Arctic Canada has seen significant ecological changes since the 1990s, leading to sea ice melt, increased temperatures, and increased accessibility to the Northwest Passage. The increased accessibility to the Northwest Passage has allowed for vessels to easily access maritime routes that were not previously accessible. Changes to the Arctic landscape has led to the beginning of open water shipping seasons in Arctic waters, attracting international audiences for trade, tourism, fisheries, and other economic activity. This new passageway increases options for companies to reduce costs in shipping, while also facilitating new and emerging hazards and risks for operational vessels. Comprehensive risk analysis and full assessments need to be completed to aid policy- and decision-makers to support and manage the increasing maritime traffic in Canadian Arctic waters. To fill this knowledge gap, the overarching aim of this master’s level research was to identify and preliminarily evaluate a comprehensive list of hazards (impact drivers) and risks (future impacts) for Maritime ship operations within Arctic Canada and to complete a preliminary assessment of identified maritime shipping hazards and risks throughout Arctic Canada. Hazards and risks were identified using several text-based sources, including social media, grey literature, and peer reviewed journal articles, in order to conduct a comprehensive content analysis to identify the perspectives and trends emerging among the online community. Natural language processing methods were then used, such as word frequencies, word correlation, and topic modelling to identify key phrases, terminology, and thematic groups. This allowed for the creation of an inventory of relevant hazard and risk themes and categories that could be used as a strong basis for informing a risk analysis. Emerging themes included: sea ice, navigability issues, geopolitical concerns, and operational challenges, among others. Following the identification of hazard and risk factors, a ‘failure modes, effects, and criticality analysis’ (FMECA) approach was used, along with a consequence-probability Rettinger ix matrix, as means of performing a preliminary risk analysis. The method enables the collection of information regarding hazard and risk descriptors, consequence, probability, control mechanisms, impacts, and data quality information, to establish a validated risk rating score. Risk rating scores are calculated using consequences and probability scores to determine average risk ratings for individual hazards and risks and at the sector-based category level. A total of 154 variables were inventoried: 55 hazards were identified and 99 risks were noted that influence maritime ship operations in Arctic Canada. Five variables were classified as ‘VERY HIGH’: three hazards (hydrocarbon releases, transportation of dangerous goods, and multiyear sea ice) and two risks (community member displacement and socioeconomic impacts on indigenous peoples). Five thematic groups were seen as priority risk ratings, two of which identified with “HIGH” data quality indexes (Sea Ice, Environmental). A total of 35 hazards and 36 risks are recommended for further investigation, being classified with a ‘VERY HIGH’ or ‘HIGH’ data quality score. Results of this research supports a preliminary attempt at a comprehensive risk analysis that can be used in the future to conduct a full risk assessment.

In this thesis, the credit worthiness of a company is modelled using a stochastic process. Two credit models are considered; Merton's model, which models the value of a firm's assets using geometric Brownian motion, and the distance to default model, which is driven by a two factor jump diffusion process. The probability of default and the default time are simulated using Monte Carlo and the number of scenarios needed to obtain convergence in the simulations is investigated. The simulations are performed using the probability matrix method (PMM), which means that a transition probability matrix describing the process is created and used for the simulations. Besides this, two variance reduction techniques are investigated; importance sampling and antithetic variates. / I den här uppsatsen modelleras kreditvärdigheten hos ett företag med hjälp av en stokastisk process. Två kreditmodeller betraktas; Merton's modell, som modellerar värdet av ett företags tillgångar med geometrisk Brownsk rörelse, och "distance to default", som drivs av en två-dimensionell stokastisk process med både diffusion och hopp. Sannolikheten för konkurs och den förväntade tidpunkten för konkurs simuleras med hjälp av Monte Carlo och antalet scenarion som behövs för konvergens i simuleringarna undersöks. Vid simuleringen används metoden "probability matrix method", där en övergångssannolikhetsmatris som beskriver processen används. Dessutom undersöks två metoder för variansreducering; viktad simulering (importance sampling) och antitetiska variabler (antithetic variates).

給定聯合分配，可以容易地導出對應的條件分配。反之，給定條件分配的資訊，是否能導出對應的聯合分配呢？例如根據O. Paul et al.（1963，1968）對造成心血管疾病因素之追蹤研究，可得出咖啡量、吸菸量及是否有心血管疾病三者間的條件機率模型資料，是否能找到對應的聯合機率模型，以便可以更深入地研究三者之關係，是一個重要的議題。在選定參考點下，Chen（2010）提出以勝算比法找條件密度函數相容的充要條件，以及在相容性成立時，如何求得聯合分配。在二維中，當兩正值條件機率矩陣不相容時，郭俊佑（2013）以幾何平均法修正勝算比矩陣，並導出近似聯合分配，同時利用幾何平均法之特性，提出最佳參考點之選擇法則。本研究以二維的勝算比法為基礎，探討三維離散的相容性問題，獲得下列幾項結果：一、證明了三個三維條件機率矩陣相容的充要條件就是兩兩相容。二、當三維條件機率矩陣不相容時，利用幾何平均法導出近似聯合分配。三、利用兩兩相容的充要條件，導出三維條件機率矩陣相容的充要條件，並證明該充要條件與Chen的結果一致。四、在幾何平均法下，提出最少點法，有效率地找出最佳參考點，以產生總誤差最小的近似聯合分配。五、設計出程式檢驗三維條件機率矩陣是否相容，並找出最佳參考點，同時比較最少點法與窮舉法之間效率的差異。 / Given a joint distribution, we can easily derive the corresponding fully conditional distributions. Conversely, given fully conditional distributions, can we find out the corresponding joint distribution? For example, according to a longitudinal study of coronary heart disease risk factors by O. Paul et al. (1963, 1968), we obtain conditional probability model data among coffee intake, the number of cigarettes smoked and whether he/she has coronary heart disease or not. Whether we can find out the corresponding joint distribution is an important issue as the joint distribution may be used to do further analyses. Chen (2010) used odds ratio method to find a necessary and sufficient condition for their compatibility and also gave the corresponding joint distribution for compatible situations. When two positive discrete conditional distributions in two dimensions are incompatible, Kuo (2013) used a geometric mean method to modify odds ratio matrices and derived an approximate joint distribution. Kuo also provided a rule to find the best reference point when the geometric mean method is used. In this research, based on odds ratio method in two dimensions, we discuss their compatibility problems and obtain the following results on three-dimensional discrete cases. Firstly, we prove that a necessary and sufficient condition for the compatibility of three conditional probability matrices in three dimensions is pairwise compatible. Secondly, we extend Kuo’s method on two-dimensional cases to derive three-dimensional approximate joint distributions for incompatible situations. Thirdly, we derive a necessary and sufficient condition for the compatibility of three conditional probability matrices in three dimensions in terms of pairwise compatibility and also prove that this condition is consistent with Chen’s results. Fourthly, we provide a minimum-points method to efficiently find the best reference point and yield an approximate joint distribution such that total error is the smallest. Fifthly, we design a computer program to run three-dimensional discrete conditional probability matrices problems for compatibility and also compare the efficiency between minimum-points method and exhausting method.

Les outils et méthodes d’analyse d’images de documents (DIA) donnent aujourd’hui la possibilité de faire des recherches par mots-clés dans des bases d’images de documents alors même qu’aucune transcription n’est disponible. Dans ce contexte, beaucoup de travaux ont déjà été réalisés sur les OCR ainsi que sur des systèmes de repérage de mots (spotting) dédiés à des documents textuels avec une mise en page simple. En revanche, très peu d’approches ont été étudiées pour faire de la recherche dans des documents contenant du texte multi-orienté et multi-échelle, comme dans les documents graphiques. Par exemple, les images de cartes géographiques peuvent contenir des symboles, des graphiques et du texte ayant des orientations et des tailles différentes. Dans ces documents, les caractères peuvent aussi être connectés entre eux ou bien à des éléments graphiques. Par conséquent, le repérage de mots dans ces documents se révèle être une tâche difficile. Dans cette thèse nous proposons un ensemble d’outils et méthodes dédiés au repérage de mots écrits en caractères bengali ou anglais (script Roman) dans des images de documents géographiques. L’approche proposée repose sur plusieurs originalités. / Word spotting in graphical documents is a very challenging task. To address such scenarios this thesis deals with developing a word spotting system dedicated to geographical documents with Bangla and English (Roman) scripts. In the proposed system, at first, text-graphics layers are separated using filtering, clustering and self-reinforcement through classifier. Additionally, instead of using binary decision we have used probabilistic measurement to represent the text components. Subsequently, in the text layer, character segmentation approach is applied using water-reservoir based method to extract individual character from the document. Then recognition of these isolated characters is done using rotation invariant feature, coupled with SVM classifier. Well recognized characters are then grouped based on their sizes. Initial spotting is started to find a query word among those groups of characters. In case if the system could spot a word partially due to any noise, SIFT is applied to identify missing portion of that partial spotting. Experimental results on Roman and Bangla scripts document images show that the method is feasible to spot a location in text labeled graphical documents. Experiments are done on an annotated dataset which was developed for this work. We have made this annotated dataset available publicly for other researchers.

給定兩個隨機變數的條件機率矩陣A和B，相容性問題的主要課題包 含：(一)如何判斷他們是否相容？若相容，則如何檢驗聯合分配的唯一性 或找出所有的聯合分配；(二)若不相容，則如何訂定測量不相容程度的方 法並找出最近似聯合分配。目前的文獻資料有幾種解決問題的途徑，例 如Arnold and Press (1989)的比值矩陣法、Song et al. (2010)的不可約 化對角塊狀矩陣法及Arnold et al. (2002)的數學規劃法等，經由這些方法 的啟發，本文發展出創新的特徵向量法來處理前述的相容性課題。 當A和B相容時，我們觀察到邊際分配分別是AB′和B′A對應特徵值1的 特徵向量。因此，在以邊際分配檢驗相容性時，特徵向量法僅需檢驗滿足 特徵向量條件的邊際分配，大幅度減少了檢驗的工作量。利用線性代數中 的Perron定理和不可約化對角塊狀矩陣的概念，特徵向量法可圓滿處理相 容性問題(一)的部份。 當A和B不相容時，特徵向量法也可衍生出一個測量不相容程度的簡單 方法。由於不同的測量方法可得到不同的最近似聯合分配，為了比較其優 劣，本文中提出了以條件分配的偏差加上邊際分配的偏差作為評量最近似 聯合分配的標準。特徵向量法除了可推導出最近似聯合分配的公式解外， 經過例子的驗證，在此評量標準下特徵向量法也獲得比其他測量法更佳的 最近似聯合分配。由是，特徵向量法也可用在處理相容性問題(二)的部份。 最後，將特徵向量法實際應用在兩人零和有限賽局問題上。作業研究的 解法是將雙方採取何種策略視為獨立，但是我們認為雙方可利用償付值表 所提供的資訊作為決策的依據，並將雙方的策略寫成兩個條件機率矩陣， 則賽局問題被轉換為相容性問題。我們可用廣義相容的概念對賽局的解進 行分析，並在各種測度下討論賽局的解及雙方的最佳策略。 / Given two conditional probability matrices A and B of two random variables, the issues of the compatibility include: (a) how to determine whether they are compatible? If compatible, how to check the uniqueness of the joint distribution or find all possible joint distributions; (b) if incompatible, how to measure how far they are from compatibility and find the most nearly compatible joint distribution. There are several approaches to solve these problems, such as the ratio matrix method(Arnold and Press, 1989), the IBD matrix method(Song et al., 2010) and the mathematical programming method(Arnold et al., 2002). Inspired by these methods, the thesis develops the eigenvector approach to deal with the compatibility issues. When A and B are compatible, it is observed that the marginal distributions are eigenvectors of AB′ and B′A corresponding to 1, respectively. While checking compatibility by the marginal distributions, the eigenvector approach only checks the marginal distributions which are eigenvectors of AB′ and B′A. It significantly reduces the workload. By using Perron theorem and the concept of the IBD matrix, the part (a) of compatibility issues can be dealt with the eigenvector approach. When A and B are incompatible, a simple way to measure the degree of incompatibility can be derived from the eigenvector approach. In order to compare the most nearly compatible joint distributions given by different measures, the thesis proposes the deviation of the conditional distributions plus the deviation of the marginal distributions as the most nearly compatible joint distribution assessment standard. The eigenvector approach not only derives formula for the most nearly compatible distribution, but also provides better joint distribution than those given by the other measures through the validations under this standard. The part (b) of compatibility issues can also be dealt with the eigenvector approach. Finally, the eigenvector approach is used in solving game problems. In operations research, strategies adopted by both players are assumed to be independent. However, this independent assumption may not be appropriate, since both players can make decisions through the information provided by the payoffs for the game. Let strategies of both players form two conditional probability matrices, then the game problems can be converted into compatibility issues. We can use the concept of generalized compatibility to analyze game solutions and discuss the best strategies for both players in a variety of measurements.