Fall 2019

NCTU Applied Mathematics Colloquium are held every Tuesday 2:00-3:00PM.

For questions, please contact Te-Sheng Lin.


Date Speaker and Title
September 10 No colloquium
September 17 Yu-Ting Lin, Department of Anesthesiology, Taipei Veterans General Hospital.
(林祐霆, 臺北榮民總醫院麻醉部.)
Manifold Learning in Medical Signal Processing and Challenging Problems in Engineering
September 24 Yi-Hsuan Lin, Department of Applied Mathematics, National Chiao Tung University.
(林奕亘, 國立交通大學應用數學系.)
Inverse problems and partial differential equations.
October 1
Hsieh-Chen Tsai, Department of Mechanical Engineering, National Taiwan University.
(蔡協澄, 國立台灣大學機械工程學系.)
An strongly-coupled immersed-boundary formulation for rigid-bodies interacting with fluid flow

Jack Koolen, School of Mathematical Sciences, University of Science and Technology of China, China.
On the classification of Q-polynomial distance-regular graphs
October 8 13:20-15:10 戴雀芬諮商心理師(新竹市學生輔導諮商中心)
October 15 Ray-Bing Chen, Department of Statistics and Institute of Data Science, National Cheng Kung University.
(陳瑞彬, 國立成功大學統計學系.)
Global Optimization of Expensive Functions Using Adaptive RBF-Based Surrogate Model via Uncertainty Quantification
October 22 Mark Blyth, School of Mathematics, University of East Anglia, UK.
Critical free surface flow over topography
October 29 Chia-Chieh Chu, Department of Mathematics, National Tsing Hua University.
(朱家杰, 國立清華大學數學系.)
November 5 No colloquium
November 12 Yen-Huan Li, Department of Computer Science and Information Engineering, National Taiwan University.
(李彥寰, 國立臺灣大學資訊工程學系.)
Towards efficient and rigorous learning with the logarithmic loss
November 19 Jeng-Nan Tseng, Department of Mathematical Sciences, National ChengChi University.
(曾正男, 國立政治大學應用數學系.)
A gentle introduction to numerical error
November 26 Yi-Ren Yeh, Department of Mathematics, National Kaohsiung Normal University.
(葉倚任, 國立高雄師範大學數學系.)
December 3 Ching-Sung Liu, Department of Applied Mathematics, National University of Kaohsiung.
(劉青松, 國立高雄大學應用數學系.)
The numerical methods for nonlinear eigenvalue problems
December 10 Chia-Yu Hsieh, Department of Mathematics, The Chinese University of Hong Kong.
(謝佳佑, 香港中文大學數學系.)
Singular Solutions to Some Semilinear Elliptic Equations: An Approach of Born-Infeld Approximation
December 17
Ya-Lun Tsai, Department of Applied Mathematics, National Chung Hsing University.
(蔡亞倫, 國立中興大學應用數學系.)
Three points of view in solving polynomial systems

Li Wang, Department of Mathematics and Department of Computer Science and Engineering, University of Texas at Arlington, USA.
Probabilistic Structure Learning for EEG/MEG Source Imaging with Hierarchical Graph Prior
December 24 Lien-Yung Kao, Department of Mathematics, University of Chicago.
(高連庸, 芝加哥大學數學系.)
Dynamics, Geometry and Rigidity


Speaker Title and abstract
Sep. 17, Yu-Ting Lin Title: "Manifold Learning in Medical Signal Processing and Challenging Problems in Engineering"


The waveform morphology in the cardiovascular signal data reflects physiological dynamic interaction inside the human body. By organizing the subtle change of waveform morphology from large amount of data, unsupervised manifold learning help delineate a high dimensional structure. Using diffusion map, we may gain more insight for signal processing, data analysis and classification. Development in engineering warrants the reliability of clinical application. Therefore, I will present several challenging problems for further discussion.

Sep. 24, Yi-Hsuan Lin Title: "Inverse problems and partial differential equations."


In this talk we will introduce several inverse problems, such as the famous Calder\'on problem. Roughly speaking, inverse problems investigate the question of determining the interior physical information of a medium from its boundary measurements. Furthermore, we also introduce linear, non-linear and non-local inverse problems in this talk.

Oct. 1, Hsieh-Chen Tsai Title: "An strongly-coupled immersed-boundary formulation for rigid-bodies interacting with fluid flow"


We present a strongly-coupled immersed-boundary method for flow–structure interaction problems involving rigid bodies. The method is stable for arbitrary choices of solid-to-fluid mass ratios and for large rigid-body motions. Dynamics of rigid bodies is characterized by the velocity of the center of mass and the angular velocity about the center of mass, which are governed by the translational and rotational equations of motion involving boundary forces. By introducing the summation and distribution operators, equations of motion are coupled with the incompressible Navier-Stokes equations through the no-slip constraint and boundary forces. Boundary forces are regarded as Lagrange multipliers that enable the no-slip constraint to be implicitly determined to arbitrary precision without associated time-step restrictions. Through projections, the current method removes not only slip component of the velocity field but also components of rigid-body dynamics that do not satisfy equations of motion. We verify our method by simulating the free fall of a circular cylinder and further apply our method for investigating the starting of a flow-driven vertical-axis wind turbine.

Oct. 1, Jack Koolen Title: "On the classification of Q-polynomial distance-regular graphs"


In the early 1980 Bannai asked whether the Q-polynomial distance-regular graphs with large diameter can be classified. In this talk I will first give an overview what is known. If there is time I will discuss some open problems.

Oct. 15, Ray-Bing Chen Title: "Global Optimization of Expensive Functions Using Adaptive RBF-Based Surrogate Model via Uncertainty Quantification"


Global optimization of expensive functions has important applications in physical and computer experiments. It is a challenging problem to develop efficient optimization scheme, because each function evaluation can be costly and the derivative information of the function is often not available. We propose a novel global optimization framework using adaptive Radial Basis Functions (RBF) based surrogate model via uncertainty quantification. The framework consists of two iteration steps. It first employs an RBF-based Bayesian surrogate model to approximate the true function, where the parameters of the RBFs can be adaptively estimated and updated each time a new point is explored. Then it utilizes a model-guided selection criterion to identify a new point from a candidate set for function evaluation. The selection criterion adopted here is a sample version of the expected improvement (EI) criterion. We conduct simulation studies with standard test functions, which show that the proposed method is more efficient and stable in searching the global optimizer than two existing methods.

Oct. 22, Mark Blyth Title: "Critical free surface flow over topography"


Two-dimensional free-surface flow over a localised bottom topography is examined with an emphasis on calculating steady, forced solitary-wave solutions. In particular we focus on the case of a Gaussian dip topography. Most of the focus is on the weakly-nonlinear limit where a forced KdV equation is applicable, and the problem essentially boils down to solving a forced nonlinear ODE with a single parameter that quantifies the amplitude of the topography. This equation has a rich solution space with a large (probably infinite) number of solution branches. Asymptotic analysis for small topography amplitude reveal some interesting features, for example an internal boundary layer which mediates a change from exponential to algebraic decay of the free-surface in the far-field. Traditional boundary-layer theory fails beyond the first two solution branches, where the surface profiles feature multiple waves trapped over the topography. The stability of the steady solutions will also be briefly discussed.

Oct. 29, Chia-Chieh Chu Title: "淺談數學對產業界的影響與可壓縮歐拉方程接近真空解的研究"


這個演講分成兩個部分,前半段分享美國工業與應用數學會(Society for Industrial and Applied Mathematics,簡稱 SIAM)在2012年發表了一篇報告: 產業中的數學(SIAM Report on Mathematics in Industry)。他們發現不論是在傳統或嶄新產業,數學與科學計算皆有愈來愈多的應用。這些應用會對公司的盈虧造成極大幅的影響。我將跟大家分享我個人的經驗裡數學在哪些產業與應用提供了什麼貢獻,並且稍微介紹計算數學的一些核心思想。 後半段我介紹近期在可壓縮歐拉方程問題中,解接近真空時的一個簡化模型。在這研究中我們提中一個新的角度來思考當密度接近0時,如何逼近歐拉方程的解。我們提出的簡化模型可以解決Glimm方法中,因為解接近真空而造成逼近解的總變化量過大的問題。進而證明了當初使密度夠小時,歐拉方程的解都會在O(1)時間存在。這份工作是與中央大學洪盟凱教授與李信儀博士一起完成的。

Nov. 12, Yen-Huan Li Title: "Towards efficient and rigorous learning with the logarithmic loss"


Minimizing the logarithmic loss is an essential task to many applications, such as positron emission tomography, optimal portfolio selection, and quantum state tomography. The optimization problems are indeed convex. However, the logarithmic loss violates standard smoothness assumptions in optimization literature, so most existing optimization algorithms and/or their convergence guarantees do not directly apply. In this talk, I will introduce some of our recent developments in addressing the logarithmic loss.

Nov. 19, Jeng-Nan Tseng Title: "A gentleintroduction to numerical error"


To understand and manipulate the numerical error is an important issue in scientific computing. The behavior of errors is various and interesting. Errors are not always a bad things in applications. In this lecture, I will introduce some interesting and unexpected examples. Moreover, some useful applications designed by the numerical error will be shown.

Nov. 26, Yi-Ren Yeh Title: "機器學習實務案例分享"



Dec. 3, Ching-Sung Liu Title: "The numerical methods for nonlinear eigenvalue problems"


In this talk, we will introduce nonlinear eigenvalue problems, including tensor eigenvalue problems and nonlinear Schrödinger equations. We will discuss its numerical methods and some numerical results. A great advantage of this method is that it converges quadratically and is positivity preserving in the sense that the vectors approximating the Perron vector (or the ground state vector) are strictly positive in each iteration.

Dec. 10, C.-Y. Hsieh Title: "Singular Solutions to Some Semilinear Elliptic Equations: An Approach of Born-Infeld Approximation"


We construct singular solutions to a semilinear elliptic equation with exponential nonlinearity on a bounded domain in $\mathbb{R}^2$. To show the existence of singular solutions, we introduce an inverse problem and utilize a Born-Infeld approximation scheme. Ruling out a possible occurrence of bubbling phenomenon, we show that as the Born-Infeld parameter tends to infinity, solutions of the inverse problem on a subdomain with finitely many holes can be used to approximate singular solutions to the original problem. Our work rigorously justifies the Born-Infeld-Higgs approximation to the abelian Maxwell-Higgs theory. This is a joint work with Yong Yu and Ho Man Tai (CUHK).

Dec. 17, Ya-Lun Tsai Title: "Three points of view in solving polynomial systems"


In this talk, I will first describe briefly my backgrounds about how to encounter such a fascinating topic of solving polynomial systems. Three different tools, Sylvester resultants, Wu’s method, and Groebner bases will be introduced as different viewpoints in solving polynomial systems. Some applications to point vortex problems and N-body problems will be prevented.

Dec. 17, Li Wang Title: "Probabilistic Structure Learning for EEG/MEG Source Imaging with Hierarchical Graph Prior"


Brain source imaging is an important method for noninvasively characterizing brain activity using Electroencephalogram (EEG) or Magnetoencephalography (MEG) recordings. Traditional EEG/MEG Source Imaging (ESI) methods usually assume that either source activities at different time points are unrelated, or that similar spatiotemporal patterns exist across an entire study period. The former assumption makes ESI analyses sensitive to noise, while the latter renders ESI analyses unable to account for time-varying patterns of activity. To effectively deal with noise while maintaining flexibility and continuity among brain activation patterns, we propose a novel probabilistic ESI model based on a hierarchical graph prior. In our method, a spanning tree constraint is imposed to ensure that activity patterns have spatiotemporal continuity. An efficient algorithm based on alternating convex search is presented to solve the proposed model and is provably convergent. Comprehensive numerical studies using synthetic data on a real brain model are conducted under different levels of signal-to-noise ratio (SNR) from both sensor and source spaces. We also examine the EEG/MEG data from two real applications, in which our ESI reconstructions are neurologically plausible. All results demonstrate significant improvements of the proposed algorithm over the benchmark methods in terms of source localization performance, especially at high noise levels.

Dec. 24, Lien-Yung Kao Title: "Dynamics, Geometry and Rigidity"


In this talk, we aim to have a glance of the spark between dynamics and geometry. I will start from ``what are dynamical systems'' and try to answer ``how could dynamics tell us about the geometry." Along the way, I will introduce works of Sinai (2014 Abel Prize winner), Margulis (1978 Fields medalist), Thurston (1982 Fields medalist), McMullen (1998 Fields medalist), Mirzakhani (2014 Fields medalist), and some of my recent works on entropy rigidity and pressure metrics.