Event(s) on June 2019

• Wednesday, 5th June, 2019

  Title:	Inverse problems for elliptic equations with power type nonlinearities
  Speaker:	Dr Yi-Hsuan LIN, Department of Mathematics and Statistics, University of Jyväskylä, Finland
  Time/Place:	11:00  -  12:00 FSC703, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	We introduce a method for solving Calder'on type inverse problems for semilinear equations with power type nonlinearities. The method is based on higher order linearizations, and it allows one to solve inverse problems for certain nonlinear equations in cases where the solution for a corresponding linear equation is not known. Assuming the knowledge of a nonlinear Dirichlet-to-Neumann map, we determine both a potential and a conformal manifold simultaneously in dimension $2$, and a potential on transversally anisotropic manifolds in dimensions $n geq 3$. In the Euclidean case, we show that one can solve the Calder'on problem for certain semilinear equations in a surprisingly simple way without using complex geometrical optics solutions.

  
  

• Monday, 10th June, 2019

  Title:	Evidence-Based Medicine 3.0 – A look into the future
  Speaker:	Dr. Joey Sum Wing Kwong, United Nations Population Fund (UNFPA), Asia-Pacific Regional Office, Bangkok, Thailand
  Time/Place:	15:00  -  16:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	Integration of robust evidence with clinical expertise and patient values underpins the practice of evidence-based medicine. In the past, much of the focus has been on synthesizing and using “best available evidence” in delivering health care. With a growing body of research being funded and published, there is now a call to shift focus from merely producing research evidence to translating evidence into better health care. Furthermore, with such an exponential growth in quantity of research findings there is an inevitable compromise in quality, which ultimately hampers the evidence translation process to delivering effective, high-value and people-centred healthcare. What does the future hold for the devoted evidence-based medicine followers? In this seminar, Dr. Kwong will introduce the fundamental principles of evidence-based practice, and share her views on how researchers, healthcare professionals and other stakeholders can come together on a multidisciplinary team approach to drive forward into the new era of evidence synthesis and translation.

  
  

• Friday, 14th June, 2019

  Title:	Algorithms for Wave Scattering of Random Media: Fast multipole method in layered media and a phase shift deep neural network for wideband learning
  Speaker:	Prof Wei Cai, Department of Mathematics, Southern Methodist University, Dallas, United State
  Time/Place:	10:30  -  11:30 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	In this talk, we will present two algorithms and numerical results for solving electromagnetic wave scattering of random meta-materials. Firstly, a fast multipole method for 3-D Helmholtz equation for layered media will be presented based on new multipole expansion (ME) and multipole to local translation (M2L) operators for layered media Green's functions. Secondly, a parallel phase shift deep neural network (PhaseDNN) is proposed for wideband data learning. In order to achieve uniform convergence for low to high frequency content of data, phase shifts are used to convert high frequency learning to low frequency learning. Due to the fast learning of many DNNs in the low frequency range, PhaseDNN is able to learn wideband data uniformly in all frequencies.

  
  

• Wednesday, 19th June, 2019

  Title:	Fully discrete T-ψ finite element method to solve a nonlinear induction hardening problem
  Speaker:	Prof KANG Tong, School of Sciences, Communication University of China, China
  Time/Place:	16:30  -  17:30 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	We study an induction hardening model described by Maxwell's equations coupled with a heat equation. The magnetic induction field is assumed a nonlinear constitutional relation and the electric conductivity is temperature-dependent. The T-ψ method is to transform Maxwell's equations to the vector-scalar potential formulations and to solve the potentials by means of the finite element method. In this talk, we present a fully discrete T-ψ finite element scheme for this nonlinear coupled problem and discuss its solvability. We prove that the discrete solution converges to a weak solution of the continuous problem. Finally, we conclude with several numerical experiments for the coupled system.

  
  

• Wednesday, 19th June, 2019

  Title:	Fully discrete T-ψ finite element method to solve a nonlinear induction hardening problem
  Speaker:	Prof Tong Kang, Department of Applied Mathematics, School of Sciences, Communication University of China, Beijing, China
  Time/Place:	16:30  -  17:30 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	We study an induction hardening model described by Maxwell's equations coupled with a heat equation. The magnetic induction field is assumed a nonlinear constitutional relation and the electric conductivity is temperature-dependent. The T-ψ method is to transform Maxwell's equations to the vector-scalar potential formulations and to solve the potentials by means of the finite element method. In this talk, we present a fully discrete T-ψ finite element scheme for this nonlinear coupled problem and discuss its solvability. We prove that the discrete solution converges to a weak solution of the continuous problem. Finally, we conclude with several numerical experiments for the coupled system.

  
  

• Thursday, 20th June, 2019

  Title:	Mathematical Modeling and Methods of Signal Separations In Spectroscopic Sensing
  Speaker:	Prof Yuanchang SUN, Department of Mathematics and Statistics, Florida International University, Florida, USA
  Time/Place:	11:00  -  12:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	"Spectroscopic sensing is a powerful and a widely used family of techniques for detecting and identifying chemical and biological substances. For example, nuclear magnetic resonance (NMR) relies on the magnetic properties of the atomistic nucleus to determine the molecular structures. Raman spectroscopy (RS) uses laser light scattering and the resulting energy shift of photons to sense the vibrational modes of a sample. In remote sensing, hyperspectral imaging (HSI) makes use of hundreds of contiguous spectral bands to identify nearly invisible objects at subpixel level. Differential optical absorption spectroscopy (DOAS) is based on the light absorption property of matter to identify broadband and narrowband spectral structures, and analyze atmospheric trace gas concentrations. It is however a challenging problem to identify spectral signals in real-world applications due to many complicating factors. For example, a target chemical often appears in a mixture where the signature (individual) spectral fingerprint of the target is absent; measurement errors occur. Hence robust signal processing methods must be developed to process the sensing data for reliable identification and quantification. In this talk, the speaker shall address the mathematical and computational methods for separating spectral mixtures when minimal or partial knowledge of the source signals is known. Such problems arise in all aforementioned spectroscopies."

  
  

• Thursday, 27th June, 2019

  Title:	PhD Oral Exam: Model Checking for General Parametric Regression Models
  Speaker:	Ms LI Lingzhu, Department of Mathematics, Hong Kong Baptist Unviersity, HKSAR
  Time/Place:	10:00  -  12:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	Model checking for regressions has drawn considerable attention in the last three decades. Compared with global smoothing tests, local smoothing tests, which are more sensitive to high-frequency alternatives, can only detect local alternatives distinct from the null model at a much slower rate when the dimension of predictor is high. When the number of covariates is large, nonparametric estimations used in local smoothing tests lack efficiency. Corresponding tests then have trouble in maintaining the significance level and detecting the alternatives. To tackle the issue, we propose two methods under high but fixed dimension framework. Further, we investigate a model checking test under divergent dimension, where the numbers of covariates and unknown parameters go divergent with the sample size

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