|Colloquium, 國立中正大學數學系 張瑞恩教授|
Thursday, October 7, 16:10—17:00 數學系3174
Title: Stability of Regular Shrinkers in the Network Flow
Abstract:In this talk, I'll present the problem I'm working on and some partial results.
In the network flow, singularities may form. They can be described as self-similar shrinking solutions called regular shrinkers. An important problem is that if we perturb the initial
network, will the new network flow to the same singularity? All network with 2 or more enclosed regions can be perturbed away. Therefore, the problem reduces to the network
with less than 2 enclosed regions. There are infinitely many of them and they are completely classified. Here, I use the entropy argument as in Colding and Minicozzi's work to show that
the 4-ray star, the 5-ray star, the fish, and the rocket can be perturbed away.
|Colloquium, 國立中山大學應用數學系 鍾思齊教授|
Thursday, October 14, 16:10—17:00 數學系3174
Title: Discovering the Dynamics - Grouping 3D Structure Conformations Using Network Analysis on 2D Cryogenic Electron Microscopy (Cryo-EM) Projection Images
Abstract:Recently, computational and learning methods are becoming popular to determine the 3D structure of a protein. The most remarkable achievement is probably the recent release of AlphaFold 2, which can perform high accuracy structure prediction from chains of amino acid sequences. However, the these methods are mainly used to predict a static structure. To understand the function of the protein, scientists need several dynamic movies that describe the conformational changes instead of a single snapshot. Therefore, describing the motions of a protein and determining the discrete or continuous conformations of the target protein is still a challenging problem. Among the tools available, cryo-EM is a promising computational technique with high efficiency that can perform conformation analysis. However, the data characteristics include heavy noise, huge dimension, a large number of unlabeled samples (no clean target is available for training) with unknown orientations, making it very challenging to reach a robust computation conclusion for heterogeneity analysis. Traditional approaches address this problem at 3D level, which is computationally expensive and may not be applicable to datasets whose conformations differ a lot. Therefore, there is a need to develop a new algorithm that preserves accuracy while solving the scalability issue due to the fast-growing data acquisition rate. In this talk, I will first introduce the importance of 3D structure determination of protein as well as the related background of cryo-EM image processing. Second, I will elaborate our approach to the heterogeneity problem, which utilizes the network analysis to partition the dataset into several homogeneous communities. Specifically, I will discuss several novel criteria that we used to measure the conformation similarity between cryo-EM images. Finally, I will discuss some on-going directions in 3D conformation analysis.
|Colloquium, 國立高雄大學應用數學系 曾昱豪教授|
Thursday, October 21, 16:10—17:00 數學系3174
|Colloquium, 國立中正大學數學系 王琪仁教授|
Thursday, October 28, 15:10—16:00 數學系3174
Title: Bifurcation Diagram of Two MEMS Problems
Abstract:In this talk, we will introduce the way to determine the number of stationary solutions to both local and nonlocal MEMS problems.
The critical value is determined by a relation between two controlling parameters in the problem. We will show that this critical value exists.
The system has exactly two stationary solutions when the applied voltage is lower than this critical value, one stationary solution for applying this critical voltage, and no stationary solution above the critical voltage.