DSpace collection: 博碩士論文

配對交易策略：價差、共整合與Copula方法;Pairs Trading Strategies: Spread, Cointegration, and Copula Approaches

Fri, 06 Mar 2026 10:58:02 GMT

title: 配對交易策略：價差、共整合與Copula方法;Pairs Trading Strategies: Spread, Cointegration, and Copula Approaches abstract: 本研究以配對交易為核心，比較共整合法、價差法、二元 Copula與納入隱含波動率資訊的階層式 Copula 交易訊號於投資績效上的差異，並著重在階層式模型是否有助於提升二元模型之績效表現。其中配對組合透過共整合檢定篩選，並以總再投資報酬率作為長期績效衡量指標。實證結果顯示，共整合法、價差法長期持有、低頻交易中產生正報酬。而Copula策略能頻繁捕捉短期資產價格偏離，且階層式模型能改善二元模型績效表現，並在敏感度測試中階層式模型之績效表現皆有改善。;This study adopts pairs trading as its core framework and systematically compares the investment performance of cointegration-based strategies, spread-based strategies, bivariate Copula models, and hierarchical Copula trading signals that incorporate implied volatility information. The analysis focuses in particular on whether the hierarchical Copula structure can effectively enhance the performance of conventional bivariate Copula models. Trading pairs are selected through cointegration tests, and total reinvested return is employed as the primary measure of long-term performance. The empirical results indicate that cointegration and spread-based strategies generate positive returns under long-horizon, low-frequency trading structures. In contrast, Copula-based strategies are more effective in capturing short-term price deviations between assets. Moreover, the hierarchical Copula model consistently improves upon the performance of the bivariate Copula model, with robustness and sensitivity analyses further confirming the superior and more stable performance of the hierarchical framework.

Advanced Finite Element and Hybrid Methods for Problems in Wave Propagation, Nonlinear Optics, and Chemotaxis

Fri, 17 Oct 2025 04:56:20 GMT

title: Advanced Finite Element and Hybrid Methods for Problems in Wave Propagation, Nonlinear Optics, and Chemotaxis abstract: 本論文針對波傳遞、非線性光學與趨化作用等具挑戰性的偏微分方程，發展先進的有限元素與混合數值方法，並提出四項主要貢獻。首先，我們提出用於二維線性 Helmholtz 問題的具自適應氣泡函數增強之多尺度有限元素法；此法結合多尺度有限元素基底與局部計算的氣泡函數，以提升精度並降低污染誤差。其次，針對非線性 Helmholtz 方程，我們提出一種基於牛頓法的穩定化有限元素法，採用「先線性化、後離散化」策略並結合 Galerkin 最小平方（GLS）穩定化，可穩健模擬 Kerr 介質中的光學雙穩態與光傳播。第三，我們發展用於描述三次諧波產生的耦合非線性 Helmholtz 系統之巢狀多尺度穩定化有限元素法；透過定點迭代、穩定化與多尺度設計，能有效捕捉光子晶體結構中的強非線性多頻交互作用，並達成高轉換效率。最後，我們設計一套適用於 Keller–Segel 趨化模型的有限元素–有限差分數值方案，兼具有限元素在幾何處理上的彈性與有限差分在時間積分上的效率，能準確模擬由非線性交叉擴散與聚集效應所引發的解之爆炸（blow-up）現象。綜合而言，這些方法可為物理、光學與生物建模中的複雜偏微分方程提供精確、穩定且高效的數值解決方案。;This dissertation develops advanced finite element and hybrid methods for challenging partial differential equations in wave propagation, nonlinear optics, and chemotaxis. Four contributions are presented. First, we present the multiscale finite element method with adaptive bubble enrichment for the two-dimensional linear Helmholtz problem. This method combines a set of multiscale finite element basis functions with bubble functions, which are computed locally, to improve accuracy and reduce pollution errors. Second, a Newton-based stabilized finite element method is proposed for the nonlinear Helmholtz equation, employing a linearize–then–discretize strategy with Galerkin least-squares stabilization to robustly simulate optical bistability and light propagation in Kerr media. Third, a nested-multiscale stabilized finite element method is developed for coupled nonlinear Helmholtz systems modeling third-harmonic generation. Employing a fixed-point iteration, stabilization, and a multiscale approach, the method efficiently captures strongly nonlinear multi-frequency interactions in photonic crystal structures and achieves high conversion efficiency. Finally, a finite element–finite difference scheme is designed for the Keller–Segel chemotaxis model. This scheme leverages the geometric flexibility of the finite element method and the time-stepping efficiency of the finite difference method. It is capable of accurately simulating blow-up phenomena arising from nonlinear cross-diffusion and aggregation effects. These methods collectively provide accurate, stable, and efficient solutions for complex partial differential equations arising in physics, optics, and biological modeling.

Semantic-Aware Informative Path Planning via Submodularity

Fri, 17 Oct 2025 04:56:01 GMT

title: Semantic-Aware Informative Path Planning via Submodularity abstract: 資訊軌跡規劃（例如，物件搜尋、地圖探索）是機器人技術的關鍵技術。由於大型語言模型技術的進步，可以利用更多語意資訊來提升規劃效能。本研究提出了一種語意認知的資訊軌跡規劃(SA-IPP)演算法偵測率假說(HPD)。由於HPD的目標函數具有自適應次模性，因此它提供了理論保證。實驗表明，該演算法的性能優於基準方法。;Informative path planning (e.g., object search, map exploration) is a key technology in robotics. Due to advances in large language model technology, more semantic information can be leveraged to boost the planning performance. This research proposes a semantic-aware informative path planning (SA-IPP) algorithm, hypothesis probability of detection (HPD). Since the objective function of HPD has adaptive submodularity, it provides theoretical guarantees. The experiments demonstrate that the proposed algorithm outperforms benchmark approaches.

TILT 中基於參數變換的廣義影像轉換;Generalized Image Warping via Subtau-Based Transformations in TILT Processing

Fri, 17 Oct 2025 04:55:47 GMT

title: TILT 中基於參數變換的廣義影像轉換;Generalized Image Warping via Subtau-Based Transformations in TILT Processing abstract: 本研究基於TILT演算法模型，提出一套可高度自訂的幾何變換流程，作為TILT 操作中的影像轉換模組。傳統流程中常使用MATLAB內建的imtransform函數進行仿射與投影轉換，但其參數形式固定，難以處理較為複雜或非線性的幾何變形。為此，我們設計了新的影像轉換函數gsubtau，以一組參數向量τ 描述可調變換模型。該模型可支援單應性矩陣、相機校準的旋轉與平移（RT），以及額外的曲線扭曲項，提供更高的靈活度與應用擴展性。此外，我們重新設計了Jacobian計算方法，採用數值差分方式估算參數偏導數，以因應τ結構可變的特性。初步實驗結果顯示，此方法可維持TILT 操作的收斂特性與變換方向，並支援多樣的變形組合。;This research presents a highly customizable geometric transformation workflow based on the TILT algorithm, serving as the image transformation module within the TILT opera tion. Traditional workflows often utilize MATLAB’s built-in imtransform function for affine and projective transformations; however, its fixed parameter format hinders handling complex or nonlinear geometric deformations. To address this, we designed a new image transformation function, gsubtau, described by a parameter vector τ. This model supports homography ma trices, camera calibration rotation and translation (RT), and additional curve distortion terms, offering greater flexibility and application scalability. Furthermore, we redesigned the Jacobian calculation method, employing numerical differentiation to estimate parameter partial deriva tives to accommodate the variable structure of τ. Preliminary experimental results indicate that this method maintains the convergence characteristics and transformation direction of the TILT operation while supporting diverse deformation combinations.