
3月演講

Colloquium, 國家理論中心 Dr. Seonghyeon Jeong Thursday, March 7, 16:10—17:00 數學系3174
Title: Boundedness and Existence of a Minimizer of tSNE Algorithm with Mild Conditions on the Data Points Abstract: tSNE is a nonlinear dimensionality reduction algorithm which is a method to represent high dimensional data in low dimension such as or \mathbb{R}^3. When we reduce the dimension of data, we lose some information, hence we have to choose which information we want to preserve. In tSNE, we quantify similarity of data points using Gaussian and student tdistribution function, and try to find a point distribution in low dimension which preserves the similarity of data by minimizing KLdivergence \sum p \log {p\over q}. tSNE shows clusters of data pretty well, and therefore it is used in many area. In this talk, I present some researches regarding the tSNE algorithm and discuss boundedness and existence of a minimizer of the KLdivergence.

Colloquium, 台灣大學數學系 陳俊全教授 Thursday, March 14, 16:10—17:00 數學系3174
Title: Propagating Direction in the Two Species LotkaVolterra Competition Diffusion System Abstract:The sign of the traveling wave speed in the two species LotkaVolterra competitiondiffiusion system under strong competition provides important information about the competitive advan tage of the species. To study the sign problem of the speed, we propose a minimax charac terization of the coefficients in the reaction terms when the wave speed is zero. Applying our characterization, some explicit conditions under which the speed sign can be determined are obtained.

Colloquium, 清華大學數學系 陳國璋教授 Thursday, March 21, 16:10—17:00 數學系3174
Title: The TwoCenter Problem Revisited Abstract: The twocenter problem, also known as the Euler’s threebody problem, concerns the motion of a mass point in the gravitational field generated by two other mass points that are fixed in space. It is a classic example of integrable systems and is widely considered a wellunderstood problem. Developments and applications of variational methods in celestial mechanics in the past two decades motivate a revisit to this problem by variational approaches. In this talk I will briefly outline its history and recent discoveries from variational perspective

Colloquium, 成功大學數學系 關汝琳教授 Thursday, March 28, 15:10—16:00 數學系3174
Title: The Enclosure Method in Inverse Boundary Value Problems Abstract:The enclosure method is a reconstruction method in inverse boundary value problems. In this talk, I will briefly introduce how the enclosure method works, then delve into my two recent works focusing on complex conductivity equations and semilinear elliptic equations with powertype nonlinearities. I will discuss the difficulties encountered and the extensions made to the enclosure method in addressing these specific issues.

Colloquium, 陽明交通大學應用數學系 蘇承芳教授 Thursday, March 28, 16:10—17:00 數學系3174
Title: Introduction to Quantum Monte Carlo Methods and Related Issues Abstract:演講摘要





