<p dir="ltr">This thesis presents advances in numerical methods for partial differential equations (PDEs) and optimization problems, with a focus on improving efficiency, stability, and accuracy across various applications. We begin by addressing 3D Poisson-type equations, developing a GPU-accelerated spectral-element method that utilizes the tensor product structure to achieve extremely fast performance. This approach enables solving problems with over one billion degrees of freedom in less than one second on modern GPUs, with applications to Schrödinger and Cahn<i>–</i>Hilliard equations demonstrated. Next, we focus on parabolic PDEs, specifically the Cahn<i>–</i>Hilliard equation with dynamical boundary conditions. We propose an efficient energy-stable numerical scheme using a unified framework to handle both Allen<i>–</i>Cahn and Cahn<i>–</i>Hilliard type boundary conditions. The scheme employs a scalar auxiliary variable (SAV) approach to achieve linear, second-order, and unconditionally energy stable properties. Shifting to a machine learning perspective for PDEs, we introduce an unsupervised learning-based numerical method for solving elliptic PDEs. This approach uses deep neural networks to approximate PDE solutions and employs least-squares functionals as loss functions, with a focus on first-order system least-squares formulations. In the realm of optimization, we present an efficient and robust SAV based algorithm for discrete gradient systems. This method modifies the standard SAV approach and incorporates relaxation and adaptive strategies to achieve fast convergence for minimization problems while maintaining unconditional energy stability. Finally, we address optimization in the context of machine learning by developing a structure-guided Gauss<i>–</i>Newton method for shallow ReLU neural network optimization. This approach exploits both the least-squares and neural network structures to create an efficient iterative solver, demonstrating superior performance on challenging function approximation problems. Throughout the thesis, we provide theoretical analysis, efficient numerical implementations, and extensive computational experiments to validate the proposed methods. </p>

Customers adoption of Internet banking has become a widely-researched topic, although it is fair to state that some research gaps still exist. This research aims to fill some of the research gaps by examining the factors that determine the relevant behaviour of three different categories of Internet banking customers in China (i.e. current users, non-users, and discontinued users), and by developing two conceptual models that are derived from different, but complementary, theoretical approaches. The Decision Making Model and the Service and Relationship Evaluation Model are developed in this research. The Decision Making Model is grounded in the technology acceptance model (TAM) and it incorporates an additional construct of perceived value of using Internet banking. Additionally, the Service and Relationship Evaluation Model is derived from the service quality evaluation and relationship quality evaluation literature. Unlike in most other Internet banking adoption studies, these two conceptual models are used complementarily to deliver a comprehensive understanding of customers Internet banking adoption in China. The models are tested using a sample of 614 Chinese Internet banking customers collected via mall-intercept personal interviews based on questionnaires. Partial Least Square (PLS) path modelling and mediation analysis are applied to test the hypotheses advanced in the two models. The key findings of this research show that perceived value is a major factor for explaining customers Internet banking adoption, thus indicating to the banks that they should reduce costs associated with using Internet banking while providing more (perceived) benefits to customers; the importance of incorporating perceived value in Internet banking adoption model(s) is also demonstrated. The findings also confirm that perceived usefulness and perceived ease of use are important factors that determine the adoption of Internet banking by all categories of customers. Current users and non-users perceptions of their behavioural control over using Internet banking contribute to their adoption of Internet banking, and such control perceptions are shaped by self-efficacy, perceived government support and technological support. Additionally, it is demonstrated that both current users and discontinued users perceived value and perceived service quality of Internet banking have positive associations with their satisfaction with Internet banking, which lead to their Internet banking adoption. Moreover, the findings reveal that current users are more likely to continue with Internet banking if they are affectively committed to their banks; they are less likely to continue with Internet banking if they are calculatively committed to their banks due to the costs associated with leaving the banks. These therefore indicate the importance of establishing high-quality customer-bank relationships and placing less strict switching cost barriers that impose less pressure on their existing customers. This research contributes to the Internet banking adoption literature by (i) identifying the important category of Internet banking discontinued users, apart from current users and non-users; and (ii) using two complementary conceptual models, which are grounded in different theoretical streams, to investigate the relevant adoption behaviour of all three categories of Internet banking customers. It hence delivers a comprehensive understanding of personal customers adoption of Internet banking in China.

大陸的金融市場近年開放快速，推出的產品也漸趨多樣化，主要在市場上較為活躍的是股權衍生性商品與利率衍生性商品。在2007下半年，爆發次級房貸風暴，美國採取降息的手段來挽救經濟，美國的經濟仍屬疲弱，對於全球，乃至於大陸都有一定程度的影響。此時，對一般投資人而言，投資若能同時具有保本的功能，將具有相當的吸引力。 本文主要是針對大陸金融市場已發行的衍生性商品做為評價與分析，能夠讓一般的投資人知道目前大陸的金融產品發展的情況。並且分析商品適合的投資人，以及所面對的風險；對發行者來說，則探討其獲利表現與發行策略的分析。 分析的產品為興業銀行發行的掛鉤紅籌股的結構債與東亞銀行發行的每日區間計息債券以3個月期LIBOR標的。分別以蒙地卡羅模擬法與LIBOR Market Model(也稱為BGM模型)進行分析，探討發行者的利潤與何種投資人適合購買。

本論文將信用風險模型CreditGrades model延伸至可轉債評價。相對 Hung and Wang (2002) 與 Chambers and Lu (2007), 本文信用風險模型的設定較有經濟意涵。除了結構式模型(structural models) 本身就比縮減式模型 (reduced-form models) 較具經濟意涵外, 本文模型在股價愈低時, 發生違約的機率愈高, 與在真實世界公司股價愈低愈有可能發生違約的現象一致。但是 Hung and Wang (2002) 與Chambers and Lu (2007) 的設定隱含假設公司股價高低於皆不影響違約發生機率。Ayache, Forsyth and Vetzal (2003) 雖然將違約強度設定為股價的遞減函數, 試圖捕捉股價愈低違約機率愈高的現象。卻沒有說明如何估計該設定的參數。本文模型的參數校準容易而且快速。 / 本研究選用最小平方蒙地卡羅法(Least Square Monte Carlo, LSM) 進行評價。相對於樹狀法與有限差分法, 蒙地卡羅法能夠輕易評價具有路徑相依性質條款的可轉債。此外, 未來如果需要新增其它隨機因子, 比起樹狀法與有限差分法更有彈性。蒙地卡羅法的缺點為評價時間冗長, 本文以準隨機亂數(quasi-random sequences) 輔助, 縮短評價時間。 / 本文有以下發現:考慮信用風險的模型價格比起未考慮信用風險更接近市場價格; 可轉債對波動度較不敏感, 與Brennan and Schwartz (1988) 的觀察一致; 股價波動度愈大會使得可轉債價值提高, 但具有贖回條款的可轉債, 提高幅度不如沒有贖回條款的可轉債; 加入賣回條款的可轉債對利率較不敏感, 利率上升會降低可轉債的價值, 但具有賣回條款的可轉債, 下跌幅度小於沒有賣回條款的可轉債。

Dans un marché en permanente progression et pour répondre aux besoins des brasseurs en malt de qualité, la maîtrise du procédé de maltage est indispensable. La qualité du malt est fortement dépendante des conditions opératoires, en particulier des conditions de trempe, mais également de la qualité de la matière première : l'orge. Dans cette étude, nous avons établi des modèles polynomiaux qui mettent en relation les conditions opératoires et la qualité du malt. Ces modèles ont été couplés à nos algorithmes génétiques et nous ont permis de déterminer les conditions optimales de maltage, soit pour atteindre une qualité ciblée de malt (friabilité), soit pour permettre un maltage à faible teneur en eau (pour réduire la consommation en eau et maîtriser les coûts environnementaux de production) tout en conservant une qualité acceptable de malt. Cependant, la variabilité de la matière première est un facteur limitant de notre approche. Les modèles établis sont en effet très sensibles à l'espèce d'orge (printemps, hiver) ou encore à la variété d'orge utilisée. Les modèles sont surtout très dépendants de l'année de récolte. Les variations observées sur les propriétés d'une année de récolte à une autre sont mal caractérisées et ne sont donc pas intégrées dans nos modèles. Elles empêchent ainsi de capitaliser l'information expérimentale au cours du temps. Certaines propriétés structurelles de l'orge (porosité, dureté) ont été envisagées comme nouveaux facteurs pour mieux caractériser la matière première mais ils n'ont pas permis d'expliquer les variations observés en malterie.Afin de caractériser la matière première, 394 échantillons d'orge issus de 3 années de récolte différentes 2009-2010-2011 ont été analysés par spectroscopie MIR. Les analyses ACP ont confirmé l'effet notable des années de récolte, des espèces, des variétés voire des lieux de culture sur les propriétés de l'orge. Une régression PLS a permis, pour certaines années et pour certaines espèces, de prédire les teneurs en protéines et en béta-glucanes de l'orge à partir des spectres MIR. Cependant, ces résultats, pourtant prometteurs, se heurtent toujours à la variabilité. Ces nouveaux modèles PLS peuvent toutefois être exploités pour mettre en place des stratégies de pilotage du procédé de maltage à partir de mesures spectroscopiques MIR / In a continuously growing market and in order to meet the needs of Brewers in high quality malt, control of the malting process is a great challenge. Malt quality is highly dependent on the malting process operating conditions, especially on the steeping conditions, but also the quality of the raw material: barley. In this study, we established polynomial models that relate the operating conditions and the malt quality. These models have been coupled with our genetic algorithms to determine the optimal steeping conditions, either to obtain a targeted quality of malt (friability), or to allow a malting at low water content while maintaining acceptable quality of malt (to reduce water consumption and control the environmental costs of malt production). However, the variability of the raw material is a limiting factor for our approach. Established models are very sensitive to the species (spring and winter barley) or to the barley variety. The models are especially highly dependent on the crop year. Variations on the properties of a crop from one to another year are poorly characterized and are not incorporated in our models. They thus prevent us to capitalize experimental information over time. Some structural properties of barley (porosity, hardness) were considered as new factors to better characterize barley but they did not explain the observed variations.To characterize barley, 394 samples from 3 years of different crops 2009-2010-2011 were analysed by MIR spectroscopy. ACP analyses have confirmed the significant effect of the crop-years, species, varieties and sometimes of places of harvest on the properties of barley. A PLS regression allowed, for some years and for some species, to predict content of protein and beta-glucans of barley using MIR spectra. These results thus still face product variability, however, these new PLS models are very promising and could be exploited to implement control strategies in malting process using MIR spectroscopic measurements

O sensoriamento remoto é uma estratégia que pode ajudar no monitoramento da qualidade das pastagens. Objetivou-se com esse estudo analisar a resposta espectral das folhas de Brachiaria brizantha cv. Marandú, adubada com doses crescentes de ureia, para diferenciar e predizer teores foliares de nitrogênio (TFN). Os tratamentos foram distribuídos em blocos ao acaso (DBC), composto por quatro blocos e quatro tratamentos, totalizando 16 parcelas. Foram utilizadas doses crescentes de adubação com ureia: 0, 25, 50, 75 kg de N/ha/corte. Ao longo do experimento foram realizadas 7 coletas, sendo coletadas 8 folhas por parcela. Essas folhas foram submetidas à análise hiperespectral e posterior análise química do teor de nitrogênio. Ao analisar a resposta espectral das folhas, observou-se diferenças estatísticas entre os tratamentos na região do visível em todas as coletas, com ênfase na região de 550 nm (verde). Por meio de análise discriminante linear (LDA) realizada para cada coleta, os centróides gerados por todos os tratamentos apresentaram diferenças significativas, com exceção do LD1 nas coletas 6 e 7 que não apresentou distinção entre os tratamentos de 50 e 75 kg de N/ha/corte, e LD2 na coleta 5 que não apresentou distinção entre os tratamentos de 0 e 50 kg de N/ha/corte. As equações de regressão multivariada obtidas pelo método de quadrados mínimos parciais (PLSR), geraram valores razoáveis a bons de R2 (0,53 a 0,83) na predição dos TFN, onde os comprimentos de onda com maior peso nessas regressões estão na região do red edge (715 a 720 nm). Por fim, ao testar a performance de alguns Índices de Vegetação da literatura, as coletas 4, 6 e 7 apresentaram bons coeficientes de determinação (R2) que variaram de 0,65 a 0,73; uma característica em comum nos índices que melhor estimaram os TFN é a presença de comprimentos de ondas que fazem parte da região do red edge. / Remote sensing is a set of techniques that can help to monitor pasture quality. The object of this study is to analyze the spectral response from Brachiaria brizantha cv. Marandú leaves, under contrasting nitrogen levels, to differentiate and predict leaf nitrogen content. The treatments were set in a Randomized Block Design, composed of four blocks and four treatments, totaling 16 plots. Increasing doses of urea fertilization were used: 0, 25, 50, 75 kg N/ha/mowing. During the experiment, 7 data collections were performed, and 8 leaves per plot were extracted for each data collection. These leaves were submitted to hyperspectral data extraction and subsequent chemical analysis to quantify the nitrogen content. When analyzing the spectral pattern of the leaves, statistical differences among samples with different nitrogen levels were noticeable in the visible range of the spectrum in all the collections, with emphasis on the 550 nm region (green). Through linear discriminant analysis (LDA), performed for each collection, the generated centroids by the samples of each nitrogen level presented significant differences, except for LD1 in collections 6 and 7, which did not present a distinction between treatments of 50 and 75 kg of N/ha/mowing, and LD2 in collection 5 that did not distinguish between treatments of 0 and 50 kg of N/ha/mowing. The partial least square regression (PLSR) method generated reasonable to good values of R2 (0.53 to 0.83) for the prediction of leaf nitrogen content, where the wavelengths with the highest coefficient in these models are in the red edge region of the spectrum (715 to 720 nm). Finally, when testing the performance of some Vegetation Indexes from literature, collections 4, 6 and 7 presented good determination coefficients (R2) ranging from 0.65 to 0.73; a common feature in the indexes that best estimate the nitrogen content is the presence of wavelengths from the red edge region of the spectrum.

Orientador: Douglas Domingues Bueno / Resumo: Os fenômenos associados aos sistemas aeroelásticos definem uma importante classe de problemas envolvida no projeto de aeronaves. Algumas análises podem ser realizadas utilizando a formulação no domínio da frequência, porém, para alguns problemas específicos a análise no domínio do tempo mostra-se mais conveniente, especialmente para projeto de controladores e inclusão de não linearidades. Em particular, forças aerodinâmicas não estacionárias são tipicamente obtidas no domínio da frequência reduzida. Tais formulações não permitem de maneira direta, através de uma transformada inversa, obter modelos matemáticos no domínio do tempo e, portanto, é necessário o uso de um método de aproximação, como o de Roger-Abel. No entanto, uso deste método de aproximação apresenta algumas lacunas com relação ao significado físico e escolha dos parâmetros de atraso. Desta forma, o presente texto explora a influência dos estados de atraso demonstrando que é responsável pela correção da fase entre o movimento e as forças aerodinâmicas resultantes e, também, propõe uma forma de avaliação da qualidade da aproximação obtida. A partir da aproximação das cargas aerodinâmicas se obtém o modelo matemático do sistema aeroelástico, e através de simulações numéricas computacionais, tem-se a resposta do sistema aeroelástico no domínio do tempo devido à cargas de rajada $1-cosseno$. A partir da análise da resposta à rajada é possível avaliar condições em que a rajada se apresenta de maneira mais crítica para... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: The phenomena associated with the aeroelastic systems define an important class of problems involved in aircraft design. Some analyzes may be performed in the frequency domain, however, for some specific problems time domain analysis is more convenient, especially for controller design and the inclusion of nonlinearities. In particular, non-stationary aerodynamic forces are typically obtained in the reduced frequency domain. Such formulations do not allow, by means of an inverse transform, to obtain mathematical models in the time domain, and therefore it is necessary to use an approximation method, such as that of Roger-Abel. However, the use of this approximation method presents some gaps with respect to the physical meaning and choice of lag parameters. In this way, the present text explores the influence of the lag states demonstrating that it is responsible for the correction of the phase between the movement and the resulting aerodynamic forces and also proposes a method to evaluate the quality of the approximation achieved. From the approximation of the aerodynamic loads the mathematical model of the aeroelastic system is obtained, and through computational numerical simulations, has the response of the aeroelastic system in the time domain due to the 1-cosine gust load. From the analysis of the response to the gust, it is possible to evaluate conditions in which the gust is presented in a more critical way for the study system. / Mestre

傳統的主成分分析(principal component analysis)法，只能分析二式二向的資料(2-mode 2-way data)，若是要處裡三向三式的資料(3-mode 3-way data)或是更多維的資料，則必須用其它的方法。例如將某一向資料取平均數，再做分析。此法雖然可行，但卻忽略三向資料間可能潛藏的相關性。且社會科學的研究日趨複雜，三向資料也就更常見到，而我們可能也對三向資料間彼此的關聯感到興趣。因此在1960、1970年代，學者開始研究將主成分分析的模型加以擴展成適合分析三向資料的模型。本文除了介紹三向資料主成分分析所使用的Tucker3模型及其參數估計法外，也以28家股票上市公司為實例，探討資本結構影響因素於五年間（1989~1993年）在不同公司群組間的變化情形。

給定兩個有限離散型條件分配，我們可以去探討有關相容性及唯一性的問題。Tian et al.(2009)提出一個統合的方法，將相容性的問題轉換成具限制條件的線性方程系統(以邊際機率為未知數)，並藉由 l_2-距離測量解之誤差，進而求出最佳解來。他們也提出了電腦數值計算法在檢驗相容性及唯一性時的準則。 由於 Tian et al.(2009)的方法是把邊際機率和為 1 的條件放置在線性方程系統中，從理論的觀點來看，我們認為該條件在此種做法下未必會滿足。因此，本文中將邊際機率和為 1 的條件從線性方程系統中抽離出來，放入限制條件中，再對修正後的問題求最佳解。 我們提出了兩個解決問題的方法：(一) LRG 法；(二) 干擾參數法。LRG 法是先不管機率值在 0 與 1 之間的限制，在邊際機率和為 1 的條件下，利用 Lagrange 乘數法導出解的公式，之後再利用 Rao-Ghangurde 法進行修正，使解滿足機率值在 0 與 1 之間的要求。干擾參數法是在 Lagrange 乘數法公式解中有關廣義逆矩陣的計算部份引進了微量干擾值，使近似的逆矩陣及解可快速求得。理論證明，引進干擾參數所增加的誤差不超過所選定的干擾值，易言之，由干擾參數法所求出的解幾近最佳解。故干擾參數法在處理相容性問題上，是非常實用、有效的方法。從進一步分析Lagrange 乘數法公式解的過程中，我們也發現了檢驗條件分配"理論"相容的充分條件。 最後，為了驗證 LRG 法與干擾參數法的可行性，我們利用 MATLAB 設計了程式來處理求解過程中的運算，並以 Tian et al.(2009)文中四個可涵蓋各種情況的範例來解釋說明處理的流程，同時將所獲得的結果和 Tian et al. 的結果做比較。 / Given two finite discrete conditional distributions, we could study the compatibility and uniqueness issues. Tian et al.(2009) proposed a unified method by converting the compatibility problem into a system of linear equations with constraints, in which marginal probability values are assumed unknown. It locates the optimum solution by means of the error of l_2 - discrepancy. They also provided criteria for determining the compatibility and uniqueness. Because the condition of sum of the marginal probability values being equal to one is in Tian et al.s’linear system, it might not be fulfilled by the optimum solution. By separating this condition from the linear system and adding into constraints, we would look for the optimum solution after modification. We propose two new methods: (1) LRG method and (2) Perturbation method. LRG method ignores the requirement of the probability values being between zero and one initially, it then uses the Lagrange multipliers method to derive the solution for a quadratic optimization problem subject to the sum of the marginal probability values being equal to 1. Afterward we use the Rao-Ghangurde method to modify the computed value to meet the requirement. The perturbation method introduces tiny perturbation parameter in finding the generalized inverse for the optimum solution obtained by the Lagrange multipliers method. It can be shown that the increased error is less than the perturbation value introduced. Thus it is a practical and effective method in dealing with compatibility issues. We also find some sufficient conditions for checking the compatibility of conditional distributions from further analysis on the solution given by Lagrange multipliers method. To show the feasibilities of LRG method and Perturbation method, we use MATLAB to device a program to conduct them. Several numerical examples raised by Tian et al.(2009) in their article are applied to illustrate our methods. Some comparisons with their method are also presented.

AbstractIn the field of Biomedical Optics measurement of tissue optical properties, like absorption, scattering, and reduced scattering coefficient, has gained importance for therapeutic and diagnostic applications. Accuracy in determining the optical properties is of vital importance to quantitatively determine chromophores in tissue.There are different techniques used to quantify tissue chromophores. Reflectance spectroscopy is one of the most common methods to rapidly and accurately characterize the blood amount and oxygen saturation in the microcirculation. With a hyper spectral imaging (HSI) device it is possible to capture images with spectral information that depends both on tissue absorption and scattering. To analyze this data software that accounts for both absorption and scattering event needs to be developed.In this thesis work an HSI algorithm, capable of assessing tissue oxygenation while accounting for both tissue absorption and scattering, is developed. The complete imaging system comprises: a light source, a liquid crystal tunable filter (LCTF), a camera lens, a CCD camera, control units and power supply for light source and filter, and a computer.This work also presents a Graphic processing Unit (GPU) implementation of the developed HSI algorithm, which is found computationally demanding. It is found that the GPU implementation outperforms the Matlab “lsqnonneg” function by the order of 5-7X.At the end, the HSI system and the developed algorithm is evaluated in two experiments. In the first experiment the concentration of chromophores is assessed while occluding the finger tip. In the second experiment the skin is provoked by UV light while checking for Erythema development by analyzing the oxyhemoglobin image at different point of time. In this experiment the melanin concentration change is also checked at different point of time from exposure.It is found that the result matches the theory in the time dependent change of oxyhemoglobin and deoxyhemoglobin. However, the result of melanin does not correspond to the theoretically expected result.