Registration means to bring two or more shapes into a suitable relative configuration (position and orientation). In its major applications like 3D scan alignment, the aim is to coalesce data and regions originating from the same physical region have similar local form. So, the correspondence between shapes is discoverable from the shapes themselves, and the registration makes corresponding regions coincide. This work concerns the registration of shapes to satisfy a purpose or intent, not involving data integration. Regions relevant to the purpose are marked as patches correspondingly on two input 3D meshes of objects. Then, a method of registration is used to obtain the suitable configuration. Three methods of registration are explored in the present work. The first method of registration is to align intrinsic co-ordinate frames defined on the shapes. This is used in a scenario of comparison of shapes with dissimilar local form, which are to be aligned as an expert requires, as in the comparison of dental casts and apple bitemarks in forensics. Regions recognized in dentistry are marked as patches on the cast and bitemark shapes by a dentist. From these, an intrinsic frame is defined and aligned to bring the shapes close. The alignment is used to calculate distortion of a deteriorated bitemark. Another application of frame alignment is the analysis of shape variation of contours in a population for wearable product design. A frame based on anthropometric landmarks is used to construct the contours of the product's interface with the body-part, analyze its spread through a 2D grid-statistics method, and construct the interface shape. The frame helps assess the fit of the constructed shape on an individual. The method is demonstrated with respirator masks. Frame-based alignment is seen to give unsatisfactory results with head shapes for motorcycle-helmet interior design, as it does not adequately describe the helmet-head interaction. This inspires the second method of registration. The second method of registration is the biased minimization of distance between corresponding patches on the shapes, by weighting patches to indicate their importance in the registration. The method is used to assess the small deviation of precisely-known quantities in shapes, such as in manufactured part inspection. Here, the patches marked are grouped, and the part and model shapes registered at patches in the combinations of groups, by giving a binary weighting of 1 to these patches and 0 to others. The deviation of every patch across the registrations at multiple datum systems is tabulated and analyzed to infer errors. The method is exemplified with welded bars and bent-pipes. In the analysis of head-shape variation in a population to create headforms for wearable products, the deviations are large and not precisely known. So, the head shapes are registered at patches on regions pertinent to the product's functioning, with a relatively higher weight for a reference patch. A 3D grid-statistics method is used to analyze the shapes' spread and arrive at the headform shapes. The selection of head form for a given head shape is also treated. The method is demonstrated with motorcycle helmets and respirator masks. Biased distance-minimization is applied to obtain the mechanical assembly of part meshes. Different schemes of marking patches are tested as cases. The method leads to both intended and unintended final configurations, prompting for a better objective in registration. Thus, the third method of registration, that of normals is proposed; this happens in a transformed space. By analyzing the nature of assembly in CAD systems, the face-normals of the mesh are used to obtain the intended orientation of parts. The normals of corresponding patches are registered using three methods of registration, namely on a unit-sphere, of unit-normals, and spherical co-ordinates of normals. In each method, the optimal transformation is suitably converted to be applied on the actual part shape in 3D. Unit-normal alignment gives sensible results, while the other two lead to skewed final orientations. This is attributed to the nature of the space of registration. The methods are applied to examples involving different assembly relations, such as alignment of holes. On the whole, it is shown that correspondence embodies the knowledge of importance of regions on shapes for a purpose. The registration method should lead to an apt shape placement, which need not always mean coincidence. In essence, correspondence denotes 'what' regions are of relevance, and registration, 'how' to get the relative configuration satisfying a purpose or intent.

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Includes bibliographical references (leaves 303-325) / The topic of God’s beauty, while receiving attention in theological aesthetics, is not often a focused pursuit in Christian spirituality. The study attempts to answer the question of what the nature would be of an Evangelical Protestant Christian spirituality predicated upon seeking and apprehending God’s beauty. The study establishes the relevance of beauty to Christian spirituality. It then develops a definition of God’s beauty from Jonathan Edwards. God’s beauty is found to be his love for his own being. Examining Scripture and Christian history, the study establishes that God’s beauty was regarded as an objective reality until the Enlightenment. The focus of the research then turns to the subjective apprehension of beauty, and examines the methodology of pursuing beauty in art, and finds parallels in spirituality. The study considers the epistemological dichotomy of subject and object with reference to beauty, and considers Christian proposals for a form of correspondence theory for transcendentals. The findings are united in a model of spirituality. Apprehension of God’s beauty occurs through the subject possessing a correspondent form of God’s love. Findings from the aesthetic and epistemological study are united with theology to suggest that this love can be cultivated through four areas: Christian imagination, an implanted new nature, the exposure to communion with God, and the nurture of spiritual disciplines. Each of these areas is explained and justified as means to cultivate correspondent love. The postures and approaches found in the study of art and epistemology are used for explaining the nature of correspondent love. Evangelical Protestant Christian spirituality predicated upon seeking and finding God’s beauty is one which cultivates love for God that corresponds with God’s own love. / Christian Spirituality, Church History and Missiology / D. Th. (Christian Spirituality)

La simulation de la combustion turbulente connait un nouvel essor avec l'introduction de la Simulation aux Grandes Échelles (SGE) qui permet de prédire l'évolution in stationnaire de l'écoulement réactif turbulent. Dans ce contexte la prise en compte du rayonnement soulève des questions d'ordre a la fois fondamental et pratique. En effet les processus physiques du rayonnement et de la combustion sont de nature radicalement différente : la combustion est contrôlée par des échanges locaux sur une durée finie, alors que le rayonnement est instantané et fait intervenir des échanges a distance. En premier lieu il convient de s'interroger sur l'impact de la modélisation SGE de la combustion turbulente sur le rayonnement. Cette question est traitée dans le cadre plus général de l'interaction rayonnement-turbulence. A partir d'études théoriques et numériques, il est montre que cette interaction est faible et qu'une solution SGE peut être directement utilisée pour un calcul radiatif, sans modélisation supplémentaire. Il s'agit ensuite de mettre en place de façon pratique le couplage in stationnaire rayonnement-combustion turbulente. Un point clé est la réduction du temps de calcul pour le rayonnement, et diverses stratégies sont proposées. En particulier un nouveau modèle spectral est introduit, utilisant une technique de tabulation et garantissant un niveau de précision suffisant. Le temps de calcul radiatif a ainsi été réduit de deux ordres de grandeur, permettant la réalisation d'un calcul couple sur une configuration de flamme pré-melangée turbulente. / Simulation of turbulent combustion has gained high potential with the Large Eddy Simulation (LES) approach, allowing to predict unsteady turbulent reactive flows. In this context, taking into account radiation rises new fundamental and practical questions. Indeed the physics involved in radiation and in combustion are completely different : combustion is controlled by local exchanges and finite times whereas radiation is instantaneous and is based on non-local exchanges. In a first step, the impact of LES modelling of turbulent combustion on radiation is regarded. This question is treated in the more general frame of the turbulence-radiation interaction. From theoretical and numerical studies, it is shown that this interaction is weak in the LES context so that LES solutions can be directly coupled to radiative calculations, without further modelling. Then the unsteady coupling of radiation and turbulent combustion is realised. A key point is the reduction of calculation time of radiation, and several strategies are proposed. In particular a new global spectral model is introduced, using a tabulation technique and ensuring a sufficient level of accuracy. The radiative time calculation is finally decreased by two orders of magnitude, enabling the realization of a coupled calculation of a turbulent premixed flame

近來地理資訊系統(GIS)之資料庫受到不同領域的統計學家廣泛的研究，以期建立及分析可描述空間聚集效應及變異之模型，而描述空間相關存活資料之統計模式為公共衛生及流行病學上新興的研究議題。本文擬建立多維度半參數的貝氏階層模型，並結合空間及非空間隨機效應以描述存活資料中的空間變異。此模式將利用多變量條件自回歸(MCAR)模型以檢驗在不同地理區域中是否存有空間聚集效應。而基準風險函數之生成為分析貝氏半參數階層模型的重要步驟，本研究將利用混合Polya樹之方式生成基準風險函數。美國國家癌症研究院之「流行病監測及最終結果」(Surveillance Epidemiology and End Results, SEER)資料庫為目前美國最完整的癌症病人長期追蹤資料，包含癌症病人存活狀況、多重癌症史、居住地區及其他分析所需之個人資料。本文將自此資料庫擷取美國愛荷華州之癌症病人資料為例作實證分析，並以貝氏統計分析中常用之模型比較標準如條件預測指標(CPO)、平均對數擬邊際概似函數值(ALMPL)、離差訊息準則(DIC)分別測試其可靠度。 / The databases of Geographic Information System (GIS) have gained attention among different fields of statisticians to develop and analyze models which account for spatial clustering and variation. There is an emerging interest in modeling spatially correlated survival data in public health and epidemiologic studies. In this article, we develop Bayesian multivariate semiparametric hierarchical models to incorporate both spatially correlated and uncorrelated frailties to answer the question of spatial variation in the survival patterns, and we use multivariate conditionally autoregressive (MCAR) model to detect that whether there exists the spatial cluster across different areas. The baseline hazard function will be modeled semiparametrically using mixtures of finite Polya trees. The SEER (Surveillance Epidemiology and End Results) database from the National Cancer Institute (NCI) provides comprehensive cancer data about patient’s survival time, regional information, and others demographic information. We implement our Bayesian hierarchical spatial models on Iowa cancer data extracted from SEER database. We illustrate how to compute the conditional predictive ordinate (CPO), the average log-marginal pseudo-likelihood (ALMPL), and deviance information criterion (DIC), which are Bayesian criterions for model checking and comparison among competing models.

當造成失敗的原因不只一種時，若各對象同一時間最多只經歷一種失敗原因，則這些失敗原因稱為競爭風險。然而，有些個體不會失敗或者經過治療之後已痊癒，我們稱這部分的群體為治癒群。本文考慮同時處理競爭風險及治癒率的混合模式，即競爭風險的治癒率模式，亦將解釋變數結合到治癒率、競爭風險的條件失敗機率，或未治癒下競爭風險的條件存活函數中，並以建立在完整資料上之擴充的概似函數為貝氏分析的架構。對於右設限對象則以插補方式決定是否會治癒或會因何種風險而失敗，並推導各參數的完全條件後驗分配及其性質。由於邊際後驗分配的數學形式無法明確呈現，再加上需對右設限者判斷其狀態，所以採用屬於馬可夫鏈蒙地卡羅法的Gibbs抽樣法及適應性拒絕抽樣法(adaptive rejection sampling) ，執行參數之模擬抽樣及設算右設限者之治癒或失敗狀態。實證部分，我們分析Klein and Moeschberger (1997)書中骨髓移植後的血癌病患的資料，並用不同模式之下的參數模擬值計算各對象之條件預測指標(CPO)，換算成各模式的對數擬邊際概似函數值(LPML)，比較不同模式的優劣。 / In case that there are more than one possible failure types, if each subject experiences at most one failure type at one time, then these failure types are called competing risks. Moreover, some subjects have been cured or are immune so they never fail, then they are called the cured ones. This dissertation discusses several mixture models containing competing risks and cure rate. Furthermore, covariates are associated with cure rate, conditional failure rate of each risk, or conditional survival function of each risk, and we propose the Bayesian procedure based on the augmented likelihood function of complete data. For right censored subjects, we make use of imputation to determine whether they were cured or failed by which risk and derive full conditional posterior distributions. Since all marginal posterior distributions don’t have closed forms and right censored subjects need to be identified their statuses, we take Gibbs sampling and adaptive rejection sampling of Markov chain Monte Carlo method to simulate parameter values. We illustrate how to conduct Bayesian analysis by using the bone marrow transplant data from the book written by Klein and Moeschberger (1997). To do model selection, we compute the conditional predictive ordinate(CPO) for every subject under each model, then the goodness is determined by the comparing the value of log of pseudo marginal likelihood (LMPL) of each model.

當母體中有部份對象因被治癒或免疫而不會失敗時，需考慮這群對象所佔的比率，即存活分率。本文主要在探討如何以貝氏方法對含存活分率之治癒率模式進行分析，並特別針對兩種含存活分率的迴歸模式，分別是Weibull迴歸模式以及對數邏輯斯迴歸模式，導出概似函數與各參數之完全條件後驗分配及其性質。由於聯合後驗分配相當複雜，各參數之邊際後驗分配之解析形式很難表達出。所以，我們採用了馬可夫鏈蒙地卡羅方法（MCMC）中的Gibbs抽樣法及Metropolis法，模擬產生參數值，以進行貝氏分析。實證部份，我們分析了黑色素皮膚癌的資料，這是由美國Eastern Cooperative Oncology Group所進行的第三階段臨床試驗研究。有關模式選取的部份，我們先分別求出各對象在每個模式之下的條件預測指標（CPO），再據以算出各模式的對數擬邊際概似函數值（LPML），以比較各模式之適合性。 / When we face the problem that part of subjects have been cured or are immune so they never fail, we need to consider the fraction of this group among the whole population, which is the so called survival fraction. This article discuss that how to analyze cure rate models containing survival fraction based on Bayesian method. Two cure rate models containing survival fraction are focused; one is based on the Weibull regression model and the other is based on the log-logistic regression model. Then, we derive likelihood functions and full conditional posterior distributions under these two models. Since joint posterior distributions are both complicated, and marginal posterior distributions don’t have closed form, we take Gibbs sampling and Metropolis sampling of Markov Monte Carlo chain method to simulate parameter values. We illustrate how to conduct Bayesian analysis by using the data from a melanoma clinical trial in the third stage conducted by Eastern Cooperative Oncology Group. To do model selection, we compute the conditional predictive ordinate (CPO) for every subject under each model, then the goodness is determined by the comparing the value of log of pseudomarginal likelihood (LPML) of each model.