Course Info
- Term: Feb 23, 2026 – June 12, 2026
- Meeting time: Tuesday, 1:20 pm – 3:10 pm @ SA213
- Instructor: Jephian Lin | 林晉宏
- Email: jephianlin [at] nycu.edu.tw
- Office: SA336
- Office Hours: By appointment
Tentative Schedule
- February 24 13:20課程介紹
- February 26
11:10李志光教授, College of William and Mary
Linear preservers of matrix pairs with some extremal norm properties [ slides ]
Abstract
We present some recent results on linear maps $T$ on matrix pairs $(A,B)$ preserving some extremal norm properties such as
- $\|T(A) + T(B)\| = \|T(A)\| + \|T(B)\|$ whenever $\|A+B\| = \|A|\ + \|B\|$, or
- $\|T(A)T(B)\| = \|T(A)\| \|T(B)\|$ whenever $\|AB\| = \|A|| \|B\|$.
Related results and open problems will be mentioned.
- March 3
13:30台積電智能製造中心 ★ 2026 校園講座：智能製造．智造未來 ★ (to 15:00)
Details
- March 10
14:00呂秉澤教授, 國立中正大學
Geometry-Aware Iterative and Direct Methods for Unitary Quantum Channel Reconstruction
Abstract
Unitary quantum channels play a central role in modeling coherent quantum dynamics and quantum circuits. Reconstructing such channels from finite input–output data is inherently challenging, particularly in the presence of noise, and is closely related to nonconvex optimization on matrix manifolds.
In this work, we develop a unified geometry-aware framework for unitary quantum channel reconstruction by formulating the problem as a constrained optimization task on the Stiefel manifold. For noisy measurement data, we propose an iterative algorithm based on polar decomposition that embeds the unitary constraint directly into the update rule. We prove that the resulting sequence monotonically decreases the objective function and converges to a critical point on the manifold.
In the noise-free setting, we further introduce a direct reconstruction methodology. We show that the global minimizers of the objective function form an equivalence class of unitary matrices, differing only by a global phase factor, and establish conditions under which the underlying quantum channel can be recovered exactly. Leveraging spectral properties of non-degenerate quantum states, we derive a reconstruction procedure that significantly reduces the effective search dimension and requires only a minimal number of quantum observables.
Together, the proposed iterative and direct methods provide a theoretically rigorous and computationally efficient approach for approximating or exactly recovering unitary quantum channels from limited data.
- March 17
14:00王新博教授, 國立臺灣大學
Group Testing in 6G: Downlink and Uplink
Bio
Hsin-Po Wang is an Assistant Professor at National Taiwan University (EE + GICE). He received a BSc in Mathematics from NTU and a PhD in Mathematics from UIUC, and he has worked at UC San Diego, UC Berkeley, and the Simons Institute before joining NTU.
Hsin-Po Wang is interested in applying math tools such as algebra, combinatorics, calculus, and probability theory to information theory and coding. Particular topics he has worked on include polar codes (for wireless communication), group testing (this talk), regenerating codes (for cloud storage), distributed matrix multiplication (for cloud computation), DNA digital data storage (for very long-term storage), differential privacy (for privacy), exact distribution shaping (for randomized algorithms and ML), and pessimistic cardinality estimation (for database optimization).
Abstract
Group testing (GT) is a mathematical trick to identify a small number of targets from a large population using pooled tests, and it has become increasingly relevant in modern communications. For instance, for uplink, the challenge is to arrange devices who want to talk into frequency–time slots; for downlink, on the other hand, the challenge is to send messages to devices without Alice mistaking Bob's message for her own. 6G will benefit from group testing tricks to support a massive number of devices with highly irregular activity.
This talk applies GT to both downlink and uplink through a single design idea that we call cutting the plum pudding (CTPP). The analogy is simple: plums are randomly distributed in a pudding, and it is difficult to cut out exactly one plum. In our setting, the base station performs randomized cuts over device sets so that exactly one device is highlighted. Once the singleton is found, the task reduces to one-to-one communication, which is significantly easier to handle reliably.
- March 24
14:00尤釋賢教授, 中央研究院
Singular regular decomposition of the Green's function for a linearized compressible Navier–Stokes equation
Abstract
One will present a two expansions of the spectral information to yield the pointwise structure of the Green's function.
- March 31
14:00Professor Swee Hong Chan, Rutgers University
Spanning trees and continued fractions
Abstract
Consider the set of positive integers representing the number of spanning trees in simple graphs with n vertices. How quickly can this set grow as a function of n? In this talk, we discuss a proof of the exponential growth of this set, which resolves an open problem of Sedlacek from 1966. The proof uses a connection with continued fractions and advances towards Zaremba’s conjecture in number theory. This is joint work with Alex Kontorovich and Igor Pak. This talk is intended for general audience.
- April 7
13:20陳庭美諮商心理師, 若竹心理諮商所 [性別平等課程宣導] (to 15:10)
How to love－談親密關係建立與經營
- April 14
14:00陳柏廷醫師, 臺大醫院
Application of Artificial Intelligence in Medical Imaging
Abstract
Artificial intelligence (AI) has become increasingly integrated into modern radiology, offering tools that support image interpretation, quantitative analysis, workflow prioritization, and clinical decision-making. Recent advances in machine learning and deep learning have enabled the detection of subtle imaging patterns and the efficient analysis of large-scale imaging data, helping to enhance diagnostic accuracy and improve workflow efficiency. In current radiology practice, AI is already being applied in areas such as lesion detection, organ segmentation, triage, and risk prediction.
Pancreatic cancer remains one of the most lethal malignancies, in part because of its subtle imaging features and the difficulty of early diagnosis on routine CT. In this talk, we will review the emerging role of AI in pancreatic cancer detection using CT imaging, with a focus on recent advances in AI-based detection models and their potential to facilitate earlier diagnosis. We will also briefly discuss the broader real- world applications of AI in radiology and consider the challenges and opportunities for translating these technologies into clinical practice.
- April 21
14:00吳德琪教授, 中央研究院
Long-Time Asymptotics for the Kadomtsev–Petviashvili II Equation
Abstract
The Kadomtsev-Petviashvili II (KPII) equation is one of the few physically relevant integrable systems in more than one spatial dimension. In this talk, we present an overview of the inverse scattering theory and the stationary phase method, and explain how these tools are used to derive the long-time asymptotic behavior of solutions.
- April 28
13:20黃楓台處長, 國家太空中心
TBA14:20黃楓南教授, 國立中央大學
Abstract
TBA
Newton-Type Methods, Stiffness, and Nonlinear Preconditioning: A Dynamical ViewAbstract
Newton-type methods are among the most effective tools for solving large-scale nonlinear systems arising in scientific computing. Despite their fast local convergence, their global behavior can be unpredictable, with common issues such as overshooting, stagnation, and sensitivity to problem scaling—especially in stiff or highly unbalanced systems.
In this talk, we present a dynamical systems perspective for understanding these behaviors by interpreting Newton iterations as discrete approximations of an underlying continuous-time flow. This viewpoint provides an intuitive characterization of nonlinear imbalance in terms of stiffness, offering insight into why classical globalization strategies, particularly line search, may become ineffective or overly restrictive.
Motivated by this perspective, we revisit line search methods and introduce improved strategies, including curve search techniques, that better align with the intrinsic dynamics of the nonlinear system. We further show that nonlinear preconditioning can be naturally interpreted as a transformation that reduces stiffness and restores balance, leading to improved robustness and convergence.
Numerical examples from nonlinear PDEs illustrate how this framework not only enhances performance, but also provides a unified viewpoint for understanding globalization, acceleration, and stabilization in Newton-type methods.
- May 5
14:00Professor Yu-Ting Chen, University of Victoria
TBA
Abstract
TBA
- May 12
14:00李宜霖博士, 國立臺灣師範大學
TBA
Abstract
TBA
- May 19 無安排演講
- May 26
14:00張昌祐教授, 中央研究院
TBA
Abstract
TBA
- June 2 無安排演講
- June 9
14:00平行計算演講
TBA
Abstract
TBA
Policies/Ethics
Accessibility
Students with diverse learning styles and needs are welcome in this course. In particular, if you have a disability/health consideration that may require accommodations, please feel free to approach me.
Grading
Percentage scores will be converted to letter grades according to Regulations for Grading of Students (國立陽明交通大學學生成績作業要點).
Attendance
You are expected to attend the classes.
Missing work
If you miss some course components due to illness, accident, family affliction, or religious observances, please talk to me and provide the documentation. In such cases, the course component is excused, and your course score will be calculated by distributing the weight of the missed item(s) across the other course components. Missing components are limited to at most 20%.
Academic integrity
Do not copy others' work, including others' homework, the textbook, online materials, and others' answers in an exam; if it is really necessary, add proper citations to your references. It makes no point (and gives you no point) if the work is not yours since you learned nothing.