歷史演講 PAST TALKS

NCTS/NCU Seminar on Computational Optimization with Applications

Online Seminar via Google Meet

https://meet.google.com/ehe-snix-bpc

Abstract:

The objective of this online seminar is to continue the study of the following papers:

[1] F. Zhou, Y. Cui, B. Peng, and Y. Wang, A novel optimization method of camera parameters used for vision measurement, Optics & Laser Technology, 44 (2012), pp. 1840-1849.

[2] Z. Zhang, A flexible new technique for camera calibration, IEEE Transactions on Pattern Analysis and Machine Intelligence, 22 (2000), pp. 1330-1334.

20220812_鄭經斆

NCTS/NCU Seminar on Computational Optimization with Applications

Online Seminar via Google Meet

https://meet.google.com/ehe-snix-bpc

Abstract:

The objective of this online seminar is to introduce the following papers:

[1] F. Zhou, Y. Cui, B. Peng, and Y. Wang, A novel optimization method of

camera parameters used for vision measurement, Optics & Laser

Technology, 44 (2012), pp. 1840-1849.

[2] Z. Zhang, A flexible new technique for camera calibration, IEEE

Transactions on Pattern Analysis and Machine Intelligence, 22 (2000), pp.

1330-1334.

20220805_鄭經斆

開放線上聽演講：

(1) https://meet.google.com/afn-gzmo-btm

(2) 開啟google meet並輸入下列代碼：afn-gzmo-btm

Abstract：

Schramm-Loewner Evolution (SLEκ) was introduced by Oded Schramm in 2000 to study the asymptotic behavior (scaling limit) of loop-erased random walks for κ=2 and uniform spanning trees for κ=8. A well-known application of SLE is that the Hausdorff dimension of the outer boundary of a planar Brownian motion is almost surely 4/3, which was conjectured by Benoit Mandelbrot and proved by Gregory F. Lawler, Oded Schramm, and Wendelin Werner by showing that the outer boundary of a planar Brownian motion has the same law as an SLE6. In this talk, I will introduce the development of SLE, and a series of measures defined on the space of curves in the complex plane, including Brownian excursion measures, Boundary bubble measures, and Loop measures. We obtain an expression for the Radon-Nikodym derivative of dipolar SLEκ in a domain with respect to dipolar SLEκ in a subdomain for 0<κ≤8/3.

20220701演講_卓冠宇先生 (國立中央大學數學系)

Representation and Combinatorics Seminar

線上演講連結：

(1) https://meet.google.com/fpf-bhbk-wvo  

(2) 開啟google meet並輸入下列代碼：fpf-bhbk-wvo

(3) 也可至中央大學鴻經館M107一起聽線上演講

Abstract

註：演講者為本系系友

Abstract：

In this paper, we propose an estimation algorithm for the shape of the road using trails of leading vehicles via a linear mixed model (LMM) approach. A vehicle trail is essentially the motion trajectory of a vehicle where samples of the historical path are longitudinally collected from the same vehicle at different points in time. Such measurements can be obtained from the fusion system for single or multiple sensor tracking. The aim is to use trails of leading vehicles to depict the road geometry in highway scenarios. The proposed estimation method uses a polynomial-based road model and is built from a LMM, which is one of the most widely used statistical techniques. To avoid the overload of memory usage from trail samples, trail data are first processed by the newly developed compression and chopping mechanisms before being imported into the LMM framework. Moreover, the profile likelihood function is used to alleviate the computational burden and reduce the number of iterations in the Newton-Raphson algorithm in the LMM. Finally, the proposed method is then evaluated by two publicly available next generation simulation (NGSIM) datasets. The large-scale simulation results show that the road shape estimated by the proposed method has the root mean square error (RMSE) less than 0.5 meters in average for all ranges compared with the ground truth road shape. This suggests that our method provides an accurate road shape estimation and captures the shape of the road successfully.

20220428演講_張逸塵博士 (Isuzu Technical Center of America, Inc.)

Abstract：

Deep neural network (DNN) models are being investigated for clustering unlabeled image data. Most existing DNN approaches train the model by inputting the training data, and preserve the data features in terms of embeddings. Those embeddings are certain dependent on their training data. This may raise the concerns such as generalizability, transferability, privacy, and security. Although self-supervised learning has made rapid progress, data clustering with a fixed embedding, which is low dependent on the training data, is rarely explored. In this talk, I will introduce our proposed Merge & Expand (ME) algorithm to cluster image data by using a fixed embedding and a DNN classification model. In brief, the proposed ME algorithm groups the embedded data into several small and tight clusters termed regions. Then, select the quite dissimilar regions as the seed regions along with the tentative labels. It merges similar seed regions, and expand the region size according to the outcomes by DNN’s assistance. Finally, assigns cluster memberships. We further introduce into an idea of “clean” and “unclean” images in the clustering problem. ME reports the “clean” and “unclean” images where their geometric relations in the embedded space are compatible and incompatible with their cluster structure respectively. ME achieves a compatible performance on clustering unlabeled image data while comparing to other existing works.

20220421演講_陳彥賓博士 (中研院統計所)

Abstract：

In computer experiments, Gaussian process models are commonly used for emulation. However, when both qualitative and quantitative factors are in the experiments, emulation using Gaussian process models becomes challenging. In particular, when the qualitative factors contain many categories in the experiments, existing methods in the literature become cumbersome due to curse of dimensionality. Motivated by the computer experiments for the design of a cooling system, a new tree-based Gaussian process for emulating computer experiments with many-category qualitative factors is proposed. The proposed method incorporates a tree structure to split the categories in the qualitative factors, and Gaussian process models are employed for modeling the simulation outputs in the leaf nodes. The splitting rule takes into account the cross-correlations between the categories of the qualitative factors, which have been shown by a recent theoretical study to be a crucial element for improving the prediction accuracy, and then there is a pruning procedure via the cross validation error to identify a proper tree structure. The application to the design of a cooling system indicates that the proposed method not only enjoys marked computational advantages and produces accurate predictions, but also provides valuable insights into the cooling system by discovering the tree structure.

20220407演講_陳瑞彬教授 (國立成功大學統計系)

Abstract：

Financial engineering is an interdisciplinary study that applies mathematics, statistics, and programming tools to the financial market to evaluate the fair price of financial derivatives and analyze the variations in the market. In this talk, we focus on applying mathematical tools to financial engineering, and there are four topics included. (1) We describe how to construct the stochastic differential equation (SDE) models for the financial asset price. We will introduce models from the basic Black-Scholes to advanced dynamics models. (2) The parameter estimation under the state-space model. We present the particle filter method and the EM algorithm to estimate models' parameters with hidden variables. (3) We introduce how to evaluate the fair value of financial derivatives by solving characteristic functions and applying numerical methods. (4) The application of financial engineering, including the risk management for the financial and insurance market and portfolio construction with dynamic risk preference through reinforcement learning.

20220324演講_陳亭甫教授 (逢甲大學應用數學系)

Abstract：

Topological Data Analysis (TDA) is a fast-growing research topic in applied mathematics that uses algebraic topology techniques to capture features from data. Many applied topologists have discovered its importance in many areas, such as medical image processing, molecular biology, machine learning, and pattern recognition. Persistent homology (PH) is one of the essential tools in TDA that measures the robustness and significance of homological objects (e.g., connected components, loops, or higher dimensional voids) in spaces' deformation. In the last decade, a generalization of PH called the multi-parameter persistent homology (or multi-parameter persistence) had become one of the most exciting research topics in TDA. So far,  finding methods to extract features in multi-parameter persistence is still an open and concentrating topic in TDA. Also,  examples of multi-parameter filtration are still rare and limited. In this talk, I will briefly introduce TDA development and propose a framework for constructing multi-parameter filtrations from digital images through mathematical morphology. Multi-parameter persistence derived from mathematical morphology is more efficient for computing. It contains intuitive geometric attributes of objects, such as the sizes or robustness of local objects in digital images. We involve these features to remove the salt and pepper noise in digital images as an application. Finally, I will discuss possible future approaches, such as using sheaf theory to extract features from this generalized algebraic model.

20220317演講_胡全燊博士 (國立臺灣師範大學數學系)