歷史演講 PAST TALKS

Abstract

We propose a new framework and algorithm pipeline to address the problem of diffeomorphic registration and discrete approximation of a large class of geometric objects that can be described as distributions of local direction vectors. It builds on the large deformation diffeomorphic metric mapping (LDDMM) model to generate deformation groups as well as the idea of representing shapes as oriented varifolds. We study in detail the construction of kernel metrics on space of varifolds and the resulting topological properties of those metrics, then propose a deformation model acting directly on the space of varifolds for diffeomorphic registration. In the LDDMM framework, such registration problem is formulated as an optimal control problem. We also address the problem of optimal finite approximations (quantization) for those metrics and show a Γ-convergence property for the corresponding registration functionals. Some numerical examples of registration (curves, surfaces, point clouds) will be demonstrated during the talk.

20190614_ 謝希微演講1000_1130

Abstract：

Manifold learning(ML) is a branch of machine learning, which is used to do clustering, visualization, and nonlinear dimensionality reduction, etc. Roughly speaking, ML is to "learn the invisible manifold by embedding a whole lot of sample points in it into the plane or the space." Since 2000, graph theory and spectral methods have been greatly used in the algorithms of ML. When the number of sample points is getting larger and larger, the graph constructed by sample points shall converge to the manifold. To understand the limiting behavior and thus justify the algorithms, tools from differential geometry, PDE, or functional analysis must be involved. In this talk, I will give some concrete examples to demonstrate how geometry plays a role in this theoretical analysis of ML.

20190613演講_陳志偉教授 (國立中山大學應用數學系)

20190530演講_Discussions Meeting on Mathematical Biology with Prof. Eiji Yanagida (Tokyo Institute of Technology)

20190523演講_Prof. Carl Mueller (University of Rochester)

20190520演講_Hyein Choi (Pusan National University)

20190520演講_Eun-Kyung Cho (Hankuk University of Foreign Studies (HUFS))

Abstract：

The Dvoretzky random covering problem is to find the conditions for which almost surely every point on the circle is covered infinitely many times by a sequence of random intervals with decreasing lengths and random initial points (an i.i.d. sequence of random variables uniformly distributed on the circle). It has drawn a lot of interest of many mathematicians for the last decades and the sizes of the random covering sets have been widely studied. The Hausdorff dimensions and hitting probabilities of random covering sets will be given in the talk. The covering setting also was generalized to many different cases, for example, covering the torus with rectangles or open sets, or even just Lebesgue measure sets, or balls with singular distributions, some recent related results will be surveyed. Also some Fourier dimensional result will be introduced in the talk.

20190514演講_李兵教授 (華南理工大學)

20190507演講_丁瑜瑄先生徐仕杰先生 (鴻海精密工業(股)公司)

20190503_ 陳俊英演講

Abstract：

In this talk, we will review the current development and applications of artificial intelligence, specifically the machine-learning approach, in radiology. Machine-learning techniques have shown promising benefits in the image acquisition, lesion detection, differential diagnosis, tumor grading, and outcome prediction. In the field of cancer imaging, growing evidence further reveals the feasibility of using image phenotypes to probe the underlying genotypes and predict the clinical outcomes using machine learning. We will start by introducing the common categories of machine learning, including traditional approaches and deep learning, and elucidating their usages for the different clinical purposes. The application of machine learning combined with radiomics, a high-throughput feature extraction method, to predict the molecular subtypes of lesion and patient survivals based on multimodal MRI will be introduced. Finally, perspectives of current limitations and future developments of machine learning in radiology will be proposed and discussed to facilitate the machine-learning based precision medicine.

20190502演講_盧家鋒教授 (國立陽明大學生物醫學影像暨放射科學系)

Abstract

In this paper, we implement a stochastic deflator with five economic and financial risk factors: interest rates, market price of risk, stock prices, default intensities, and convenience yields. We examine the deflator with different financial assets, such as stocks, zero‐coupon bonds, vanilla options, and corporate coupon bonds. We find required regularity conditions to implement our stochastic deflator. Our numerical results show the reliability of the deflator approach in pricing financial derivatives.

20190426_Po-Keng Cheng演講

Abstract

A beautiful example of the use of the convergence to types theorem is the derivation of the extreme value distributions. These are the possible limit distributions of centered and scaled maxima of i.i.d. random variables. Surprisingly, there are only three types of limiting distributions, the Gumbel, Frechet, and Weibull distributions, known collectively as the extreme value distributions. In this talk, we will state and prove the celebrated Extremal Types Theorem.

Keywords: maximum domain of attraction, extremal types theorem, convergence to types theorem.

20190412_ 翁新傑演講1000_1100

Abstract

In this paper, we consider an optimal investment and reinsurance problem by an insurer. The insurer invests in a market consisting of a bank account and a risky asset. The insurer has some influence on the dynamics of prices and inside information. Moreover, the information of the insider is the final price plus a blurring noise that disappears as the final time approaches. The wealth of the insurer is described by a Cramer-Lundberg process. In such a setting, we try to obtain the explicit solution of maximizing the expected exponential utility.

20190322_ Hata演講1000_1200