歷史演講 PAST TALKS

Abstract：

The ever-increasing importance of computing in medical image reconstruction can hardly be overestimated, and fast medical image reconstruction is the research focus of AI technologies and healthcare. In this talk, Dr. Lin will review some topics, from fundamental computing methods of magnetic resonance imaging (MRI) and computerized tomography (CT), to recent advances in MRI reconstruction methods. Some of his studies of the compressed sensing MRI, iterative reconstruction of the PROPELLER technique, spatiotemporal reconstruction, and open-source software are covered in this talk. One aspect of his work is the Python non-uniform fast Fourier transform (PyNUFFT), which allows researchers to share the same infrastructure and it is still actively maintained. It offers high-performance computing through PyCUDA and PyOpenCL backends. Thanks to the accurate min-max interpolator algorithm (Fessler and Sutton, IEEE TSP 2003), PyNUFFT has been used in MRI reconstruction, accelerated tomography, learning-based MRI reconstruction, motion estimation, and the ISMRM reproducible study.

20210114演講_Dr. Jyh-Miin Lin, MD, MSc, PhD (University of Cambridge)

Abstract：

代數學（algebra）是數學重要的分支，從國民義務教育開始，學生就要學習「代數」，一邊設未知數，一邊思考為什麼這世界上有那麼多人喜歡把雞和兔子放在同一個籠子裡。有趣的是，不同的群體對於代數是什麼有著截然不同的看法。中學生覺得代數就是解 x，大學生覺得代數就是群環體，而數學家則通常沒辦法很簡潔的告訴你答案，因為數學家知道的太多了。本演講中我們試著從歷史演進出發，聊聊不同時代的代數一詞代表的意義，最後簡單介紹近世代數中重要的子領域——表現理論（representation theory）。

20210107演講_賴俊儒教授 (中研院數學所)

12/31 (Thu) – AIMGroup – AI Special Seminar II  Agenda

Abstract：

The backtracking line search (LS) is one of the most commonly used techniques for enhancing the robustness of Newton-type methods. The Newton method consists of two key steps: search and update. LS tries to find a decreasing-most updated point along Newton’s search direction with an appropriate damping factor from the current approximation. The determination of Newton’s search direction relies only on current information. When Newton’s search direction is a weakly descent direction, the damping factor determined by LS will be unacceptably small, which often happens for the numerical solution of large, sparse systems of equations with strong local nonlinearity. As a result, the solution process fails into the vicious cycle between no update and the same search. The intermediate solution is trapped within the same region without any progress. This work’s main contribution is to propose a new globalization strategy, namely the hybrid line and curve search (HLCS) technique for Newton-type methods to resolve their potential failure problems when line-search is used. If the classical line search fails, we activate the curve search phase. In that case, we first decompose the solution space into two orthogonal subspaces based on the predicted value obtained from Newton’s search direction, referred to good and bad subspaces. The bad one responds to the components causing the violation of the sufficient decrease condition. Next, we project the original predicted value on the good subspace and then perform the nonlinear elimination process to obtain a new updated solution that satisfies the sufficient decrease condition globally. In this talk, we use a simple problem with unbalanced nonlinearity to illustrate how our proposed globalization strategy works. Next, we will generalize the idea and implement it for the general system of large, sparse, nonlinear equations, and then describe its application to drift-diffusion semiconductor device simulation. It is known in the literature that solving numerically drift-diffusion equations imposes many challenges due to the strong nonlinearity, the drift-dominated nature, and the presence of internal and boundary layers. We focus on investigating how these issues affect the convergence of an inexact Newton line-search method. As proof of concept, we present four one-dimensional numerical examples to illustrate our proposed approach's effectiveness.

20201231演講_ 蔡尚融先生 (國立中央大學數學系)

Combinatorics Seminar (Colloquium)

Abstract：

This is an introductory talk to the combinatorial tiling theory, will be focusing on domino tilings of the Aztec diamond. The tilings on the Aztec diamond first came from the study of alternating sign matrices in 1992, there were several nice and interesting enumerative results on it over past 30 years. We will discuss some methods and some results on it, then see the variations of the Aztec diamond, such as the Aztec rectangle, the symmetry classes of tilings on the Aztec diamond.

20201230演講_李宜霖先生 (Indiana University Bloomington)

109-1-NCU_AI_Math_Group-20201224-AI_Special_Seminar_I_and_Lunch_Party_Agenda

Abstract：

AI的發展過程中, 數學絕對扮演了骨架的角色. 然而, 以數學為專長的同學, 要從事AI方面的工作, 聽起來近在咫尺, 做起來卻遠在天邊. AI界李白資工系蔡老師將以自己帶學生的經驗, 提供一些讓數學系同學進入AI領域貢獻的方向。

20201224演講_ 蔡宗翰教授 (國立中央大學資工系)

109-1-NCU_AI_Math_Group-20201217-5th_Student_Seminar

Abstract：

本次演講分為學術和通俗演講兩個部份。(學術)本演講將回顧波動度選擇權(volatility option)的評價模型，並說明永續美式波動度選擇權(perpetual American volatility option)的評價公式，最後介紹波動度選擇權未來可能的研究方向。(通俗)本演講將從一般投資人的角度介紹股票交易的相關概念與思維，進而透過常見的移動平均線和標準差提出程式交易的範例，協助投資大眾瞭解股票交易可能存在的獲利機會。

20201210演講_ 劉宣谷教授 (國立臺北教育大學)

國立中央大學 數學系  AI Math Group (AIMGroup)  -  11/26 (Thu)   社團活動公告

109-1 學期AIMGroup社團 第四次 研究生學術講座 (Student Seminars)的相關資訊如下 (同時，會在 中大數學系 官網公告)，歡迎對講座議題有興趣的各界先進與同學們參與活動。 謝謝！

109-1-NCU_AI_Math_Group-20201126-4th_Student_Seminar

Abstract：

In this talk, I will first discuss some current efforts in early detection of lung cancer and then discuss issues in building clinical prediction models, including performance evaluation criteria, explanation, and bias-variance tradeoff.

Lung cancer is the leading cause of cancer death worldwide. Most lung cancer is diagnosed at late stage and hence prevention and early detection are important. In view of the landmark 2011 National Lung Screening Trial report that a 20% mortality reduction was observed in the low-dose CT (LDCT) screening arm among heavy smokers, USPSTF recommends annual LDCT screening for those ages 55—80, has smoked 30 or more pack-years, and smoked in the past 15 years. In addition, risk prediction models have been proposed to select high risk individuals for LDCT screening for lung cancer in the west. In Taiwan, there is also an enthusiasm in LDCT screening for lung cancer among never-smokers as well as smokers. We proposed a risk prediction model for never-smoking females in this regard and showed that it performs well, compared with the USPSTF smoking criteria for American women. This model uses only age, BMI, COPD, education, family history, and 9 genetic variants for prediction. I will use this example to discuss performance assessment criteria, explanation and bias-variance tradeoff in statistical learning. In particular, I will mention some of the roles of Hoeffding’s inequality and VC class in big data and classical large sample theories.

20201124演講_張憶壽教授 (National Health Research Institutes)

國立中央大學數學系AI Math Group (AIMGroup)-11/05 (Thu)社團活動公告

109-1學期AIMGroup社團 第三次 研究生學術講座 (Student Seminars)的相關資訊如下

歡迎對講座議題有興趣的各界先進與同學們參與活動。 謝謝！

 11/05 (Thu) – AIMGroup – the Third Student-Seminar Agenda 

Combinatorics Seminar (Colloquium)

Abstract：Linear programming approaches have been applied to derive upper bounds on the size of classical and quantum codes. The basic idea is to utilize the linear constraints induced from the MacWilliams identity that connects the weight enumerations of two orthogonal groups. In this talk, I will introduce the applications of linear programming bounds in quantum codes, including our recent results on entanglement-assisted quantum codes and quantum data-syndrome codes.

20201028演講_賴青沂教授 (交大電信所)

10/22 (Thu) – AIMGroup – Second Student-Seminar Agenda

AI Math Group (AIMGroup)