陽明交通大學應用數學系

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.

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.

Abstract
One will present a two expansions of the spectral information to yield the pointwise structure of the Green;s function.

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.

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.

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.

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