電腦視覺三維建模的精確度，仰賴影像中對應點的準確性。以前的研究大多採取兩張影像，透過極線轉換(epipolar transfer)取得影像間基礎矩陣(fundamental matrix)的關係，然後進行比對或過濾不良的對應點以求取精確的對應點。然極線轉換存在退化的問題，如何避免此退化問題以及降低兩張影像之間轉換錯誤的累積，成為求取精確三維建模中極待解決的課題。 本論文中，我們提出一套機制，透過三焦張量(trifocal tensor)的觀念來過濾影像間不良的對應點，提高整體對應點的準確度，從而能計算較精確的投影矩陣進行三維建模。我們由多視角影像出發，先透過Bundler求取對應點，然後採用三焦張量過濾Bundler產生的對應點，並輔以最小中值平方法(LMedS)提升選點之準確率，再透過權重以及重複過濾等機制來調節並過濾對應點，從而取得精確度較高的對應點組合，最後求取投影矩陣進行電腦視覺中的各項應用。 實作中，我們測詴了三組資料，包含一組以3ds Max自行建置的資料與兩組網路中取得的資料。我們先從三張影像驗證三焦張量的幾何特性與其過濾對應點的可行性，再將此方法延伸至多張影像，同樣也能證實透過三焦張量確實能提升對應點的準確度，甚至可以過濾出輸入資料中較不符合彼此間幾何性的影像。 / The accuracy of 3D model constructions in computer vision depends on the accuracy of the corresponding points extracted from the images. Previous studies in this area mostly use two images and compute the fundamental matrix through the use of the epipolar geometry and then proceed for corresponding point matching and filtering out the outliers in order to get accurate corresponding points. However, the epipoler transform suffers from the degenerate problems and, also, the accumulated conversion errors during the corresponding matches both will degrade the model accuracy. Solving these problems become crucial in reconstructing accurate 3D models from multiple images. In this thesis, we proposed a mechanism to obtain accurate corresponding points for 3D model reconstruction from multiple images. The concept of trifocal tensor is used to remove the outliers in order to improve the overall accuracy of the corresponding points. We first use Bundler to search the corresponding points in the feature points extracted from multiple view images. Then we use trifocal tensor to determine and remove the outliers in the corresponding points generated by Bundler. LMedS is used in these processes to improve the accuracy of the selected points. One can also improve the accuracy of the corresponding points through the use of weighting function as well as repeated filtering mechanism. With these high precision corresponding points, we can compute more accurate fundamental matrix in order to reconstruct the 3D models and other applications in computer vision. We have tested three sets of data, one of that is self-constructed data using the 3ds Max and the other two are downloaded from the internet. We started by demonstrating the geometric properties of trifocal tensor associated with three images and showed that it can be used to filter out the bad corresponding points. Then, we successfully extended this mechanism to more images and successfully improved the accuracy of the corresponding points among these images.

住宅抵押貸款保險(Mortgage Insurance)為管理違約風險的重要工具，在2008年次級房貸風暴後更加受到金融機構的關注。為了能更準確且更有效率的預測房價及合理評價住宅抵押貸款保險，本文延續Christoffersen, Heston and Jacobs (2006)對股票報酬率的研究，提出新的GARCH模型，利用Inverse Gaussian分配取代常態分配來捕捉房價序列中存在的自我相關以及典型現象(stylized facts)，並且同時考慮房價市場中所隱含的價格跳躍現象。本文將新模型命名為IG-GARJI模型，以便和傳統GARCH模型作區分。由於傳統的GARCH模型在計算保險價格時，通常不存在封閉解，必須藉由模擬的方法來計算價格，會增加預測的誤差，本文提供IG-GARJI模型半封閉解以增進預測效率與準確度，並利用Bühlmann et al. (1996)提出的Esscher transform方法找出其風險中立機率測度，而後運用Heston and Nandi (2000)提出之遞迴方法，找出適合的住宅抵押貸款保險評價模型。實證結果顯示，在新建房屋市場中，使用Inverse Gaussian分配會比常態分配的表現要好；對於非新建房屋，不同模型間沒有顯著的差異。另外，本文亦引用Bardhan, Karapandža, and Urošević (2006)的觀點，利用不同評價模型來比較若房屋所有權無法及時轉換時，對住宅抵押貸款保險價格帶來的影響，為住宅抵押貸款保險提供更準確的評價方法。 / Mortgage insurance products represent an attractive alternative for managing default risk. After the subprime crisis in 2008, more and more financial institutions have paid highly attention on the credit risk and default risk in mortgage market. For the purpose of giving a more accurate and more efficient model in forecasting the house price and evaluate mortgage insurance contracts properly, we follow Christoffersen, Heston and Jacobs (2006) approach to propose a new GARCH model with Inverse Gaussian innovation instead of normal distribution which is capable of capturing the auto-correlated characteristic as well as the stylized facts revealed in house price series. In addition, we consider the jump risk within the model, which is widely discussed in the house market. In order to separate our new model from traditional GARCH model, we named our model IG-GARJI model. Generally, traditional GARCH model do not exist an analytical solution, it may increase the prediction error with respect to the simulation procedure for evaluating mortgage insurance. We propose a semi-analytical solution of our model to enhance the efficiency and accuracy. Furthermore, our approach is implemented the Esscher transform introduced by Bühlmann et al. (1996) to identify a martingale measure. Then use the recursive procedure proposed by Heston and Nandi (2000) to evaluate the mortgage insurance contract. The empirical results indicate that the model with Inverse Gaussian distribution gives better performance than the model with normal distribution in newly-built house market and we could not find any significant difference between each model in previously occupied house market. Moreover, we follow Bardhan, Karapandža, and Urošević (2006) approach to investigate the impact on the mortgage insurance premium due to the legal efficiency. Our model gives another alternative to value the mortgage contracts.

由於違約事件不斷發生以及在財務實證上顯示證券的報酬率有厚尾與高狹峰的現象，本文使用縮減式模型與Lévy過程來評價有信用風險下的可轉換公司債。在Lévy過程中，本研究假設股價服從NIG及VG模型，發現此兩種模型比傳統的GBM模型更符合厚尾現象。此外，在Lévy過程參數估計方面，本文使用最大概似法估計參數，在評價可轉換公司債方面，本研究採用最小平方蒙地卡羅法。本文之實證結果顯示，Lévy模型的績效比傳統GBM模型佳。 / Due to the reason that the default events occurred constantly and still continue taking place, empirical log return distributions exhibit fat tail and excess kurtosis, this paper evaluates convertible bonds under Lévy process with default risk using the reduced-form approach. Under the Lévy process, the underlying stock prices are set to be normal inverse Gaussian (NIG) and variance Gamma (VG) model to capture the jump components. In the empirical analysis, we use the maximum likelihood method to estimate the parameters of Lévy distributions, and apply the least squares Monte Carlo Simulation to price convertible bonds. Five examples are shown in pricing convertible bonds using the traditional model and Lévy model. The empirical results show that the performance of Lévy model is better than the traditional one.

本文主要以時間序列為基礎，透過一般化自我相關條件異質變異模型、介入分析、誤差修正、多元轉換函數及組合預測等方法，來建立台灣加權股價指數的預測模型。 從預測精確度之結果顯示，多元轉換函數納入介入分析模型為單一預測模式的最佳預測模型，且其預測績效具有穩定性，而透過最小誤差迴歸組合預測模型可以再改善預測模型在MSPE、RMSPE、MAPE及Theil’s U等量的預測績效。 從多元轉換函數納入介入分析模型中發現，台灣加權股價指數會受到美國道瓊工業指數、台幣兌美元之匯率及消費者物價指數等經濟變數所影響。由於股票市場是重要景氣領先指標，因而當台灣或美國股票市場發生重大事件時，將會對台灣經濟發展產生衝擊，而從本文研究發現，政府可藉由短期政策的施行，產生另一股力量來平衡股市的波動，進而穩定台灣整體經濟發展。 / This research introduces GARCH, ECM, transfer function, and combined forecasting model to predict the changes of TAIEX, and to evaluate the forecasting performance of different models. The results show that the intervention analysis integrated into transfer function yields an accurate prediction model, and the forecasting performance is stable. According to the weighted average of forecasts by minimizing regression error, the resulting forecasting performance such as MSPE, RMSPE, MAPE and Theil’s U will be improved. The intervention analysis integrated into transfer function model shows that the TAIEX is affected by external factors, INDU, exchange rate, and consumer price index. The stock market is one of the major leading indictor, when the Taiwan or U.S. stock market had been impacted, and then Taiwan’s economic development will also be fluctuated. This paper shows that short-term implementation of policies could result in another force to balance the fluctuations in the stock market, and to stabilize the economic development in Taiwan.

過去漢語與格研究多圍繞在給字句的分析上，包括給字句的類別，以及不同類別中的「給」應為何種詞類。本文以當代與格結構的核心問題為起點，主張介詞與格和雙賓與格並不具備衍生關係，而是動詞的兩個面向──中心語PLoc／轉移性質（allative）或中心語PHave／所屬性質（possessive），所決定的兩種不同的論元結構和句法形式。以其觀點而論，漢語的介詞與格由前者形成，而雙賓與格由後者形成，而漢語與格的不對稱性，即所謂巴克詭題（Baker’s Paradox），亦可從前述兩個動詞面向加以解釋。本文認為漢語的給字句和把字句的語法形式，亦是前述兩個動詞面向的展現。並且，相關的分析不止適用於漢語與格類動詞，非與格類動詞亦能獲得闡述。

十二年國教及中小學教師評鑑即將上路，教學方向的調整與教師能力的提升在不久的將來將列為重要的教師績效指標之一。教師應如何轉型，及如何提升學生的上課狀況，都可透過教學問卷的回饋來作參考；教學問卷可直接且快速的反應學生想法並成為師生溝通的交流管道，使教師反省自我教學方式及技巧，進而改善；因此，在使用問卷時，若利用傳統的統計分析方式來研究結果，強迫學生採用二元邏輯的方式思考與解釋問卷結果，將可能會導致偏差或錯誤的結論。本論文應用模糊理論的概念，以模糊問卷為工具，利用模糊德菲法探討學生喜歡的數學老師類型，再提出新反模糊化值，並藉由模糊威克生等級和檢定及變異數檢定方法，分析學生滿意度是否會因性別、年紀、成績、背景而有所不同，最後討論學校老師及校外老師間的滿意度是否有差別。由實證例子分析結果顯示，我們提出的檢定方法，能有效分析模糊樣本的問題，進而期望能對教學問卷的分析和決策有所貢獻，並將此方法運用於其它模糊性議題之研究。 / The twelve-year compulsory education and the evaluation of the primary and secondary school teachers are brought into practice. The way teachers organizing their teaching strategies and improving their capability will be the key indicators of teachers’ performance review in the coming future. How will teachers fine-tune their instructional skill to attract students’ focus and then to boost students’ learning motivation and academic performance, is binding to the result of a practical Teaching Assessment System. The satisfaction questionnaires designed to students as teachers’ Teaching Assessment is a good evaluation tool to have student’s feedback on teachers’ performance. The questionnaires can quickly and directly reflect the thoughts of the students and serve as a communication channel between the teachers and the students, which can help teachers examine and ameliorate how and what they teach. The result could be used as reference for teachers to enhance the quality and effectiveness of teaching. In those varies of statistical methods used as analysis, if conventional statistical analysis is adapted to analyze the questionnaires and force the students to think and to explain through binary logic, it may result in deviations or erroneous consequences. Furthermore, it may drive to the exaggerated interpretation and detrimental decision. The study, based on Fuzzy Delphi Methods, aims to apply the concept of fuzzy theory and uses fuzzy questionnaires as a tool to analyze what kinds of mathematics teachers the students like. We propose the counter-fuzzy transformation, by using the Fuzzy Wilcoxon Rank-Sum Test and variance test to assay whether the students’ satisfaction differ owing to gender, age, grade, or their family background. Lastly, we will discuss whether the satisfaction is different between the school teachers and the teachers in other schools. The result demonstrates that assaying method, as using fuzzy statistics analysis, is a functional and competent way to analyze fuzzy sampling data through its aims and objectives. We believe it could sustain to support related analysis and decision making on Teaching Assessment, and also could be used to other fuzzy test study.

本文應用資產報酬率的多重碎形模型，該模型為一整合財務時間序列上的厚尾及波動持續性的連續時間過程。多重碎形的方法允許我們估計隨時間變動的報酬率高階動差，進而推論財務時間序列的產生機制。我們利用小波轉換的模數最大值計算多重碎形譜，透過譜分解得到資產報率分配的高階動差資訊。根據實證結果，我們得到S&P和DJIA的股價指數期貨報酬率符合動差尺度行為且資料也展現幕律的形態。根據估計出的譜形態為對數常態分配。實證結果也顯示S&P和DJIA的股價指數期貨報酬率均具有長記憶及多重碎形的特性。 / We apply the multifractal model of asset returns (MMAR), a class of continuous-time processes that incorporate the thick tails and volatility persistence of financial time series. The multifractal approach allows for higher moments of returns that may vary with the time horizon and leads to infer about the generating mechanism of the financial time series. The multifractal spectrum is calculated by the Wavelet Transform Modulus Maxima (WTMM) provides information on the higher moments of the distribution of asset returns and the multiplicative cascade of volatilities. We obtain the evidences of multifractality in the moment-scaling behavior of S&P and DJIA stock index futures returns and the moments of the data represent a power law. According to the shape of the estimated spectrum we infer a log normal distribution.The empirical evidences show that both of them have long memory and multifractal property.

意識的議題古老而難解，但是近年來認知神經科學領域對此議題的探討已經熱烈展開，本研究之主要目的即在探索視覺意識與大腦功能性連結之間的關係。 根據一項人臉知覺的實驗結果，本研究依照線性對非線性、局部對整體等兩項條件所構成的四個取向，分別擬定用以反映視覺意識的腦電波指標。結果發現，線性的局部指標—即γ波的強度，以及線性的整體指標—即γ波的相位耦合程度，兩者皆無法有效反映視覺意識。然而，非線性的局部指標—即吸子的相關維度，在特定通道上可以反映視覺意識；至於非線性的整體指標—即廣義的同步化程度，乃為四者中最能穩定反映視覺意識的指標。 除了得到上述若干可以有效反映視覺意識的腦電波指標之外，本研究實質上整合了認知神經科學、非線性動力系統理論、小波轉換理論以及小世界理論等當代思維，因此文中亦做出大量而深入的理論探討，並且提出對現有相關研究在邏輯或方法上的改進與澄清。 / Consciousness is an ancient and puzzling mystery. Until recently, scientists have made little significant progress on it. This study is aimed to search for the neural correlates of visual awareness. / Based on empirical data from an experiment of face perception, this study explores linear vs. nonlinear and local vs. global human EEG indexes of visual awareness. The results indicate that neither linear local index, i.e. γ-band power, nor linear global index, i.e. γ-band phase coherence, can reveal the participant’s state of awareness validly. However, nonlinear local index, i.e. correlation dimension of attractor, can be a valid index of visual awareness, but only on specific channels. Last but not least, nonlinear global index, i.e. generalized synchrony, can be the most valid and efficient index of visual awareness. / In addition to the empirical findings listed above, this study, an interdisciplinary combination of cognitive neuroscience, chaos theory, wavelet transform and small-world theory, also presents numerous theoretical discussions and modifications to other related studies logically or methodologically.

本研究旨在探討雅美語雙及物結構是否也有與英文，及其他語言如日語、希臘語、國語，一樣有與格轉換的語言現象。雅美語有一特別的強調系統可將名詞組移到主詞的位置上。在探討雅美語的雙及物結構前，必須先探討幾個問題。首先，研究名詞組的格位標記是否會因動詞的性質（動詞的及物性、動詞的論元結構）不同而有所改變，其次，提出論證證明強調系統並不適用於形容雅美語特殊的移位系統，而語態系統較能更進一步的形容此一名詞移位現象。最後，提出雅美語並不是一個作格語言，而是一個valency-neutral的語態系統。解決這些問題後，發現雅美語中也有類似英文中的與格轉換的語言現象，此一發現也驗證了Harley的提案，擁有“有”動詞的語言就會有與格轉換的現象。 / The aim of the present study is to examine the existence of dative alternation in Yami, a language with a rich case marking system, that is similar to Japanese and Greek which are both reported to have dative alternation, as well as very unique ‘focus’ systems that can promote any argument into the subject position. Several issues have to be addressed: first, the case marking on the nominal is investigated in four most commonly observed ‘focus’ constructions from various aspects including degree of transitivity, thematic structure, and event classes,…etc; second, the term ‘focus’ is misleading and is identified as ‘voice’; third, arguments against Yami as an ergative language and supports for a valency-neutral voice system are provided.　Once these basic linguistic properties have been clarified, an examination of trivalent verbs shows positive evidence of dative alternation in Yami. Dative alternation is found with the two trivalent Yami verbs meaning ‘distribute out/give out’ and ‘mail’. This finding is in accordance with Harley’s proposal of the co-existence verbal HAVE and dative alternation, and also suggests that dative alternation is not a language-specific property.

預測市場的研究近年來在學界逐漸受到重視，因為它利用價格具有訊息加總的功能，每每創造出良好的預測績效，但一個預測市場的建立在諸多原因下，通常不易吸引大規模的參與者，例如為免觸犯法令規定，以虛擬貨幣代替真錢進行交易，在缺乏真實貨幣的獲利誘因下，很難有效吸引參與者，即便真能以真實貨幣交易，若實驗的議題並非一般大眾感興趣的話題也不易吸引多數人參與，在這種情況下無法避免要面臨市場交易過於淺薄的問題，雖然不少文獻標榜淺薄市場不會影響預測市場的預測精準度，但並不表這是一個可以置之不理的問題。 本文以預測市場預測2006年北高市長選舉為實證基礎，闡明淺薄市場對價格產生的影響，以及這些影響將導致對未來事件的錯誤評價與推論，要避免這種錯誤的評價與推論唯有設法消除淺薄市場引發的干擾，因此我們提出了五種可以消除這些干擾的方法並從中選擇一較佳者。如同一般文獻的讚揚，我們再次從預測市場獲得精確的預測效果，同時證明所謂淺薄市場不影響預測市場的預測精準度前提乃在消除淺薄市場對價格產生的干擾之後才能還原這個真相。