated in a given subdomain while nearly vanishing in another given subdomain. The theoretical results may have potential applications in telecommunication, inductive charging and medical therapy. We also derive a related Runge approximation result for the time-harmonic anisotropic Maxwell system with partial boundary data.

MS5-3: Inverse Boundary Value Problem for Non-linear Hyperbolic PDEs

Manmohan Vashisth, TIFR Centre for Applicable Mathematics, Bangalore, India


Abstract: In this talk, we will present an inverse boundary value problem for a non-linear wave equation of divergence form with space dimension 3n . This non-linear wave equation has a trivial solution, i.e. zero solution. By linearizing this equation at the trivial solution, we

have the usual linear isotropic wave equation with the speed ( ) x at each point x in a given

spacial domain. For any small solution u=u(t, x) of this non-linear equation, we have the linear isotropic wave equation perturbed by a divergence with respect to x of a vector whose components are quadratics with respect to ( , )xu t x by ignoring the terms with smallness

3(| ( , ) | )xO u t x . We will show that we can uniquely determine ( ) x and the coefficients of these quadratics by many boundary measurements at the boundary of the spacial domain over finite time interval. More precisely the boundary measurements are given as the so-called the hyperbolic Dirichlet to Neumann map.

This is a joint work with Gen Nakamura (Emeritus Professor at Hokkaido University, Japan).

MS5-4: Data recovery: from limited-aperture to full-aperture



Abstract: Many methods have been proposed for inverse scattering problems in the past thirty years. Most of them use full-aperture data, i.e., data of all the observation directions due to all incident directions. However, in many cases of practical interest, it is not possible to measure the full-aperture data. Consequently, only limited-aperture data over a range of angles are available. Various reconstruction algorithms using limited-aperture data have been developed. However, the quality of the reconstructions are not satisfactory. Other than developing methods using limited-aperture data, we take some alternative approaches to recover the data that can not be measured directly[2,3]. Based on these data, using a recent proposed direct sampling method [1], the quality of the shape and location reconstructions will be greatly improved [2,3].

References

[1] X. Liu, A novel sampling method for multiple multiscale targets from scatteringamplitudes at a fixed frequency, Inverse Problems 33 (2017), 085011.[2] X. Liu and J. Sun, Data recovery: from limited-aperture to full-aperture, arXiv:1708.03029:2017[3] H. Liu, X. Liu and Y. Wang, A joint reconstruction scheme for inverse shape problemswith limited-aperture data, preprint, 2018

Minisymposium 6


Organizer: Gen Nakamura (Hokkaido University, Japan)

Masahiro Yamamoto (Tokyo University, Japan)

Time: 14:00-15:40, Aug 15 (W), Room: E1-06-06

MS6-1: Linearized inverse scattering analysis for defect in anisotropic materials

T. Saitoh, Gunma University


Abstract: In this paper, a linearized inverse scattering technique with the aid of the convolution quadrature time-domain boundary integral equation method (CQBIEM) [1] has been developed for the reconstruction of a defect in anisotropic materials. The CQBEM is utilized to obtain scattered wave data in time-domain from a defect. The obtained time-domain data are transformed into the corresponding frequency-domain ones using the Fourier Transform. The transformed data are adequately treated to implement the shape reconstruction of a defect in anisotropic materials. The Born and Kirchhoff approximations for unknown displacements of a defect are used to linearize this inverse scattering problem. A far-field approximation of the 2-D fundamental solution in frequency-domain for general anisotropic elastodynamics is derived using the stationary phase method, and is used for the proposed inverse scattering formulation.

As numerical examples, some shape reconstruction results for a defect in an austenitic steel are presented. The austenitic steel is widely used in nuclear power plants, and it sometimes has a stress corrosion cracking (SCC) under the corrosion environment due to high temperature and pressure. In addition, the proposed inverse scattering technique is applied to the shape reconstruction of a defect in a carbon fiber reinforced plastic (CFRP). The CFRP has been widely used as one of the important aerospace materials. The austenitic steel and CFRP has anisotropic property. The anisotropic property makes it difficult for non-destructive inspection engineers to detect a defect in such anisotropic materials using ultrasonics. Numerical results show that the proposed inverse scattering method may have a potential to become one of the effective ultrasonic non-destructive evaluation (NDE) tools for anisotropic materials.

This work was supported by JSPS KAKENHI Grant-in-Aid for Scientific Research (B) (Grant number 17H0329400).

MS6-2: A fully nonlinear optimization approach to acousto-electric tomography

Venky Krishnan, TIFR Centre for Applicable Mathematics, Bangalore


Abstract: We consider the nonlinear inverse problem of reconstructing an electric conductivity distribution from the interior power density in a bounded domain. Applications include the novel tomographic method known as acousto-electric tomography, in which the measurement setup in Electrical Impedance Tomography is modulated by ultrasonic waves thus giving rise to a method potentially having both high contrast and high resolution. We formulate the inverse problem as a regularized non-linear optimization problem, show the existence of a minimizer, and derive optimality conditions. We propose a nonlinear conjugate gradient scheme for finding a minimizer based on the optimality conditions. The proposed nonlinear optimization framework can potentially be generalized to other hybrid imaging modalities.

MS6-3: The time-discretized one-harmonic flow with constraint in Lie group and its numerical

simulation



CANCELLED

MS6-3: Born approximation and sequence for hyperbolic equations

Gen Nakamura, Hokkaido University


Abstract: The Born approximation and the Born sequence are considered for hyperbolic equations when we perturb their leading parts. The Born approximation is a finite successive approximation such as the finite term Neumann series for the solution of a hyperbolic equation in terms of the smalleness of the perturbation and if the successive approximation is infinitely many times, then we have the Born series. Due to the so called regularity loss for solutions of hyperbolic equations, we need to assume that data such as the inhomogeneous term of the

equation, Cauchy datum and boundary datum are and also they satisfy the compatibility condition of any order in order to define the Born series. Otherwise we need to smooth each term of the Born series. The convergence of the Born series and the Born series with smoothing are very natural questions to be asked. Also giving an estimate of approximating the solution for finite terms Born series is also an important question in practice. The aims of this talk are to discuss about these questions. We would like to emphasize that we found a small improvement in the usual energy estimate for solutions of an initial value problem for a hypebolic equation, which is very useful for our aims. Since the estimate of approximation is only giving an worst estimate for the approximation, we also provide some numerical studies on these questions which are very suggestive for further theoretical studies on the Born approximation for hyperbolic equations.

Minisymposium 7





Time: 14:00-15:40, Aug 15 (W), Room: E3-06-02

MS7-1: A joint reconstruction scheme for inverse scattering problems with limited aperture

data

Yuliang Wang, Hong Kong Baptist University


Abstract: The talk is concerned with the inverse problem of reconstructing the shape of an unknown/inaccessible scatterer from the corresponding acoustic probing. We are particularly interested in the case with limited-aperture observation data, which arises in a variety of important applications. Though it brings essentially no theoretical difference, the lack of measurement information can cause severe deterioration for the shape reconstruction in various imaging schemes. There have been some research proposals in the literature to deal with this challenging issue that are mainly based on data recovery. In this paper, from a different perspective, we propose a completely novel scheme that concatenates the data recovery and the shape reconstruction. The two processes are closely related, restricting each other and promoting each other. A crucial ingredient for the concatenation is the localizing property of the direct imaging method used for the shape reconstruction. The proposed joint scheme can also incorporate any a prior knowledge of the underlying scatterer in a natural manner. We provide theoretical explanations to the proposed joint scheme, and moreover we conduct extensive numerical experiments to demonstrate the promising features of the scheme in significantly enhancing both the data recovery and the shape reconstruction.

MS7-2: Computation of Interior Transmission Eigenvalues for Elastic Waves

Xia Ji, Chinese Academy of Sciences


Abstract: The goal of this talk is to develop numerical methods computing a few smallest elastic interior transmission eigenvalues, which are of practical importance in inverse scattering theory. The problem is challenging since it is nonlinear, non-self-adjoint, and of fourth order. We construct a nonlinear function whose values are generalized eigenvalues of a series of self-adjoint fourth order problems. The roots of the function are the transmission eigenvalues. Using an H2-conforming finite element for the self-adjoint fourth order

eigenvalue problems, we employ a secant method to compute the roots of the nonlinear function. The convergence of the proposed method is proved. In addition, a mixed finite element method is developed for the purpose of varication. Numerical examples are presented to verify the theory and demonstrate the effectiveness of the two methods.

MS7-3: Inverse problems with one measurement

Eemeli Blåsten, HKUST Jockey Club Institute for Advanced Study


Abstract: Inverse scattering and boundary value problems were traditionally solved by an infinite number of measurements, as done by Sylvester and Uhlmann. It is also well known that a single measurement is not always enough. However under quite general conditions it is possible to find useful information about the unknown from a single measurement. Such conditions include for example the scatterer having a polyhedral shape. This topic also has wide-ranging implications: to invisibility, the interior transmission problem, non-scattering sources and the inverse source problem.

MS7-4: Uniqueness in inverse scattering problems with phaseless far-field data at a fixed

frequency

Haiwen Zhang, Chinese Academy of Sciences


CANCELLED

Minisymposium 8


Organizer: Jianbin Yang, Hohai University, [email protected]

Time: 16:10-17:50, Aug 15 (W), Room: E1-06-06

MS8-1: A finite element method of self-consistent field theory on a general curved surface

Kai Jiang, Xiangtan University


Abstract: In this talk, we will propose a computational framework for the study of self-assembled phases of block copolymers on a general curved surface based on the self-consistent field theory (SCFT). We use the triangulated surface finite element in spatial discretization. Meanwhile, an adaptive approach of optimizing the size of a general curved surface has been proposed to capture its characteristic surface of a given self-assembled patterns. To demonstrate the power of the approach, we investigate the self-assembled patterns of diblock copolymers on several distinct curved surfaces，including spherical, ellipsoid, torus, orthocircle, and parabolic surfaces. The results are consistent with the representative patterns on standard surfaces, such as sphere and torus. Numerical results illustrate the efficiency of our methods.

MS8-2: Data-driven method for image restoration problems

Tongyao Pang, National University of Singapore, Singapore


Abstract: A typical model for image restoration problems consists of two terms, the fidelity term and the penalty term. The former one is usually designed according to the noise statistics, for example, the well-known least square fidelity for Gaussian noise and Kullback-Leibler(KL)-divergence fidelity for Poisson noise. The latter one provides some regularization determined by the prior of the underlying truth, for example, the sparsity prior of the gradients or wavelet coefficients. In this talk, I will present how to design both of these two terms in a data-driven way for image restoration problems.

MS8-3: Stable recovery of analysis based approaches

Yi Shen, Zhejiang Sci-Tech University


Abstract: The theory of compressed sensing shows that it is highly possible to recover a sparse signal from few measurements. Due to its wide applications, compressed sensing has drawn attention of many researchers from the fields of signal and image processing, applied

mathematics, and statistics. In this paper we are interested in signals, which are sparse under redundant tight frames. Some sufficient conditions are provided to guarantee the stable recovery via solving analysis based approaches.

MS8-4: The Stability of SVMs

Daohong Xiang, Zhejiang Normal University


Abstract: In the practical application of kernel based methods like SVMs, practitioner often chooses model parameters, such as regularization parameter and scaling parameter of the kernels, empirically. It is natural to ask what would happen on SVMs estimator when the data points deviate from the structure of the data set. In this talk, I will present many kernel based methods like SVMs have nice stability properties if simultaneously the distribution, the regularization parameter and the kernel change slightly.

Minisymposium 9

MS9: Efficient Reconstruction Methods for Electrical Impedance Tomography

Organizers: Dong Liu, University of Science and Technology of China, China

Maokun Li, Tsinghua University, China

Time: 16:10-17:50, Aug 15 (W), Room: E1-06-07

Description: Inverse scattering and electrical impedance tomography have become indispensable tools for a wide range of applications. Therefore, intriguing inverse problems occur in both fields, involving a variety of different aspects including theory, algorithms, and applications. The mini-symposium focuses on research in this direction, considering both numerical algorithms, real applications, and related experimental studies.

MS9-1: Study on the Feasibility of EIT Absolute Imaging for Human Pulmonary Monitoring

Ke Zhang1,2, Maokun Li1,2, Fan Yang1,2, Shenheng Xu1,2, and Aria Abubakar3 1State Key Laboratory on Microwave and Digital Communications,

Beijing National Research Center for Information Science and Technology (BNRist), 2Department of Electronic Engineering, Tsinghua University, Beijing 100084, China 3Schlumberger, Houston, TX 77478, USA


Abstract: Many lung diseases, such as atelectasis and pulmonary edema, are related to the abnormity of air or liquid contents in the lung. The changes of air or liquid contents can cause the change of conductivity in the lung. As an electrical imaging modality, electrical impedance tomography (EIT) is sensitive to the conductivity contrast interior of the thorax. In EIT measurement, a number of electrodes are attached around the surface of human thorax. Constant currents are injected through some of the electrodes, and the induced surface voltages are measured on other electrodes according to a certain protocol. Compared with differential imaging that invert the difference between data measured at different time, absolute imaging inverts thorax conductivity directly from measured data. It is more appealing to medical applications because the conductivity distribution reflects the structure of the thorax.

The difficulty of absolute imaging for human thorax mainly comes from two aspects. Firstly, the tissues in human thorax are highly inhomogeneous. As a result, a gradient-based optimization method is easily to be stuck in local minima if the initial model is not chosen to be good enough. Secondly, some factors for forward modeling, which often occur on the surface of body, are hard to be exactly known. These factors include boundary shape of the body, positions of the electrodes, skin-electrode contact impedance, complicated current owing around the surface and so on.

In this work, we studied the feasibility of EIT absolute imaging for pulmonary monitoring. EIT data were collected from a human subject. X-ray computed tomography (X-CT) scan images were used to reconstruct the boundary shape of the thorax as well as its inner structures such as lungs, heart, and ribs. It was found that low-conductivity ribs have a strong effect on the simulated data and inversion results of EIT. In addition, the inversion results are also affected by boundary shape and electrode positions in forward modeling. Some unknown surface effect may also need to be considered in the forward modeling. With all the factors analyzed, we may be able to reconstruct the conductivity in thorax with a reasonable accuracy.

MS9-2: New FFT Subspace-Based Optimization Method for Electrical Impedance

Tomography

Zhun Wei and Chen Xudong

Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117583, Singapore


Abstract: Electrical impedance tomography has attracted intense interests recently in both mathematical and engineering communities. It is well-known that EIT is a very challenging problem due to its nonlinear and highly ill-posed properties. Various methods have been proposed to solve EIT problems such as factorization method, unconstrained least squares methods, variationally constrained numerical method, and subspace-based optimization method (SOM).

This paper proposes a new FFT subspace-based optimization method for electrical impedance tomography in a domain with arbitrary boundary shape. Instead of solving problems with circular boundary, where analytical Green's function is available, the proposed method extends to be applicable to a domain with an arbitrary boundary shape. It is found that, compared with SOM, NFFT-SOM can obtain better reconstructed results in dealing with high noise EIT problem. Also, the computational complexity of the proposed method is significantly reduced. It is also found that NFFT-SOM is robust to the change of number of significant singular values (the integer L) for both high and low noise cases, which is an important conclusion for the application EIT.

MS9-3: A parametric level set method for imaging multiphase conductivity using electrical

impedance tomography

Dong Liu1,2,3 and Jiangfeng Du1,2,3 1CAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern

Physics, University of Science and Technology of China (USTC), Hefei 230026, China 2Hefei National Laboratory for Physical Sciences at the Microscale, USTC, China 3Synergetic Innovation Center of Quantum Information and Quantum Physics, USTC, China


Abstract: Electrical impedance tomography (EIT) that provides a cross-sectional image of the interested object from the surface measurement is helpful in biomedical field, e.g., monitoring of lung function. This talk presents a parametric level set (PLS) based reconstruction scheme for reconstructing region boundaries in EIT. The proposed scheme involves applying a level set model to solve the inverse problem of finding the boundaries between the regions having different profiles. The conductivity to be estimated was assumed to be piecewise constant but unknown, and the region boundaries were represented by a PLS function. The parametric representation of the PLS function provides flexibility in presenting a larger class of shapes with fewer terms, significantly reduces the number of unknowns, and consequently speed-up the reconstruction process. Numerical simulations and phantom experiments are performed to validate the performance of the proposed method.

Minisymposium 10


Organizer: Zhiyuan Li, Shandong University of Technology


Time: 14:00-15:40, Aug 16 (Th), Room: E3-06-02

MS10-1: Stability analysis for homogenized diffusion equations

Manabu Machida, Hamamatsu University School of Medicine


Abstract: We consider an inverse problem of determining coefficients of diffusion equations which are obtained by homogenization of two-scale diffusion equations. Suppose that the domain is divided by fractures, which are thin paths. Then the diffusion process in the domain is governed by two diffusion equations at the microscopic scale: one is for the medium and the other is for fractures. Different diffusion equations are obtained by homogenization at the macroscopic scale depending on the boundary condition between the medium and fractures. There is a case that the time derivative of the obtained diffusion equation becomes fractional. We investigate the inverse problem of determining coefficients in the diffusion equations at the macroscopic level and study stability by means of Carleman estimates. This is a joint work with Atsushi Kawamoto (The University of Tokyo).

MS10-2: Unique continuation property for multi-terms time fractional diffusion Equations

Gen Nakamura, Hokkaido University


Abstract: We concern about a Carleman estimate which can give the unique continuation property of solutions for a multi-terms time fractional diffusion equation up to order

(0 2) with general time dependent second order strongly elliptic operator for the diffusion. By using a special Holmgren type transformation which is linear with respect to time, the estimate giving a local unique continuation of solutions is derived via some subelliptic estimate for an operator associated to this transformed equation using calculus of pseudo-differential operators. After that we have given a new argument to derive the global unique continuation of solutions. Here the global unique continuation means as follows.

If u is a solution of the multi-terms time fractional diffusion equation in a domain over the time interval (0, T) and it is supported on 0t , then a zero set of solution over a subdomain

of can be continued to (0, )T .

MS10-3: Uniqueness of the conductivity in a space-time fractional diffusion equation

Lauri Ylinen, University of Helsinki


Abstract: We consider an inverse problem in the space-time fractional diffusion equation

( , ) ( , ) ( , ), t x t x t f x t ( , ) (0, ). x t

Here, ( ) x and (0, ) (0, ) f W . The interested inverse problem is to use the source-to-solution map

(0, ): ( , ) ( , ) | Wf x t u x t

to determine the conductivity ( ) x . The results for direct problem are built at first, such as the spectral representation and a regularity estimate of the solution. Finally the uniqueness theorem is proved.

MS10-4: An inverse random source problem in a fractional diffusion equation

Zhidong Zhang, University of Helsinki


Abstract: In this work we consider an inverse source problem in the following stochastic fractional diffusion equation

( , ) ( , ) ( ) ( ) ( ) ( ),

t x t x t f x h t g x W t

The interested inverse problem is to reconstruct f(x) and g(x) by the statistics of the final time data u(x,T) Some direct problem results are proved at first, such as the existence, uniqueness, representation and regularity of the solution. Then the reconstruction scheme for f and g is given. To tackle the ill-possedness, the Tikhonov regularization is adopted. Finally we give a regularized reconstruction algorithm and some numerical results are displayed.

Contributed Papers 1

Time: 16:10-17:50, Aug 13 (M), Room: E1-06-02 Chair: Won-Kwang Park

CP1-1: A modification of the factorization method for scatterers with different physical

properties

Takashi Furuya, Nagoya University


Abstract: We consider the inverse scattering problem of time-harmonic acoustic plane wave by a mixed type scatterer. Such a scatterer is given as the union of finite components with different physical properties. Some of them are impenetrable obstacles, while the others penetrable inhomogeneous mediums. For the purpose, we derive the factorization method. To remove the a priori assumption of eigenvalues for unknown obstacles in the mixed type scatterer, we modify the far field operator by adding that corresponding to artificial inner and outer domains.

CP1-2: Application of the Floquet-Transform to the Helmholtz Equation and Maxwell

Equations on Locally Perturbed Bi-periodic Structures

Alexander Konschin, University of Bremen


Abstract: We consider time-harmonic scattering problems of electromagnetic and acoustic waves on a bi-periodic inhomogeneous medium which is absorbing on an open set and locally perturbed. Such problems are occurring, e.g., in non-destructive testing methods. For the existence theory, we apply the Bloch-Floquet-transform to reformulate the problem as an equivalent system of coupled variational problems on a bounded domain. This system possesses a unique solution and allows us to construct the solution to the original problem. Apart from existence theory, the framework also serves for numerical calculation of the solution using the finite element method. We use the solver then to reconstruct the perturbation of the refractive index from artificial noisy data by an inexact newton method.

CP1-3: Real-Time Microwave Imaging of Small Anomalies Without Diagonal Elements of the

Scattering Matrix

Won-Kwang Park, Kookmin University


Abstract: We consider a real-time microwave imaging for finding location of small anomalies from scattering matrix whose elements are scattering parameters measured by a small number of dipole antennas. Designed imaging algorithm is based on the representation formula of scattering parameter, application of Born approximation, and the physical interpretation of the measurement data. We carefully explore the mathematical structure of proposed imaging function by finding relationships with the infinite series of Bessel functions of integer order and antenna configuration. The explored structure reveals certain properties of imaging function such as feasibility, uniqueness of imaging, etc. We present the experimental results using real data at f = 925MHz frequency to demonstrate the effectiveness of imaging technique.

The author is grateful to Kwang-Jae Lee and Seong-Ho Son at the Radio Technology Research Department, Electronics and Telecommunications Research Institute (ETRI) for helping in generating scattering matrix data from microwave machine. This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No. NRF-2017R1D1A1A09000547).

CP1-4: Inverse problem for fractional-Laplacian operator with lower order non-local perturbations

Tuhin Ghosh, Hong Kong University of Science and Technology


Abstract: We consider a non-local inverse problem and determine more than one lower order coefficients from the associate Cauchy data. Apart from the global non-locality in the principal part, our operator exhibits regional non-locality in its lower order perturbation. This is a joint work with Dr. S. Bhattachariya and Prof. G. Uhlmann.


Time: 14:00-15:40, Aug 15 (W), Room: E1-06-07 Chair: Mikyoung Lim

CP2-1: Hanke-Raus Heuristic Rule for Landweber Iteration with General Nonsmooth convex

Penalty Functional

Rommel R. Real, The Australian National University


Abstract: In 1994 Hanke and Raus published a seminal paper about a heuristic parameter

choice rule to the Landweber iteration (and Tikhonov regularization) for solving linear ill-posed inverse problems. This parameter choice rule does not require the noise level, which may be inaccessible and prone to improper estimation in many instances. We extend this heuristic rule to the same iteration method, this time with a general nonsmooth convex penalty functional, for solving both linear and nonlinear ill-posed inverse problems problems. We allow the penalty term to be nonsmooth to cover the L1 and TV-penalty terms, which are used to recover solutions with special features, such as sparsity and piecewise constancy. By introducing assumptions on the noisy data, we establish convergence of the iterative method using some tools from convex analysis. We also provide numerical simulations to illustrate performance.

The talk will be based on an ongoing doctoral research.

CP2-2: New geometric factors of the planar inclusion

Doo Sung Choi, Johan Helsing, Mikyoung Lim, KAIST


Abstract: We consider the perturbation of an electric potential due to an a simply connected inclusion with corners. This perturbation admits an expansion whose coefficients are linear combinations of generalized polarization tensors. We define new geometric factors of an insulating planar domain in terms of the associated conformal mapping. The geometric factors are the Fourier coefficients of a generalized external angle of the domain boundary. The generalized external angle contains the Dirac delta singularity at corner points, so we give a criteria for the existence of corners on the domain boundary by using the geometric factors. We made numerical examples wtih integral equation techniques, the Nystr m discretization, and recursively compressed inverse preconditioning.

CP2-3: Series representation of layer potential opreators for the transmission problem

Younghoon Jung, Mikyoung Lim, Department of Mathematical Sciences, KAIST


Abstract: We propose new series solution expansion of layer potential opreators for the 2D conductivity transmission problem. Layer potential formulation arises in may applications, both forward and inverse problems. We apply the geometric function theory to the layer potential technique and derive explicit series representations of related layer potential oprators in terms of the Faber polynomials and the Grunsky's coefficients. In particular, the proposed approach provides a doubly-infinite, self-adjoint matrix representation of the Neumann-Poincare operators and thus we can approximate the eigenvalues of Neumann-Poincare operators in a simple way. In addition, we also present explicit integral formular for the exterior conformal mapping coefficients.

CP2-4: Electric field concentration between nearly touching boundaries using image line

charges

Junbeom Kim, Mikyoung Lim, Department of Mathematical Sciences, KAIST


Abstract: We analyze the gradient blow-up of the solution to the conductivity problem in two dimensions in the presence of an inclusion with eccentric core-shell geometry. Assuming that the core and shell have circular boundaries that are nearly touching, we derive an asymptotic formula for the solution in terms of the single and double layer potentials with image line charges. We also deduce an integral formula with image line charges for the problem relating to two nearly touching separated conductors.


Time: 14:00-15:40, Aug 16 (Th), Room: E3-06-03 Chair: Xinchi Huang

CP3-1: Inverse problems for a magnetohydrodynamic system

Xinchi Huang, The University of Tokyo


Abstract: In this talk, we consider a magnetohydrodynamics (MHD) system which describes the motion of electrically conducting fluids such as plasmas and liquid metals. We follow the formulation derived in Li and Qin [2] for governing equations and we mainly discuss the inverse problems including the determination of a spatially varying factor in the source term as well as the determination of its timeindependent viscosity and resistance. This work is based on the method called Carleman estimate (see [1]). As our main results, we give the uniqueness and stability inequalities for the above inverse problems under some suitable partial boundary measurements.

References

[1] T. Carleman, Sur un probleme d’unicite pour les systemes d’equations aux deriveespartielles a deux variables independentes, Ark. Mat. Astr. Fys., 2 B (1939), 1-9.

[2] T. Li and T. Qin, Physics and Partial Differential Equations, Higher Education Press,Beijing, Vol. 1, 2013.

CP3-2: Inverse Source Problem related to the Gravitational Wave in General Relativity

Hiroshi Takase, The University of Tokyo


Abstract: The gravitational wave is a propagation of distortion of space-time caused by, for instance, collisions of black holes. These days, its observation makes us be interested in this phenomena. The equation which the gravitational wave should satisfy is a system of quasi-linear hyperbolic type equations gained from the Einstein equation by imposing some physical assumptions. In this time, we focus the inverse source problem of the gravitational wave and consider the linearized equation.

CP3-3: Manufacturer's production plan for products sold with warranty in an imperfect

production system under preventive maintenance and trade credits

Chun-Tao Chang1, Mei-Chuan Cheng2* 1Department of Statistics, Tamkang University, Tamsui, Taipei, Taiwan 25137, R.O.C., [email protected] 2Department of International Business, Hsin-Sheng Junior College of Medical Care and Management, Longtan, Taoyuan 32544, Taiwan, R.O.C., [email protected]

Abstract: In the real production system, imperfect quality items may be produced due to imperfect production process or other factors. To avoid economic loss and breakdowns of the system, management should give attention to regular preventive maintenance immediately after production. In addition, trade credit is a popular payment method and represents an important proportion of company finance. In this paper, we provide a manufacturer’s plan for products sold with warranty and preventive maintenance under trade credits. We first establish a proper model, and then provide an easy-to-use method to obtain optimal production plan for the manufacturer to achieve its minimum total cost. Finally, one numerical example is given to illustrate the solution procedure.

CP3-4: Bayesian Estimation of Diffusion, Decay and Source in An Evolution Model with

Application to Biology

J.-C. Croix1, N. Durrande2, M. A. Alvarez3 1GMI, 158 cours Fauriel, 42023 Saint-Etienne, France, [email protected] 2PROWLER.io, 3rd Floor, Charter House, 66-68 Hills Road, Cambridge, CB2 1LA, UK, [email protected] 3Department of Computer Science, The University of Sheffield, 148 Regent Court, 211 Portobello, S1 4DP, UK, [email protected]

Abstract: In experimental sciences, a common task is to fit mathematical models to real-world measurements to improve understanding of natural phenomenon (reverse-engineering or inverse modeling). When complex dynamical systems are considered, such as partial differential equations, this task may become challenging and ill-posed. In this work, we consider the phenomenon of post-transcriptional regulation of Kni gap gene in the early development of Drosophilia melanogaster [1]. More particularly, the production of protein from mRNA is modeled assuming a diffusive evolution model. The objective is then to infer mRNA concentration and both diffusion and decay constant rates (all under positivity constraints) from noisy measurement of the protein concentration. The Bayesian methodology from [2] is applied, providing a form of regularization as well as quantification of uncertainties. The solution is an infinite dimensional (non-Gaussian) probability distribution, which must be dealt with accordingly. Finally, we use both a variational characterization of MAP estimators from [3] and state-of-the-art geometric MCMC sampling from [4] to obtain promising numerical results.

References

1. K. Becker, E. Balsa-Canto, D. Cicin-Sain, A. Hoermann, H. Janssens, J. R. Banga and J. Jaeger, Reverse-Engineering Post-Transcriptional Regulation of Gap Genes in Drosophilia melanogaster, PLOS Computational Biology, 9(10), 2013. 2. A. M. Stuart, Inverse Problems: A Bayesian perspective, Acta Numerica, 19, pp 451-559, 2010. 3. M. Dashti, K. Law, A. Stuart and J. Voss, MAP estimators and their consistency in Bayesian nonparametric inverse problems, Inverse Problems, N°9, vol. 29, 2013 4. A. Beskos, M. A. Girolami, S. Lan, P. E. Farrell and A. Stuart, Geometric MCMC for infinite-dimensional inverse problems, Journal of Computational Physics, pp 327-351, 2017.

Map of Kent Ridge Campus, National University of Singapore

Scan QR code for campus map

University Town

DOVER

CLE

ME

NT

IR

OA

D

WEST COAST ROAD

Ù TO JURONGÙTO

BU

KIT

TIMA

H

AYER RAJAH EXPRESSWAY

PASIR PANJANG ROAD

KENT VALE

ENGINEERING DRIVE 3

INSTITUTE OF SYSTEMS SCIENCE

TEMASEK LIFE SCIENCES LABORATORY

NUS ENTERPRISEMINIMUM VIABLEPRODUCT STUDIO

CENTRE FORMARITIME STUDIES

SINGAPORE SYNCHROTRONLIGHT SOURCE

KENT RIDGE HALL SHEARES HALL

ENG

INEERIN

G D

RIVE 1

CENTRE FORDEVELOPMENT OF TEACHING & LEARNING

Ù TO

HO

LLAN

D RO

AD

TO CITY Ú

KENT VALEHOUSING

MAP NOT TO SCALE

CREATE WAY

CREATE WAY

COLLEGEAVENUE

EAST

COLLEGEAVENUE

EAST

DOVER ROADENTRANCE

CO

LLEGE

AVENU

EW

EST

CREATE WAY

SCIENCEPARK

LT5

E3A

E1AEW1A

EW1

E1

SDE3

SDE1

SDE2

CELC

T-LAB RUNME SHAWCFA STUDIO

ESTATE OFFICE DRIVE

LEE KONG CHIANNATURAL HISTORY

MUSEUM

CO

NSERVATO

RYD

RIVE

UNIVERSITY CULTURAL

CENTRE

NUSMUSEUM

KENT RIDGE CRESCENT

ENGINEERING DRIVE 1ENGINEERING DRIVE 1

EN GINEERING DRIVE 2 LT3LT4

EUSOFFHALL

TEMASEK HALL

KENT RIDGETERMINAL

LT10

LT11

LT8

LT13 LT12

LT9AS 1

AS 2

AS 3 AS 4

AS 7

ARTS LINK

BIZ 1MOCHTAR RIADY

BUILDINGHON

SUI S

ENDRIV

E

COM

PUTI

NGDR

IV

E

AS 5

HENG MUI KENG TERRACE

BUSI

NES

SLI

NK

RESEARCH LINK

AS 6

LT14

LT15

KENT RIDGEGUILD HOUSE

SHAWFOUNDATION

ALUMNIHOUSE

KENT RIDGE DRIVE

SINGAPOREWIND

TUNNELFACILITY

MULTI-PURPOSESPORTS HALL 4

MPSH5

MPSH6

UNIVERSITYHEALTH CENTRE

UNIVERSITYSPORTS CENTRE

(U/C)

SPORTS DRIVE 2

MULTI-PURPOSECOURTS

SPORTSFIELDS

MULTI-PURPOSEFIELDS

FOOTBALLFIELD

HANDBALL/NETBALL

COURTS

TENNIS COURTS

TENNIS COURTS

RUN

NIN

G

TENNIS COURTS

29

INSTITUTE OF SOUTH ASIAN STUDIES

MIDDLE EASTINSTITUTE ENERGY

STUDIESINSTITUTE

9

8

14A

14 15 16

7 65 4

3

18

17

2

INSTITUTE FOR MATHEMATICAL

SCIENCES

PRINCE GEORGE’S PARK RESIDENCES

OFFICE OF CAMPUS SECURITY HQ

6 5 4

3 21

109

18 14 12A12

11CENTRE FOR PROTECTIVETECHNOLOGY

TROPICAL MARINESCIENCE INSTITUTE

KENT R IDGE ROAD

LEE WEE KHENGBUILDING (S1A)

BRENNER CENTRE FOR MOLECULAR MEDICINE

LT32

S2

S3

S4

S4AS5

S1

S17

DSO@KENT RIDGE

MEDICALLIBRARY

LT34 LT33

LT31

S6

LT37TAHIR FOUNDATION

BUILDING (MD1)

MD2

MD3

MD4

MD11

LT35

LT36

SCIENCELIBRARY

SOU

THB

UO

NA

VIS

TA R

OA

D

NUHMEDICALCENTRE

NUHKENT RIDGE

WING

NUHSTOWERBLOCK

NUHSERVICEBLOCK

NATIONALUNIVERSITYCENTRE FORORAL HEALTH

(U/C)

COLLEGE AVENUE EAST

CENDANACOLLEGE

CREATETOWER

CREATETOWER

TOWN GREEN

EDUCATIONRESOURCE

CENTRE

COLL

EGE AVENUE WEST

ELM COLLEGE

SAGACOLLEGE

STEPHEN RIADY CENTRE

SCIEN

CE D

RIVE 3

SCIENCE DRIVE 4

SCIENCE DRIVE 2

SCIEN

CE D

RIVE 1

KENT RIDGE

LOWER KENT RIDGE ROAD

SEPAKTAKRAW

ARCHERY CORNER/VOLLEYBALL COURTS

BASKETBALLCOURTS

LT1

LT2

LT6

MUSICLIBRARY

ALICE LEE PLAZA

LT21

LT20

Ù TO JURONG

CL

EM

EN

TI

RO

AD


KENT RIDGE CRESCENT

PRINCE GEORGE’S PARK

SHAWFOUNDATIONBUILDING

ENGINEERING DRIVE 4

S12

S11

S7 S8 (U/C)

MD7

E7(U/C)

AS 8

ARCHITECTURE

DRIVE

SDE4 (NZEB@SDE)(U/C)

DOVER ROAD

S2S

LT25

LT24

YUSOF ISHAK HOUSE

EW2(WS2)

E6

E4A

E4

E3

E5

COMPUTERCENTRE

E2

S14S13

S15

S16

FRONTIER PHASE 1

CHUA THIAN POH HALL

LOW TUCK KWONG HALL

TEMBUSU COLLEGE

NORTH TOWER

SOUTHTOWER

COLLEGE OF ALICE & PETER TAN

RESIDENTIAL COLLEGE 4

CINNAMONCOLLEGE

LT50

LT51

LT52

LT53

UTOWNRESIDENCE

TOWN PLAZA

RAFFLESHALL

KUOKFOUNDATIONHOUSE

VENTUS (UNIVERSITY

CAMPUS INFRASTRUCTURE)

COM1

YUSOF ISHAKHOUSE PLAZA

NUSSTAFF CLUB

UNIVERSITYHALL

LT26

LT28LT29

LT27MD9 MD10

FRONTIER PHASE 2

(U/C)

MED

ICAL D

RIVE

NATIONALUNIVERSITYHOSPITAL

(NUH)

NUHMAIN

BUILDING

CENTRE FORLIFE SCIENCES

KING EDWARD VII HALL

PGP HOUSE

COM2

LT16

LT17

LT19

LT18 BIZ2

HON SUI SENMEMORIALLIBRARY

I3

TECHNOLOGY CENTRE

FOR OFFSHORE AND MARINE,

SINGAPORE (U/C)

CHINESELIBRARY

LIBRARYANNEXE

CENTRALLIBRARY

THEDECK

TECHNOEDGE

THETERRACE

ENTRANCE D

NUS GRADUATESCHOOL FORINTEGRATIVE SCIENCES AND ENGINEERING

CENTRE FOR TRANSLATIONALMEDICINE (MD6)

ENTRANCE E

COLL

EGE

LINK

FACULTY OFDENTISTRY

YONG LOO LINSCHOOL OF MEDICINE

SAW SWEE HOCKSCHOOL OF

PUBLIC HEALTH

E2A

FACULTY OF SCIENCE

NUS BUSINESS SCHOOL

FACULTY OF ARTS & SOCIAL

SCIENCES

SCHOOL OF DESIGN AND

ENVIRONMENT

FACULTY OF ENGINEERING

SCHOOL OF COMPUTING

YONG SIEW TOHCONSERVATORY

OF MUSIC

YALE-NUSCOLLEGE

SCHOOL OFCONTINUING

AND LIFELONGEDUCATION

UNIVERSITYSCHOLARS

PROGRAMME

LT7A

LT7

EA EA

NATIONALCYBERSECURITYR&D LABORATORY

ENTRANCE A

ENTRANCE B

ENTRANCE C

RIDGE VIEWRESIDENTIAL COLLEGE

96151B2

CBTC1

C

33183188

3396

183188

33183188

95151

9596151

95151

A2B1B2C

D1

9596151

A1B1D1

BTC1

96151

A2, A2E B1, B2 C, D1UT-CCE

151A2, CBTC1, BTC2

D1, D2

A1B2 D1

BTC1

A1B1D1

BTC1

A1A2D1

A2B2D1

A1B1

A1ED1

BTC1

B1, B2, CBTC1, BTC2

10, 33, 95151, 200, 201

A1, C D2, A1E

A2C

D2

95

95

A1A1EB1 D1

BTC1

183188

183188

A2A2EB1D1

10, 30, 51, 143183, 188, 200

10, 30, 51, 143183, 188, 200

95

95

A1C

D2

A2C

D2

9595

A1, A1E, CD2, FoS-UT

A2A2E

CD2

A2

A2

A1

A1

A1A2D2

BTC1

A1, A1E, D2

A2, A2E, D2

95

95

95

97197963

95

97197198963

92200

92200

33196

3396

151183196

D1D2

UT-FoSB1B2

3396183188

B2C

BTC2

97197198963

97197198963

9596151

A2B2D1

A

A A

A

A

A

A

A

A

AA

A

A A

A

A

AA

P

P

P

16

14

13

11

15

15

12

12B

11A

P

10A

9

10

8

6

6A

6B

5A

3A

4

2

2A

2B

2B

4

5

3

10A

10B

17

1

P

12A

10C

18

11B

11

4A

A

B

C

D

E

F

G

H

I

1 2 3 4 5 6 7 8

Kent RidgeCampus

Legend

Internal Shuttle Bus Stop

Public Bus Stop

Security Post

Student / Visitor Centre

Emergency Call Point

Library

Accommodation

Affiliated Institute

Facility / Resource

Faculty / School / RIC

Clinic / Wellness Centre

Food & Beverage

Auditorium

21 Lower Kent Ridge Road, Singapore 119077

Handicap Route

CarparkP

ATM

Bicycle Rack

Linkway

SCHOOLS BLK NO./NAME GRIDArts & Social Sciences www.fas.nus.edu.sg Shaw Foundation Building B2/B3Business bschool.nus.edu.sg Mochtar Riady Building B4Computing www.comp.nus.edu.sg COM1 C3/C4Continuing and Lifelong Educationscale.nus.edu.sg

Education of Service Centre G2

Dentistry www.dentistry.nus.edu.sg Faculty of Dentistry E6Design & Environment sde.nus.edu.sg SDE1 C2Engineering www.eng.nus.edu.sg EA D1/D2Integrative Sciences and Engineeringnus.edu.sg/ngs

Centre for Life Sciences (CeLS) C6

Medicine medicine.nus.edu.sg NUHS Tower Block C8/D6Music music.nus.edu.sg Yong Siew Toh Conservatory of Music E2/F2Public Health sph.nus.edu.sg Tahir Foundation Building D6Science science.nus.edu.sg S16 D5/D6University Scholars Programmeusp.nus.edu.sg

Cinnamon College H2

Yale-NUS College yale-nus.edu.sg Yale-NUS College G1/H1

RESEARCH CENTRES OF EXCELLENCE BLK NO./NAME GRIDCancer Science Institute of Singapore Centre for Translational Medicine (MD6) D7Centre for Quantum Technologies S15 D6/E6Mechanobiology Institute, Singapore T-Lab D2

KENT RIDGE CAMPUS LISTINGUNIVERSITY-LEVEL RESEARCHINSTITUTES/CENTRES (RCs)

BLK NO./NAME GRID

Life Sciences Institute CeLS C6Lloyd’s Register Foundation Institute for thePublic Understanding of Risk

University Hall (interim) D5

Middle East Institute Blk B, 29 Heng Mui Keng Terrace A6NUS Environmental Research Institute T-Lab D2NUS Global Asia Institute S17 E6NUS Nanoscience and Nanotechnology Institute E3 D2NUS Risk Management Institute I3 B4/B5Singapore Institute for Neurotechnology CeLS C6Singapore Nuclear Research and Safety Initiative CREATE Tower F2/F3/G3Singapore Synchrotron Light Source 5 Research Link C4Solar Energy Research Institute of Singapore E3A D2/E2Temasek Laboratories T-Lab D2The Logistics Institute-Asia Pacific I3 B4/B5Tropical Marine Science Institute S2S D3

UNIVERSITY-LEVEL RESEARCHINSTITUTES/CENTRES (RICs)

BLK NO./NAME GRID

Asia Research Institute AS8 C3Biomedical Institute for Global HealthResearch and Technology

Centre for Translational Medicine (MD6) D7

Centre for Advanced 2D Materials S14 D5/D6Centre for Maritime Studies 15 Prince George’s Park B5/C5Centre for Remote Imaging, Sensingand Processing

S17 E6

Energy Studies Institute Blk A, 29 Heng Mui Keng Terrace A6Institute for the Application of LearningScience and Educational Technology

University Hall D5

Institute for Mathematical Sciences 3 Prince George’s Park C6Institute of Data Science AS6 (interim) C3Institute of Operations Research and Analytics University Hall D5Institute of Real Estate Studies I3 B5Institute of South Asian Studies Blk B, 29 Heng Mui Keng Terrace B6Interactive & Digital Media Institute I3 B5

ADMINISTRATIVE OFFICES/CENTRES/TEACHING UNITS

BLK NO./NAME GRID

Office of Alumni Relations Shaw Foundation Alumni House B4Office of Campus Amenities Ventus (University Campus Infrastructure) B2Office of Campus Security 17 & 18 Prince George’s Park B6/C6Office of Corporate Relations University Hall D5Office of Privacy and Compliance University Hall D5Office of the Deputy President (Administration) University Hall D5Office of the Deputy President(Research & Technology)

University Hall D5

Office of Environmental Sustainability Ventus (University Campus Infrastructure) B2Office of Estate Development Ventus (University Campus Infrastructure) B2Office of Facilities Management Ventus (University Campus Infrastructure) B2Office of Financial Services University Hall D5Office of Housing Services Kent Vale E1Office of Human Resources University Hall D5Office of Internal Audit University Hall D5Office of Legal Affairs University Hall D5Office of the President University Hall D5Office of the Provost University Hall D5Office of Resource Planning University Hall D5Office of Risk Management University Hall D5Office of Safety, Health & Environment Ventus (University Campus Infrastructure) B2Office of Student Affairs Yusof Ishak House D3Office of the Vice President(Campus Infrastructure)

Ventus (University Campus Infrastructure) B2

Office of the Vice President(University & Global Relations)

University Hall D5

Office of Professional Engineering &Executive Education

E1 D2

Registrar’s Office University Hall D5Student Service Centre Yusof Ishak House D3Temasek Defence Systems Institute E1 D2University Health Centre University Health Centre E4University Town Management Office Stephen Riady Centre G1Visitors Centre Stephen Riady Centre G1

LECTURE THEATRES GRID LECTURE THEATRES GRID LECTURE THEATRES GRIDLT 1 D2 LT 15 C3 LT 33 E6LT 2 D2 LT 16 B4 LT 34 E6LT 3 D3 LT 17 B4 LT 35 (Peter & Mary Fu

Lecture Theatre)D6

LT 4 D3 LT 18 B4 LT 36 (Alice & Peter TanLecture Theatre)

D7

LT 5 D2 LT 19 B4 LT 37 D6LT 6 D2 LT 20 D5 LT 50 F2LT 7 D2 LT 21 D6 LT 51 F2LT 7A D1/E1 LT 24 D6 LT 52 F2LT 8 B3 LT 25 D6 LT 53 F2LT 9 B3 LT 26 D6 Engineering Auditorium D1/E1LT 10 B3 LT 27 (Lim Seng Tjoe

Lecture Theatre)D6/E6 Hon Sui Sen Auditorium B4

LT 11 B2/C2

LT 28 E6 The Ngee Ann KongsiAuditorium

G2

LT 12 B2 LT 29 E6 UTown Auditorium 1 F2LT 13 (NUS Theatrette) B2 LT 31 (Science

Auditorium)D6 UTown Auditorium 2 F2

LT 14 C3 LT 32 D5 UTown Auditorium 3 H2

HALLS OFRESIDENCE

GRID RESIDENTIALCOLLEGES

GRID STUDENTRESIDENCES

GRID

Eusoff Hall A2/B2 Cinnamon College H2 PGP House B7Kent Ridge Hall A4/B4 College of Alice &

Peter TanH1/H2 Prince George’s Park

ResidencesB6/B7

King Edward VII Hall B7/C6/C7

Residential College 4 H1/H2/I1/I2

UTown Residence G2

Raffles Hall E2/E3 Ridge ViewResidential College

D4

Sheares Hall A5/B5 Tembusu College G2/H2Temasek Hall A3/B3


BLK NO./NAME GRID

Alice Lee Centre for Nursing Studies MD11 D6/D7Central Procurement Office University Hall D5Centre for Development of Teaching &Learning

Library Annexe C3/D3

Centre for English Language Communication CELC C2Centre for Future-ready Graduates Yusof Ishak House D3Centre for Instructional Technology Computer Centre D2/D3Centre for Language Studies AS4 B3Computer Centre Computer Centre D2/D3Design Incubation Centre SDE2 C2Development Office Shaw Foundation Alumni House B4Engineering Design and Innovation Centre E2A D2Institute of Systems Science 25 Heng Mui Keng Terrace B5International Relations Office Shaw Foundation Alumni House B4Investment Office University Hall D5Lee Kong Chian Natural History Museum Lee Kong Chian Natural History Museum E2National University Medical Institutes MD11 D6/D7NUS Centre For the Arts University Cultural Centre E1/E2NUS Enterprise I3 B4/B5NUS Entrepreneurship Centre I3 B4/B5NUS Industry Liaison Office I3 B4/B5NUS Museum University Cultural Centre E2NUS Overseas Colleges I3 B4/B5NUS Press AS3 B2/B3NUS (Suzhou) Research Institute Liaison Office University Hall D5Office of Admissions / Office of Financial Aid Stephen Riady Centre F1/F2/

G1/G2

Faculty of Engineering

Kent Ridge MRT station

University Town

DOVER

CLEM

ENTI

RO

AD

WEST COAST ROAD

Ù TO JURONGÙTO

BUK

ITTIM

AH


PASIR PANJANG ROAD

KENT VALE

ENGINEERING DRIVE 3







ENG

INEERIN

G DRIVE 1


ÙTO

HOLLA

ND

ROA

D

TO CITYÚ

KENT VALEHOUSING

MAP NOT TO SCALE

CREATE WAY

CREATE WAY

COLLEGEAVENUE

EAST

COLLEGE AVENUEEAST

DOVER ROADENTRANCE

COLLEG

EAVEN

UE

WEST

CREATE WAY

SCIENCEPARK

LT5

E3A

E1AEW1A

EW1

E1

SDE3

SDE1

SDE2

CELC


ESTATE OFFICE DRIVE


MUSEUM

CON

SERVATORY D

RIVE

UNIVERSITY CULTURAL

CENTRE

NUSMUSEUM

KENT RIDGE CRESCENT

ENGINEERING DRIVE 1ENGINEERING DRIVE 1


EUSOFFHALL

TEMASEK HALL

KENT RIDGETERMINAL

LT10

LT11

LT8

LT13 LT12

LT9AS 1

AS 2

AS 3 AS 4

AS 7

ARTS LINK

BIZ 1MOCHTAR RIADY

BUILDINGHON

SUI S

ENDRIV

E

COM

PUTI

NGDR

IV

E

AS 5


BUSI

NES

SLI

NK

RESEARCH LINK

AS 6

LT14

LT15


SHAWFOUNDATION

ALUMNIHOUSE

KENT RIDGE DRIVE

SINGAPOREWIND

TUNNELFACILITY


MPSH5

MPSH6



(U/C)

SPORTS DRIVE 2

MULTI-PURPOSECOURTS

SPORTSFIELDS

MULTI-PURPOSEFIELDS

FOOTBALLFIELD

HANDBALL/NETBALL

COURTS

TENNIS COURTS

TENNIS COURTS

RUNN

ING

TENNIS COURTS

29



STUDIESINSTITUTE

9

8

14A

14 15 16

7 65 4

3

18

17

2


SCIENCES



6 5 4

3 21

109

18 14 12A12



KENT R IDGE ROAD



LT32

S2

S3

S4

S4AS5

S1

S17

DSO@KENT RIDGE

MEDICALLIBRARY

LT34 LT33

LT31

S6


BUILDING (MD1)

MD2

MD3

MD4

MD11

LT35

LT36

SCIENCELIBRARY

SOU

THBU

ON

AV

ISTA

RO

AD

NUHMEDICALCENTRE

NUHKENT RIDGE

WING

NUHSTOWERBLOCK

NUHSERVICEBLOCK


(U/C)

COLLEGE AVENUE EAST

CENDANACOLLEGE

CREATETOWER

CREATETOWER

TOWN GREEN

EDUCATIONRESOURCE

CENTRE

COLL

EGE AVENUE WEST

ELM COLLEGE

SAGACOLLEGE


SCIENCE DRIVE 3

SCIENCE

DRIVE4

SCIENCEDRIVE 2

SCIENCE

DRIVE1

KENT RIDGE


SEPAKTAKRAW


BASKETBALLCOURTS

LT1

LT2

LT6

MUSICLIBRARY

ALICE LEE PLAZA

LT21

LT20

ÙTO JURONG

CLE

ME

NT

IR

OA

D


KENT RIDGE CRESCENT



ENGINEERING DRIVE 4

S12

S11

S7 S8 (U/C)

MD7

E7(U/C)

AS 8

ARCHITECTURE DRIVE


DOVER ROAD

S2S

LT25

LT24

YUSOF ISHAK HOUSE

EW2(WS2)

E6

E4A

E4

E3

E5

COMPUTERCENTRE

E2

S14S13

S15

S16

FRONTIER PHASE 1

CHUA THIAN POH HALL

LOW TUCK KWONG HALL

TEMBUSU COLLEGE

NORTH TOWER

SOUTHTOWER



CINNAMONCOLLEGE

LT50

LT51

LT52

LT53

UTOWNRESIDENCE

TOWN PLAZA

RAFFLESHALL

KUOKFOUNDATIONHOUSE

VENTUS (UNIVERSITY


COM1


NUSSTAFF CLUB

UNIVERSITYHALL

LT26

LT28LT29

LT27MD9 MD10

FRONTIER PHASE 2

(U/C)

MEDICAL

DRIVE


(NUH)

NUHMAIN

BUILDING



PGP HOUSE

COM2

LT16

LT17

LT19

LT18 BIZ2


I3

TECHNOLOGY CENTRE


SINGAPORE (U/C)

CHINESELIBRARY

LIBRARYANNEXE

CENTRALLIBRARY

THEDECK

TECHNOEDGE

THETERRACE

ENTRANCE D



ENTRANCE E

COLL

EGE

LINK

FACULTY OFDENTISTRY



PUBLIC HEALTH

E2A

FACULTY OF SCIENCE

NUS BUSINESS SCHOOL


SCIENCES

SCHOOL OF DESIGN AND

ENVIRONMENT


SCHOOL OFCOMPUTING


OF MUSIC

YALE-NUSCOLLEGE

SCHOOL OFCONTINUING


UNIVERSITYSCHOLARS

PROGRAMME

LT7A

LT7

EA EA


ENTRANCE A

ENTRANCE B

ENTRANCE C


96151B2

CBTC1

C

33183188

3396

183188

33183188

95151

9596151

95151

A2B1B2C

D1

9596151

A1B1D1

BTC1

96151


151A2, CBTC1, BTC2

D1, D2

A1B2 D1

BTC1

A1B1D1

BTC1

A1A2D1

A2B2D1

A1B1

A1ED1

BTC1

B1, B2, CBTC1, BTC2

10, 33, 95151, 200, 201

A1, C D2, A1E

A2C

D2

95

95

A1A1EB1 D1

BTC1

183188

183188

A2A2EB1D1

10, 30, 51, 143183, 188, 200

10, 30, 51, 143183, 188, 200

95

95

A1C

D2

A2C

D2

9595


A2A2E

CD2

A2

A2

A1

A1

A1A2D2

BTC1

A1, A1E, D2

A2, A2E, D2

95

95

95

97197963

95

97197198963

92200

92200

33196

3396

151183196

D1D2

UT-FoSB1B2

3396183188

B2C

BTC2

97197198963

97197198963

9596151

A2B2D1

A

A A

A

A

A

A

A

A

AA

A

A A

A

A

AA

P

P

P

16

14

13

11

15

15

12

12B

11A

P

10A

9

10

8

6

6A

6B

5A

3A

4

2

2A

2B

2B

4

5

3

10A

10B

17

1

P

12A

10C

18

11B

11

4A

A

B

C

D

E

F

G

H

I

1 2 3 4 5 6 7 8

Kent RidgeCampus

Legend


Public Bus Stop

Security Post



Library

Accommodation


Facility / Resource



Food & Beverage

Auditorium


Handicap Route

CarparkP

ATM

Bicycle Rack

Linkway






Cinnamon College H2




BLK NO./NAME GRID





BLK NO./NAME GRID




S17 E6


University Hall D5



BLK NO./NAME GRID


University Hall D5




University Hall D5


E1 D2



Lecture Theatre)D6


D7



LT 11 B2/C2


G2




HALLS OFRESIDENCE



GRID



ResidencesB6/B7



UTown Residence G2


D4



BLK NO./NAME GRID




G1/G2

Map of Faculty of Engineering

Registration

E4-04-02 Public bus stop and shuttle bus stop

Public bus stop for bus 188

imste

Oval

imste

Text Box

Fiesta Restaurant: Dinner reception

imste

Line

University Town

DOVER

CLEM

ENTI

RO

AD

WEST COAST ROAD

Ù TO JURONGÙTO

BUKIT

TIMA

H


PASIR PANJANG ROAD

KENT VALE

ENGINEERING DRIVE 3







ENGINEERING DRIVE 1


ÙTO

HOLLAND

ROAD

TO CITY Ú

KENT VALEHOUSING

MAP NOT TO SCALE

CREATE WAY

CREATE WAY

COLLEGE AVENUEEAST

COLLEGE AVENUE EAST

DOVER ROADENTRANCE

COLLEGEAVENUE

WEST

CREATE WAY

SCIENCEPARK

LT5

E3A

E1AEW1A

EW1

E1

SDE3

SDE1

SDE2

CELC


ESTATE OFFICE DRIVE


MUSEUM

CONSERVATORYDRIVE

UNIVERSITY CULTURAL

CENTRE

NUSMUSEUM

KENT RIDGE CRESCENT

ENGINEERINGDRIVE 1

ENGINEERING DRIVE 1


EUSOFFHALL

TEMASEK HALL

KENT RIDGETERMINAL

LT10

LT11

LT8

LT13 LT12

LT9AS 1

AS 2

AS 3 AS 4

AS 7

ARTS LINK

BIZ 1MOCHTAR RIADY

BUILDINGHON

SUI S

ENDRIVE

COM

PUTIN

GDR

IVE

AS 5


BUSI

NESS

LINK

RESEARCH LINK

AS 6

LT14

LT15


SHAWFOUNDATION

ALUMNIHOUSE

KENT RIDGE DRIVE

SINGAPOREWIND

TUNNELFACILITY


MPSH5

MPSH6



(U/C)

SPORTS DRIVE 2

MULTI-PURPOSECOURTS

SPORTSFIELDS

MULTI-PURPOSEFIELDS

FOOTBALLFIELD

HANDBALL/NETBALL

COURTS

TENNIS COURTS

TENNIS COURTS

RUNNING

TENNIS COURTS

29



STUDIESINSTITUTE

9

8

14A

14 15 16

7 65 4

3

18

17

2


SCIENCES



6 5 4

3 21

109

18 14 12A12



KENT R IDGE ROAD



LT32

S2

S3

S4

S4AS5

S1

S17

DSO@KENT RIDGE

MEDICALLIBRARY

LT34 LT33

LT31

S6


BUILDING (MD1)

MD2

MD3

MD4

MD11

LT35

LT36

SCIENCELIBRARY

SOU

THBU

ON

AVI

STA

ROA

D

NUHMEDICALCENTRE

NUHKENT RIDGE

WING

NUHSTOWERBLOCK

NUHSERVICEBLOCK


(U/C)

COLLEGE AVENUE EAST

CENDANACOLLEGE

CREATETOWER

CREATETOWER

TOWN GREEN

EDUCATIONRESOURCE

CENTRE

COLL

EGE AVENUE WEST

ELM COLLEGE

SAGACOLLEGE


SCIENCE DRIVE 3

SCIENCEDRIVE

4

SCIENCEDRIVE 2

SCIENCEDRIVE

1

KENT RIDGE


SEPAKTAKRAW


BASKETBALLCOURTS

LT1

LT2

LT6

MUSICLIBRARY

ALICE LEE PLAZA

LT21

LT20

ÙTO JURONG

CLEM

ENTI

RO

AD


KENT RIDGE CRESCENT



ENGINEERING DRIVE 4

S12

S11

S7 S8 (U/C)

MD7

E7(U/C)

AS 8

ARCHITECTUREDRIVE


DOVER ROAD

S2S

LT25

LT24

YUSOF ISHAK HOUSE

EW2(WS2)

E6

E4A

E4

E3

E5

COMPUTERCENTRE

E2

S14S13

S15

S16

FRONTIER PHASE 1

CHUA THIAN POH HALL

LOW TUCK KWONG HALL

TEMBUSU COLLEGE

NORTH TOWER

SOUTHTOWER



CINNAMONCOLLEGE

LT50

LT51

LT52

LT53

UTOWNRESIDENCE

TOWN PLAZA

RAFFLESHALL

KUOKFOUNDATIONHOUSE

VENTUS (UNIVERSITY


COM1


NUSSTAFF CLUB

UNIVERSITYHALL

LT26

LT28LT29

LT27MD9 MD10

FRONTIER PHASE 2

(U/C)

MEDICAL

DRIVE


(NUH)

NUHMAIN

BUILDING



PGP HOUSE

COM2

LT16

LT17

LT19

LT18 BIZ2


I3

TECHNOLOGY CENTRE


SINGAPORE (U/C)

CHINESELIBRARY

LIBRARYANNEXE

CENTRALLIBRARY

THEDECK

TECHNOEDGE

THETERRACE

ENTRANCE D



ENTRANCE E

COLL

EGE LIN

K

FACULTY OFDENTISTRY



PUBLIC HEALTH

E2A

FACULTY OF SCIENCE

NUS BUSINESS SCHOOL


SCIENCES

SCHOOL OFDESIGN AND

ENVIRONMENT


SCHOOL OFCOMPUTING


OF MUSIC

YALE-NUSCOLLEGE

SCHOOL OFCONTINUING


UNIVERSITYSCHOLARS

PROGRAMME

LT7A

LT7

EA EA


ENTRANCE A

ENTRANCE B

ENTRANCE C


96151B2

CBTC1

C

33183188

3396

183188

33183188

95151

9596151

95151

A2B1B2C

D1

9596151

A1B1D1

BTC1

96151


151A2, CBTC1, BTC2

D1, D2

A1B2 D1

BTC1

A1B1D1

BTC1

A1A2D1

A2B2D1

A1B1

A1ED1

BTC1

B1, B2, CBTC1, BTC2

10, 33, 95151, 200, 201

A1, C D2, A1E

A2C

D2

95

95

A1A1EB1 D1

BTC1

183188

183188

A2A2EB1D1

10, 30, 51, 143183, 188, 200

10, 30, 51, 143183, 188, 200

95

95

A1C

D2

A2C

D2

9595


A2A2E

CD2

A2

A2

A1

A1

A1A2D2

BTC1

A1, A1E, D2

A2, A2E, D2

95

95

95

97197963

95

97197198963

92200

92200

33196

3396

151183196

D1D2

UT-FoSB1B2

3396183188

B2C

BTC2

97197198963

97197198963

9596151

A2B2D1

A

A A

A

A

A

A

A

A

AA

A

A A

A

A

AA

P

P

P

16

14

13

11

15

15

12

12B

11A

P

10A

9

10

8

6

6A

6B

5A

3A

4

2

2A

2B

2B

4

5

3

10A

10B

17

1

P

12A

10C

18

11B

11

4A

A

B

C

D

E

F

G

H

I

1 2 3 4 5 6 7 8

Kent RidgeCampus

Legend


Public Bus Stop

Security Post



Library

Accommodation


Facility / Resource



Food & Beverage

Auditorium


Handicap Route

CarparkP

ATM

Bicycle Rack

Linkway






Cinnamon College H2




BLK NO./NAME GRID





BLK NO./NAME GRID




S17 E6


University Hall D5



BLK NO./NAME GRID


University Hall D5




University Hall D5


E1 D2



Lecture Theatre)D6


D7



LT 11 B2/C2


G2




HALLS OFRESIDENCE



GRID



ResidencesB6/B7



UTown Residence G2


D4



BLK NO./NAME GRID




G1/G2

Location of parallel session rooms: E1, E3 and E4

13-Aug 15-Aug 16-Aug

E1-06-02 E1-06-06 E3-06-02

E3-06-14 E1-06-07 E3-06-03

E4-04-02 E3-06-02

University Town

DOVER

CLEM

ENTI

RO

AD

WEST COAST ROAD

Ù TO JURONGÙTO

BU

KIT

TIMA

H


PASIR PANJANG ROAD

KENT VALE

ENGINEERING DRIVE 3







ENG

INEERIN

GDRIVE

1


ÙTO

HOLLA

ND

ROA

D

TO CITYÚ

KENT VALEHOUSING

MAP NOT TO SCALE

CREATE WAY

CREATE WAY

COLLEGEAVENUE

EAST

COLLEGE AVENUEEAST

DOVER ROADENTRANCE

COLLEG

EAVEN

UE

WEST

CREATE WAY

SCIENCEPARK

LT5

E3A

E1AEW1A

EW1

E1

SDE3

SDE1

SDE2

CELC


ESTATE OFFICE DRIVE


MUSEUM

CON

SERVATORY

DRIVE

UNIVERSITY CULTURAL

CENTRE

NUSMUSEUM

KENT RIDGE CRESCENT

ENGINEERINGDRIVE 1

ENGINEERING DRIVE 1


EUSOFFHALL

TEMASEK HALL

KENT RIDGETERMINAL

LT10

LT11

LT8

LT13 LT12

LT9AS 1

AS 2

AS 3 AS 4

AS 7

ARTS LINK

BIZ 1MOCHTAR RIADY

BUILDINGHON

SUI S

ENDRIV

E

COM

PUTI

NGDR

IV

E

AS 5


BUSI

NES

SLI

NK

RESEARCH LINK

AS 6

LT14

LT15


SHAWFOUNDATION

ALUMNIHOUSE

KENT RIDGE DRIVE

SINGAPOREWIND

TUNNELFACILITY


MPSH5

MPSH6



(U/C)

SPORTS DRIVE 2

MULTI-PURPOSECOURTS

SPORTSFIELDS

MULTI-PURPOSEFIELDS

FOOTBALLFIELD

HANDBALL/NETBALL

COURTS

TENNIS COURTS

TENNIS COURTS

RUNN

ING

TENNIS COURTS

29



STUDIESINSTITUTE

9

8

14A

14 15 16

7 65 4

3

18

17

2


SCIENCES



6 5 4

3 21

109

18 14 12A12



KENT R IDGE ROAD



LT32

S2

S3

S4

S4AS5

S1

S17

DSO@KENT RIDGE

MEDICALLIBRARY

LT34 LT33

LT31

S6


BUILDING (MD1)

MD2

MD3

MD4

MD11

LT35

LT36

SCIENCELIBRARY

SOU

THBU

ON

AV

ISTA

RO

AD

NUHMEDICALCENTRE

NUHKENT RIDGE

WING

NUHSTOWERBLOCK

NUHSERVICEBLOCK


(U/C)

COLLEGE AVENUE EAST

CENDANACOLLEGE

CREATETOWER

CREATETOWER

TOWN GREEN

EDUCATIONRESOURCE

CENTRE

COLL

EGE AVENUE WEST

ELM COLLEGE

SAGACOLLEGE


SCIENCE D

RIVE 3

SCIENCE

DRIVE4

SCIENCEDRIVE 2

SCIENCE

DRIVE

1

KENT RIDGE


SEPAKTAKRAW


BASKETBALLCOURTS

LT1

LT2

LT6

MUSICLIBRARY

ALICE LEE PLAZA

LT21

LT20

ÙTO JURONG

CL

EM

EN

TI

RO

AD


KENT RIDGE CRESCENT



ENGINEERING DRIVE 4

S12

S11

S7 S8 (U/C)

MD7

E7(U/C)

AS 8

ARCHITECTURED

RIVE


DOVER ROAD

S2S

LT25

LT24

YUSOF ISHAK HOUSE

EW2(WS2)

E6

E4A

E4

E3

E5

COMPUTERCENTRE

E2

S14S13

S15

S16

FRONTIER PHASE 1

CHUA THIAN POH HALL

LOW TUCK KWONG HALL

TEMBUSU COLLEGE

NORTH TOWER

SOUTHTOWER



CINNAMONCOLLEGE

LT50

LT51

LT52

LT53

UTOWNRESIDENCE

TOWN PLAZA

RAFFLESHALL

KUOKFOUNDATIONHOUSE

VENTUS (UNIVERSITY


COM1


NUSSTAFF CLUB

UNIVERSITYHALL

LT26

LT28LT29

LT27MD9 MD10

FRONTIER PHASE 2

(U/C)

MEDICAL

DRIVE


(NUH)

NUHMAIN

BUILDING



PGP HOUSE

COM2

LT16

LT17

LT19

LT18 BIZ2


I3

TECHNOLOGY CENTRE


SINGAPORE (U/C)

CHINESELIBRARY

LIBRARYANNEXE

CENTRALLIBRARY

THEDECK

TECHNOEDGE

THETERRACE

ENTRANCE D



ENTRANCE E

COLL

EGE

LINK

FACULTY OFDENTISTRY



PUBLIC HEALTH

E2A

FACULTY OF SCIENCE

NUS BUSINESS SCHOOL


SCIENCES

SCHOOL OFDESIGN AND

ENVIRONMENT


SCHOOL OFCOMPUTING


OF MUSIC

YALE-NUSCOLLEGE

SCHOOL OFCONTINUING


UNIVERSITYSCHOLARS

PROGRAMME

LT7A

LT7

EA EA


ENTRANCE A

ENTRANCE B

ENTRANCE C


96151B2

CBTC1

C

33183188

3396

183188

33183188

95151

9596151

95151

A2B1B2C

D1

9596151

A1B1D1

BTC1

96151


151A2, CBTC1, BTC2

D1, D2

A1B2 D1

BTC1

A1B1D1

BTC1

A1A2D1

A2B2D1

A1B1

A1ED1

BTC1

B1, B2, CBTC1, BTC2

10, 33, 95151, 200, 201

A1, C D2, A1E

A2C

D2

95

95

A1A1EB1 D1

BTC1

183188

183188

A2A2EB1D1

10, 30, 51, 143183, 188, 200

10, 30, 51, 143183, 188, 200

95

95

A1C

D2

A2C

D2

9595


A2A2E

CD2

A2

A2

A1

A1

A1A2D2

BTC1

A1, A1E, D2

A2, A2E, D2

95

95

95

97197963

95

97197198963

92200

92200

33196

3396

151183196

D1D2

UT-FoSB1B2

3396

183188

B2C

BTC2

97197198963

97197198963

9596151

A2B2D1

A

A A

A

A

A

A

A

A

AA

A

A A

A

A

AA

P

P

P

16

14

13

11

15

15

12

12B

11A

P

10A

9

10

8

6

6A

6B

5A

3A

4

2

2A

2B

2B

4

5

3

10A

10B

17

1

P

12A

10C

18

11B

11

4A

A

B

C

D

E

F

G

H

I

1 2 3 4 5 6 7 8

Kent RidgeCampus

Legend


Public Bus Stop

Security Post



Library

Accommodation


Facility / Resource



Food & Beverage

Auditorium


Handicap Route

CarparkP

ATM

Bicycle Rack

Linkway






Cinnamon College H2




BLK NO./NAME GRID





BLK NO./NAME GRID




S17 E6


University Hall D5



BLK NO./NAME GRID


University Hall D5




University Hall D5


E1 D2



Lecture Theatre)D6


D7



LT 11 B2/C2


G2




HALLS OFRESIDENCE



GRID



ResidencesB6/B7



UTown Residence G2


D4



BLK NO./NAME GRID




G1/G2

E3

imste

Typewritten Text

E4-04-02

imste

Line

FOO

D G

UID

E w

ithin

Fac

ulty

of E

ngin

eerin

g

Pla

typ

us

Foo

d B

ar

Engi

neer

ing

Blk

E2A

O

pera

tion

hour

s:

Mon

- Fr

i: 8.

00am

to 9

.00p

m

Hu

mb

le O

rigi

ns

Exp

ress

En

gine

erin

g B

lk E

2A

Ope

ratio

n ho

urs:

M

on -

Fri:

8.30

am to

5.3

0pm

Tec

hn

o E

dge

Fa

culty

of E

ngin

eerin

g O

pera

tion

hour

s:

Mon

- Fr

i: 7.

30am

to 7

.00p

m

McD

onal

d’s

Res

tau

ran

t En

gine

erin

g A

nnex

e O

pera

tion

hour

s:

Mon

- Fr

i: 8.

00am

to 1

1.00

pm

Ari

se &

Sh

ine

Engi

neer

ing

Blk

E4

Ope

ratio

n ho

urs:

M

on -

Fri:

7.00

am to

8.0

0pm

Su

bway

Mob

ile C

art

Engi

neer

ing

Blk

E4

Ope

ratio

n ho

urs:

M

on -

Fri:

11.0

0am

to 8

.00p

m

NUS WIFI Instructions SSID: Eduroam is available.

- Please use it if your institute is a member of the alliance. SSID: NUS_Guest is available throughout the university.

1) Connect to the "NUS_Guest" wireless network. You will be redirected to a registration page.

2) Register your mobile number online. An OTP will be sent via SMS to this mobile number.

3) Enter the OTP and start surfing!

the 9th international conference on inverse problems and ... · [ms6-3] a fully nonlinear...

Documents