選舉是實行民主政治最有效的方法之一，而選區劃分的方式將直接或間接的影響投票結果與民主政治理念的施行。 然而在選舉法規或行政區域發生變動時，舊有的選區劃分方式需要隨之調整。而傳統人工的方式具有許多缺點，如：耗費人力資源、人口分配不均、難以兼顧形狀及行政區完整等等。若每次行政區域發生變動，都需要重新劃分，將花費許多不必要的人力、物力及時間，因此利用電腦以完成自動劃分的技術逐漸受到重視。 本論文中我們打破現有的政治與人文鴻溝，嘗試以系統化的方法對選區劃分作全面性的查驗。我們利用計算幾何學的特性與人工智慧搜尋的技巧，儘量找出可能的劃分方式再進行評估。我們依據中選會的建議採用村裡為劃分之最小行政區域，從數以十萬計之合理解中，根據形狀等客觀條件篩選出較佳之劃分方式，進而將歷史投票行為加入考量，以對篩選出的劃分方式作進一步評估與分析。 實作中我們以台南市為對象，在不同的人口限制及形狀條件下，分別比較所能找到的合理解數目。同時選出一部分的劃分方式，和中選會的劃分方式比較，結果顯示我們的方法可以全面性的分析選區劃分，不同的劃分方式可能產生不同的選舉結果。 / Election is one of the most effective way of conducting democratic politics, and mean of electoral redistricting shall post effect, either directly or indirectly, on electoral outcome as well as delivering ideas of democratic politics. As election regulations or administrational districts experience alterations, the present electoral districting is forcefully accompanied with adjustments. Electoral redistricting using traditional human labor works reveal several flaws such as: human resource wastage, uneven population distributions, hard to maintain shape contiguity and compactness, as well as the completeness of administration districts. Every single alteration experience in administration district requires redistribution, thus expensing on unnecessary human labor, resources and time. As such, it had brought great attention on techniques of automatic redistribution by means of modern computer technologies. In this thesis, we shall breakthrough a giant gap between politics and humanity; conduct a thorough examination on systematic approach on electoral redistricting. We are going to utilize characteristics of computational geometry and artificial intelligence searching techniques to find out every conceivable means of redistricting then evaluation the performance of them. By recommendation of Central Election Commission (hence CEM), we will adopt the classification of township as basic unit of administrational district, from counts of thousand adequate explanations, by objective factors of shape accordance and others, select the better means of redistricting methods, and afterward put into concern of historical voting behavior, conduct a further evaluation and analysis upon chosen redistricting method. In actual practices we had selected Tainan City as the experiment target, under different population limitations and factors of form, compare the searchable numbers of decent explanation respectively. We choose some redistricting outcomes, and put into comparison with redistricting method of the CEM. The results indicated our approach is able to conduct a thorough redistricting analysis, as well as more diversified comparing to CEM's outcome. The result of this experiment also reveals different election outcome with adoption of different redistricting methods.

自動化三維建模需要準確的三維點座標，而三維點的位置則依賴高精度的對應點，因此對應點的尋找一直是此領域的研究議題，而使用稀疏光束調整法(SBA：Sparse Bundle Adjustment)來優化相機參數也是常用的作法，然而若三維點當中有少數幾個誤差較大的點，則稀疏光束調整法會受到很大的影響。我們採用多視角影像做依據，找出對應點座標及幾何關係，在改善對應點位置的步驟中，我們藉由位移三維點法向量來取得各種不同位置的三維補綴面(3D patch)，並根據投影到影像上之補綴面的正規化相關匹配法(NCC：Normalized Cross Correlation)來改善對應點位置。利用這些改善過的點資訊，我們使用稀疏光束調整法來針對相機校正做進一步的優化，為了避免誤差較大的三維點影響到稀疏光束調整法的結果，我們使用穩健的計算方法來過濾這些三維點，藉由此方法來減少再投影誤差(reprojection error)，最後產生較精準的相機參數，使用此參數我們可以自動化建出外型架構較接近真實物體的模型。 / Automated 3D modeling of the need for accurate 3D points, and location of the 3D points depends on the accuracy of corresponding points, so the search for corresponding points in this area has been a research topic, and the use of SBA(Sparse Bundle Adjustment) to optimize the camera parameters is also a common practice, however, if there are a few more error 3D points, the SBA will be greatly affected. In this paper, we establish the corresponding points and their geometry relationship from multi-view images. And the 3D patches are used to refine point positions. We translate the normal to get many patches, and project them into visible images. The NCC(Normalized Cross Correlation) values between patches in reference image and patches in visible image are used to estimate the best correspondence points. And they are used to get better camera parameters by SBA(sparse bundle adjustment). Furthermore, it is because that it usually exist outliers in the data observed, and they will influence the results by using SBA. So, we use our robust estimation method to resist the outliers. In our experiment, SBA is used to filter some outliers to reduce the reprojection error. After getting more precise camera parameters, we use them to reconstruct the 3D model more realistic.

在這篇論文中，一個熱帶亞純函數(tropical meromorphic function)若給定有限個零根(roots)與極點(poles)還有它們的重數(multiplicities)，我們證明了這個熱帶亞純函數的存在與唯一性。另外，一個熱帶週期函數(tropical periodic function)若給定一個週期區間內的有限個零根與極點還有它們的重數，我們也找到了這個熱帶週期函數的一個簡單表達式。接著，給定一個一階線性差分方程(first-order linear difference equation)，我們討論了各種情況下的所有熱帶亞純函數解的表達式。最後，對於連續函數我們提供了一個它的熱帶近似函數，希望對於解差分方程的熱帶亞純函數解時能有所助益。 / In this thesis, we find the formula of tropical meromorphic function by giving finite number of roots and poles (with multiplicities). We also find a simple formula for tropical periodic function by giving finite number of roots and poles (with multiplicities) during a period [0,T). We then discuss all cases of the tropical meromorphic solution functions of first-order linear difference equation. At last, we provide a tropical approximated function of a given continuous function. We hope it is helpful in solving the tropical meromorphic solution functions of a given difference equation.

基於SEC之要求，越來越多美國金融機構於其財務報表附註中揭露金融交易資產之風險值；然而計算風險值涉及到許多假設，於是導致過去部分文獻對於風險值資訊揭露之可靠性產生質疑。本研究以風險值之揭露對於報表使用者之資訊價值作為研究課題；為求與附註揭露之風險值資訊比較，本研究以公司帳列之金融交易資產(Trading Assets)、金融交易收入(Trading Revenue)為基礎，利用蒙地卡羅模擬法模擬帳列金融交易資產於次期可能產生之最大潛在損失，並且透過OLS regression及panel data model探討： (1)風險值及金融交易資產潛在可能損失是否可以預測次期金融交易收入波動 (2)風險值與金融交易資產潛在可能損失資訊之提供是否影響次期股票交易量 (3)風險值與金融交易資產潛在可能損失資訊是否可以有效預測次期股價報酬 率變異。 實證結果顯示，風險值之揭露與金融交易資產潛在可能損失之資訊對於預計次期金融交易收入之波動與股價報酬率變異均呈現顯著正相關；易言之，上述兩種資訊之揭露均提供增額之資訊價值。惟另方面，風險值之揭露與金融交易資產潛在可能損失之資訊卻與次期股票交易量呈正相關，也就是說上述兩種資訊的揭露反而會造成投資人降低長期投資持有的意願。 / Financial institutions in the United States are required by the Securities and Exchange Commission to disclose their Value at Risk (VaR) in the footnotes of the financial statements. Over the years, VaR has been used by institutional investors, industry consultants, and regulators as one of the key measures of market risk. However, there are a number of approaches to calculating VaR and some of them may involve various statistical models and assumptions. Due to the fact that different models and assumptions may be used, the VaR numbers produced by different institutions are difficult to compare with one another. The usefulness of these numbers is therefore decreased. This thesis examines the usefulness of disclosures of VaR information. In order to compare with VaR disclosures, the implied potential maximum losses of trading assets are simulated by using Monte Carlo simulation. We then employ the OLS regression and the panel data models to investigate the following research questions: (1)whether VaR and implied potential maximum losses of trading assets disclosed by financial institutions are instrumental in predicting the variability of trading revenue for the next quarter; (2)whether VaR and implied potential maximum losses of trading assets disclosed by financial institutions affect investors' investing decision; (3)how useful are VaR and implied potential maximum losses of trading assets in predicting the volatility of daily stock return next quarter. The empirical results indicate that VaR and implied potential maximum losses of trading assets are significantly related to the variability of trading revenue and the volatility of daily stock returns next quarter. This evidence suggests that both types of disclosures provide incremental information on predicting the variability of trading revenue and investment risk in the future. Nevertheless, we also find that both VaR disclosures and implied potential maximum losses of trading assets are positively associated with future average stock trading volume, implying that investors tend to trade stock more frequently when the market risk information is disclosed.

浮雕是雕刻藝術中重要的表現方法，藉由在平板上雕刻出高低落差，傳達出豐富的形狀視覺線索，是介於3D雕塑和2D畫作中間的一種物體外形的表現方式。本論文將針對淺浮雕這類型相對高度較低的浮雕技法，將要表達的3D場景壓縮到接近平面但盡可能保留細節。我們使用適應性直方圖均衡化技術去壓縮高度的動態範圍並盡可能強化細節，且經由降低取樣點數量的技巧加速適應性直方圖均衡化的計算，以利於使用者進行互動性自訂風格化。另外依照場景特徵的流向，增加特殊的刻紋去豐富淺浮雕的風格表現。 / Relief is a sculptural technique to express the shape feature on a flat surface. It is an art medium between 3D sculpture and 2D painting. In this thesis, we focus on bas-relief, which is a relatively low relief to compress the depth of 3D scene to a shallow overall depth and preserve details of the shape. We use the adaptive histogram equalization (AHE) to compress the depth range and enhance details, and accelerate the AHE computation by sample reduction, which is in favor of the user interaction of custom stylization. Furthermore, adding special carving patterns according to feature flows of the scene enriches the stylization of the relief generation.

京都大学 / 0048 / 新制・論文博士 / 博士(工学) / 乙第13011号 / 論工博第4136号 / 新制||工||1650(附属図書館) / 32939 / (主査)教授 門内 輝行, 教授 竹山 聖, 教授 神吉 紀世子 / 学位規則第4条第2項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

京都大学 / 新制・課程博士 / 博士(理学) / 甲第24451号 / 理博第4950号 / 新制||理||1707(附属図書館) / 京都大学大学院理学研究科生物科学専攻 / (主査)教授 本川 雅治, 准教授 中野 隆文, 教授 中務 真人 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

京都大学 / 新制・課程博士 / 博士(工学) / 甲第23872号 / 工博第4959号 / 新制||工||1775(附属図書館) / 京都大学大学院工学研究科建築学専攻 / (主査)教授 大崎 純, 教授 竹脇 出, 教授 西山 峰広 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

在過去二到三年之中，能源、金屬、軟性商品等原物料價格漲勢強勁，成為市場上最炙手可熱的商品。然而，原物料價格漲升為全球帶來了通膨隱憂，世界各國紛紛採用各種貨幣政策和財政政策試圖緩解通膨壓力。其中，利率政策即是相當重要的一環。在這樣的背景之下，是否對於能源、貴金屬和利率衍生性商品的設計和定價上產生影響，值得進一步檢視。因此，本論文選擇以中國大陸的原油與黃金連結複合式選擇權，以及利率（HIBOR）連結可贖回每日區間計息等兩種結構性存款作為研究個案，以財務工程的理論模型為中國銀行的金融創新產品作評價與分析。 在原油與黃金連結複合式選擇權部分，分別假設金價和油價服從幾何布朗運動（Geometric Brownian Motion）推導出封閉解，以及Schwartz的一因子均數回歸模型，採蒙地卡羅模擬法模擬標的資產之價格路徑並以之估算商品理論價值和發行機構利潤，之後則就避險參數和商品預期收益率作分析。在利率連結可贖回每日區間計息結構性存款部分，由於具有發行機構可提前贖回的特性，本論文採用LIBOR市場模型（BGM Model）為評價基礎，先利用市場報價資訊計算期初遠期利率及進行參數校準，再以蒙地卡羅模擬法模擬遠期利率路徑，最後以Longstaff and Schwartz（2001）提出的最小平方蒙地卡羅法（LSM）計算商品理論價值和發行機構利潤。 除估算商品理論價值以檢視中國銀行的商品定價合理性之外，本文也針對中國大陸的外匯和利率政策對金融機構在商品設計方面的影響作分析，最後則分別就財務工程與金融創新以及總體政策與金融市場兩方面提出結論與建議，以供各界參酌。 / The prices of physical commodities have risen a lot and led to pressure of inflation for several years. Many countries over the world have tried hard to tackle inflation threat with monetary and fiscal policies. Under this circumstance, the design and pricing of structured products should be affected. Therefore, the oil and gold-linked and interest rate-linked structured deposits launched by Bank of China are selected to be the case study in this thesis. Prices of the underlying assets are assumed to follow Geometric Brownian Motion, and the close-form solution of the oil and gold-linked structured deposit embedded with compound options is derived. Moreover, Schwartz’s One-Factor Mean Reversion Model is adopted to derive the fair value by simulation. In addition to the fair value and issuer’s profit, the expected rate of return, hedge parameters (Greeks) and model difference are presented in this thesis. As for the interest rate-linked Callable Daily Range Accrual Deposit, the thesis presents the steps of pricing by simulation. LIBOR Market Model (BGM Model) is adopted to derive the fair value of Callable Range Deposit with Least Squares Monte Carlo approach. Besides, the design and pricing of structured products are actually influenced by those policies in relation to interest rates and currencies adopted by government of Mainland China. The influence is discussed in the thesis as well. Eventually, the conclusions and suggestions are made with respect to macroeconomic policy and financial market as well as financial innovation.

隨著網際網路的蓬勃發展，傳統的地理資訊系統也從早期的單機系統朝Web GIS的方向發展，但是關於地理資料的格式卻仍舊莫衷一是，沒有一個為業界所共同遵從的標準，其結果除了人力與財力資源的浪費，也造成不同單位間的地理資料整合上的困難。傳統的電子地圖採用點矩陣的圖形格式，因檔案太大而常造成資料傳輸上的延遲，而且圖形的解析度與品質不佳；此外在建置上十分不便，需要專門的處理軟體才能進行編輯修改。因此傳統GIS的處理方式已經不能滿足網路化的GIS應用系統的資訊需求。 　在XML出現之後，W3C與業界也體認到這樣的需求，因此新一代的網路二維圖形標準，可變動向量圖形（Scalable Vector Graphics，SVG）便應運而生，雖然目前SVG仍在候選建議階段，但鑑於它的諸多特點與優越性，目前已獲得業界各大公司的支持。本論文便在此種情況下產生研究動機，我們期望透過SVG這種新興的向量圖形格式，找出解決目前GIS在地理空間資料上所面臨的困境。經過本研究所實作出來的雛形系統顯示，以SVG作為新一代的Web GIS地理空間資料格式不但可行，而且突破許多傳統方式的瓶頸和缺點。 / With the development of Internet, traditional GIS was being changed from single user to Web GIS. But the file formats of geographic spatial data are still various. We don’t have a simple and effective standard. The result are financial and manpower resource wasting. It is inconvenient and difficult to integrate geographic spatial data between different GIS and organizations. Traditional maps are bitmapped format, with lower quality at high resulation. We have to use particular tools when modifying bitmaps. Therefore, traditional way in GIS should be improved. 　The Scalable Vector Graphics（SVG） format is a new XML grammer for defining vector-based 2D graphics of the Web and other applications. SVG was created by World Wide Web Consortium（W3C）, the non-profit, industry-wide, open–standards consorium. Over twenty organizations, including Sun Microsystems, Adobe, Apple, IBM, and Kodak, have been involved in defining SVG. SVG is a subset of XML, which is rapidly becoming the foundation for all modern Web applications. SVG gave us a motive to do the investigation. We hope to use the SVG format to solve the problems in GIS. In the result of the prototype system in our thesis, we find out that SVG should be the better, effective spatial data format of Web GIS.