演講摘要

摘要:

TBD

摘要:

本講題從一位女數學人的生命歷程出發，思考嚴謹的數學訓練如何與信仰的呼召連結，並在校園中藉由教學、研究、陪伴、及科普推廣中展現愛的實踐；當重視結構與秩序的理性思維，遇見學術、生活和生命的難題時，信仰如何助人跨越障礙，學習生命的功課。分享內容涵蓋實際經驗與心得，以及女數學人在學術、家庭與事奉間的整合；傳承白恆光修女一生的榜樣，讓『帶著愛的數學教育』，成祝福他人生命的途徑。

摘要:

Site occupancy models have become a central tool for analyzing species presence and habitat use under imperfect detection, particularly in ecological surveys with repeated visits. In this talk, we introduce an integrated modeling framework that jointly addresses species occupancy, abundance, and detection processes across multiple survey occasions. The framework is built around a shared detectability intensity, which captures persistent site-level heterogeneity and induces dependence in detection across visits.

This shared structure provides a coherent link between classical occupancy models and N-mixture models, the latter of which explicitly incorporate latent abundance. As a result, the proposed framework allows smooth transitions between occupancy-only and abundance-based formulations, making it adaptable to a wide range of ecological survey designs.

 We present theoretical insights into the model structure and conduct simulation studies to evaluate estimation accuracy and inferential behavior under realistic levels of detection heterogeneity. The framework is further extended to accommodate count data and time-to-detection data, substantially broadening its applicability. Applications to mammal and bird survey datasets demonstrate improved interpretability and competitive performance relative to existing approaches, highlighting the potential of this framework to advance ecological inference from imperfectly detected data.

Abstract :

In the theory of viscoelasticity, an important class of models admits a representation in terms of springs and dashpots. Widely used members of this class are the Maxwell model and its extended version. This paper concerns resolvent estimates for the system of equations for the anisotropic, extended Maxwell model and its marginal realization, abbreviated as the EMM system, which includes an inertia term, and its reduced system. The reduced system is obtained from the realization of pure the extended Maxwell model which is a closed system with respect to the particle velocity and the difference between the elastic strain and viscous strain. Based on the resolvent estimates, it is shown that original and reduced systems generate $C_0$-groups and the reduced system generates a $C_0$-semigroup of contraction. In principle, the extended Maxwell model can be written in integro-differential form leading to a viscoelastic integro-differential (VID) system. However, there are subtle differences between the two systems with consequences for whether their solutions generate semigroups or not. Finally, an energy estimate is obtained for the reduced system, and it is proven that its solutions decay exponentially as time tends to infinity. The limiting amplitude principle follows readily from these two results. In the theory of viscoelasticity, especially in mechanics, there are several dashpot models. We will focus on the Maxwell model and its extended version. The paper concerns about the resolvent estimates for the system of equations for the extended Maxwell model, abbreviated as the EMM system,  (add some references) and its reduced system. The reduced system is obtained as a closed system with respect to the velocity of displacement and the difference between the elastic strain and viscous strain. In this paper, the resolvent estimates for the system and the reduced system are given which yield generation of $C_0$-semigroups of contraction for the systems. Apart from the dashpot models, there is a viscoelastic system of integro-differential form referred as the VID system. We will clarify the difference between the EMM system and the VID system from the point of view whether their solutions generate semigroups or not. Also, for the reduced system, we prove the exponential decaying of solutions by an energy estimate. Further, based on these, we show the limiting amplitude principle for the reduced system.

摘要:

本演講探討人工智慧於心血管疾病診斷、生醫訊號分析及蛋白質結構預測之應用與發展。首先，介紹結合生成對抗網路（GAN）之深度學習模型，在有限且不平衡的心肌灌流影像（MPI）資料條件下，預測阻塞性冠狀動脈疾病（OCAD）之研究成果。研究結果顯示，在病人層級與血管層級之預測效能均達良好準確度，顯示GAN架構於醫療小樣本學習情境下之潛力。

其次，說明人工智慧於心律不整機制研究之應用，透過光學映射所得之phase map影像，結合深度學習物件偵測與物件追蹤模型，自動化偵測與追蹤相位奇異點（Phase Singularity），有助於提升心律不整電燒治療定位與藥物效果評估之精準度。

最後，介紹AlphaFold於蛋白質三維結構預測之突破性成果，其以深度學習整合多重序列比對與生物物理知識，達到近原子級精度，對藥物開發與結構生物學研究具有重大影響。

本演講綜整人工智慧於醫療影像分析、生理訊號處理與結構生物資訊之關鍵應用，展現智慧醫療之臨床價值與未來發展趨勢。