歷史演講 PAST TALKS

Abstract：

     This study aims to address the limitations of current non-invasive diagnostic methods for detecting early stages of liver fibrosis by proposing a machine learning (ML) approach for prediction. The research comprises two parts, involving experiments on mice and clinical data from human subjects.

      Mouse Experiment: Mice were categorized into healthy (A0), mild (A1), moderate (A2), or severe (A3) liver fibrosis stages. Support Vector Machines (SVM) were employed as classifiers using two types of features: Euler numbers (EN) and estimated porosity related to liver fibrosis. Model comparisons included SVM models with solely estimated porosity, solely Euler numbers, and a combination of all features. Binary and grayscale images were used for training Convolutional Neural Network (CNN) models in the baseline. Human Clinical Data: Clinical data from 62 patients, including blood tests and dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) signal curves, were utilized for human liver fibrosis classification. New features simulating liver properties, such as porosity, diffusion rate, and flow speeds of the portal vein and hepatic artery, were introduced. K-Nearest Neighbors (KNN) and Naive Bayes (NB) models were employed, focusing on F0-3 vs F4-6 and F0-5 vs F6 classifications.

      Mouse Experiment: Model comparisons revealed that the SVM model using solely estimated porosity as a feature achieved superior performance across all categories with an accuracy of 93.3%, particularly excelling in the mild (A1) stage. Human Clinical Data: The ML models achieved excellent results in F0-3 vs F4-6 and F0-5 vs F6 classifications, with an overall three-class accuracy of 69.4%. The introduction of simulated liver signal concentration models significantly enhanced accuracy in liver fibrosis assessment. 

      This study demonstrates the potential of ML techniques, including SVM and CNN models, for predicting liver fibrosis stages. The use of simulated liver properties as features in human data contributes to a deeper understanding of liver fibrosis, presenting new avenues for research and potential improvements in diagnostic accuracy. The findings underscore the significance of ML applications in advancing liver disease assessment and treatment.

20240109演講_ 蘇逸鎮先生 (國立中央大學數學系)

Abstract：

This is a survey talk on the variational principles in fluid mechanics. The fluid dynamic equations will be derived from the least action principle in both Lagrangian and Eulerian coordinate systems. Physical quantities and fields will be expressed in terms of differential forms. Their dynamic laws will also be expressed in terms of Lie derivatives. Relabelling symmetry and conservation of vorticity will be explained. Finally, I will introduce Hamiltonian fluid mechanics in both Lagrangian and Eulerian coordinate systems. The Casimir invariances will be explained.

20231221演講_陳宜良教授 (台灣大學數學系)

摘要詳如附件

20231214演講_ 鄭堯教授 (淡江大學數學系)

Abstract：

In this dissertation, a modified version of conservative Physics-informed Neural Networks (cPINN) is provided to approach the solutions of Riemann problem for the hyperbolic scalar conservation laws in non-conservative form. To demonstrate the results, we use the model of generalized Buckley-Leverett equation (GBL equation) with discontinuous porosity in porous media. By inventing a new unknown, the GBL equation is transformed into a two-by-two resonant hyperbolic conservation laws in conservative form. We experiment with our idea by using a cPINN algorithm to solve the GBL equation in both conservative and non-conservative forms, as well as the cases of critical and non-critical states. This method provides a combination of two different neural networks and corresponding loss functions, one is for the two-by-two resonant hyperbolic system, and the other is for the scalar conservation law with a discontinuous perturbation term in the non-convex flux. The technique of re-scaling to the unknowns is adopted to avoid the oscillation or inaccurate speed of the Riemann solutions in the cases of critical Riemann data. The solutions constructed by the modified cPINN match the exact solutions constructed by the theoretical analysis for hyperbolic conservation laws. Finally, we compare the performance of the modified cPINN with numerical method called WENO5. Whereas WENO5 struggles with the approximate solutions for the Riemann problems of GBL equation in non-conservative form, cPINN works admirably. Moreover, the integration of meta-learning into the initialization of cPINN for the re-scaled GBL equation is being explored as an additional step forward. And as an ongoing project, definitive conclusions about the effectiveness of meta-learning integration cannot be drawn at this point due to inconsistencies in performance.

20231212演講_ 馬葵娜小姐 (國立中央大學數學系)

Abstract：

In this talk, we will explore machine learning and convex optimization problems from the perspective of online convex optimization (OCO). OCO plays a multi-round game between Learner and Reality, with the objective of minimizing regret. Importantly, both machine learning and convex optimization problems can be formulated as OCO problems. We will focus on Follow-the-Regularized-Leader (FTRL) type algorithms. To conclude, we will delve into a classic problem within this framework: online portfolio selection.

20231207演講_ 王嘉澤先生 (臺灣大學與中央研究院資料科學學位學程博士班)

Abstract：

We discuss the concept of super-resolution inspired by problems in optics, microscopy and signal processing. We present the mathematical formulation of super-resolution and discuss its recent progress.

20231207演講_ Prof. Albert Fannjiang (Department of Mathematics, UC Davis)

Abstract：

In a spring-mass vibration system, the inverse problem is to use the vibration frequency to determine the stiffness of each spring and the weight of each mass. Mathematically, this is equivalent to using the spectrum of a matrix to determine the entries of the matrix. Such a problem is studied in the inverse eigenvalue problem of a graph. In this talk, we will go through the history of this problem and introduce a tool called zero forcing for analyzing the multiplicity. Beyond that, we will use zero forcing techniques to generate liberation sets, which provide a convenient way to construct matrices with a given spectrum.

20231123演講_林晉宏教授 (中山大學應用數學系)

Abstract：

With its extraordinary efficiency, cost-effectiveness, and impressive stability, 2D perovskite holds immense promise for transforming photovoltaic technology, particularly in solar cell development. However, the limitations of current material structure representations have significantly impeded AI-based perovskite design and discovery. In this presentation, we introduce a novel framework that integrates topological data analysis (TDA), periodic geometry, and machine learning to effectively represent 2D perovskite structures and predict their bandgaps. This innovative approach enables the detection of the inherent periodic geometry and topology within the material's atomic system, surpassing the traditional focus on chemical interactions among atoms and unit cell periodicity. We employ mathematical tools such as persistent homology, quotient complexes, and density fingerprints to encode this essential periodicity in the topological and geometric aspects of the crystalline structure. Additionally, we provide a comprehensive and concise introduction to these tools in the context of TDA and periodic geometry.

20231109演講_胡全燊教授 (新加坡南洋理工大學)

Abstract：

As a natural generalization of classical modular curves, Shimura curves play a significant role in arithmetic, geometry and number theory. In this talk, we will give an introduction for their basic properties and discuss their connections with arithmetic and geometric invariants. Some methods are described in order to compute explicitly.

20231102演講_郭家瑋教授 (東吳大學數學系)

Abstract：

One milestone in the beginning stage of representation theory is Schur's 1901 thesis, which focuses on polynomial representations of the general linear groups. Schur later exhibits a double centralizer property (now known as the Schur-Weyl duality) that serves as a bridge between the representation theory of infinite-dimensional algebras and that of finite-dimensional algebras. A hundred years later, people continue to explore and build upon Schur's ideas. In this talk, I will be focusing on certain modern versions of the Schur-Weyl duality, as well as related open problems.

20231026演講_賴俊儒教授 (中央研究院數學所)

Abstract：On the one hand, Control is at the heart of the Information and Communication Technologies to most application domains [1]. Among various control system designs, the state-dependent Riccati equation (SDRE) scheme for Nonlinear Optimal Control has recently attracted considerable attention, with a variety of guaranteed or promising capabilities as well as many successful real implementations [2]. The up-to-date progress in our research outputs highlights the computationally efficient SDRE controller design, which, notably, realizes the tunable balance between solving time and accuracy in the pointwise Riccati solving. All the advantages are benchmarked against MATLAB® R2023a and validated in terms of field-programmable gate array. On the other hand, Optimization is a subject of great importance, broad significance across numerous fields, and even ubiquity in today’s world [3]; but its designs in recent years usually pose challenging nonlinear optimization problems for humans or machines, notably, computational issues that have been expected for enhancement [3]. Therefore, it is being explicitly analyzed via a novel perspective/method and from a bottom-up manner, namely “Exact Optimization” [4] rather than the classical “Numerical Optimization” [5-9]. The two subjects (Control and Optimization) largely interconnect [10], and thus we look forward to further insights by inviting more research endeavors. Up until now, the theoretical findings in our group resonate with and impact on applications to aerospace (guidance, unmanned aerial vehicle), robotics (two-wheeled), circuit, bio-medicine (cancer treatment), and marine (autonomous underwater vehicle); while we are trying to expand the spectrum to other fields such as finance.

Our Lab (me.ncu.edu.tw/en/portfolio-item/lglin/)

We provide both theoretical and practical trainings. More specifically, new lab members may choose to acquire experiences in mathematical analysis, software simulations, and/or hands-on experiments in real-time hardware; while the academia as well as industry manifests a growing interest in multi- and inter-disciplinary backgrounds. All alumni are accepted by NTU\EE, NTHU\EE, NYCU\EE, ASML, Micron, and/or TSMC (R&D position and so on); for example, the latest graduate (2021/9 ~ 2023/7) is admitted to the first three institutes. Last but not least, we are very grateful for all the academic and industrial support, including the ongoing funding from or collaborations with, to name a few, NSTC\Math, NYCU\Math, ITRI\Semiconductor, and NCSIST\Missile-and-Rocket; thus, the lab members enjoy early-career interactions that benefit future career plans.

[1] F. Lamnabhi-Lagarrigue et al.. Systems & control for the future of humanity, research agenda: Current and future roles, impact and grand challenges. Annu. Rev. Control, 43:1–64, 2017.

[2] T. Çimen. Survey of state-dependent Riccati equation in nonlinear optimal feedback control synthesis. AIAA J. Guid. Control Dyn., 35(4):1025–1047, 2012.

[3] S. K. Vadlamani, T. P. Xiao, and E. Yablonovitch. Physics successfully implements Lagrange multiplier optimization. Proc. Natl. Acad. Sci. U. S. A., 117(43):26639–26650, 2020.

[4] L. G. Lin and Y. W. Liang. Exact optimization: Part I. Taiwan. J. Math., 27(1):169–205, 2023.

[5] S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge, UK: Cambridge Univ. Press, 2004. 27th/latest printing with corrections, 2021, and its solution manual.

[6] D. G. Luenberger and Y. Ye. Linear and Nonlinear Programming. Switzerland: Springer, 5th/latest edition, 2021. and its 2nd ed., 2003.

[7] J. Nocedal and S. J. Wright. In T. V. Mikosch, S. I. Resnick, and S. M. Robinson, editors, Numerical Optimization, Springer Ser. Oper. Res. Financ. Eng. USA: Springer, 2nd/latest edition, 2006.

[8] A. S. Nemirovsky and D. B. Yudin, Problem Complexity and Method Efficiency in Optimization, A Wiley-Interscience Publication, John Wiley & Sons Inc., New York, 1983. 

[9] Y. Nesterov, Lectures on Convex Optimization, vol. 137, Springer, Cham, Switzerland, 2nd ed., 2018.

[10] L. G. Lin, Y. W. Liang, and W. Y. Hsieh, Convex quadratic equations and functions. arXiv:1906.00177v1.

20231012演講_林立岡教授 (國立中央大學機械工程學系)

Abstract：

1. 區塊鏈與去中心化金融

  -區塊鏈簡介

  -去中心化金融介紹

2. 鏈上數據

  -鏈上數據介紹

  -鏈上數據工具

3. 鏈上數據應用

  -Alpha Radar Bot

20230921演講_曾思遠博士