一些Moire patterns 的數學性質研究
Moire 為法文，其英譯為watered， 是古代織布技術的一種應用；將印有規律條?的透明薄片重疊時，稍微移動或轉動其中的一片，會形成極大的圖形變化，稱為moire pattern本作品針對三個moire pattern 的數學式加以推導：(一)、兩張透明片各印有等間隔平行線，轉動其中一片使兩線的夾角θ，亮紋垂直距離和暗?垂直距離的比值為tanθ/2tanθ 。(二)、兩張透明片各印有輻射線，重疊後行成圓系，可由代數或幾何加以證明，利用三角函數可推導出此圓系方程式為：x2+{y-rtan[π/2-(θ-?)]}2)]}={rsec[π/2-(θ-?)]}2)]}\r \r (三)、透明片A 印有等間隔平行線，B 印有符合高斯曲線的平行線，AB 重疊時，形成一系列的高斯曲線，AB 的夾角減少時，會增大曲線的曲率，我們進一步討論曲線的曲率和平行線斜率的關係。Moire is the French word “watered” and refers to an ancient technique employed in cloth making. The moire occurs whenever two or more transparent sheets with periodic strips on them are superposed. The characteristic of moire patterns is the fact that a slight shift of sheets will create dramatic alternations in the observed patterns. In the present report, We derive the equations of three different moire patterns. First of all, take a sheet with equal spaced straight lines and placed it on top of another identical sheet. They are made to intersect and form an angle of θ. As the angle changes slightly, it produces huge changes in the spacing of moire fringes. We can derive a formula related to the interfringe distance. The ratio of bright fringes and dark fringes is tanθ/2tanθ.Secondly, two transparent sheets with radial lines on them are overlapped, forming a pattern similar to the lines of force between point charges. We can find that the pattern is a series of circle by means of algebraic and geometric proofs. And proven by trigonometric functions, we canconclude that they satisfy the equation :x2+{y-rtan[π/2-(θ-?)]}2)]}={rsec[π/2-(θ-?)]}2)]}\r Thirdly, a set of lines of equal spacing is overlapped with a second set of lines whose spacing are derived from a Gaussian curve. A series of Gaussian curves is reproduced in a moire pattern. Reducing the angle of intersection between the two figures steepen the curvature. We discussed the relation between the curvature and the slope of inclined lines.
聚球藻 RF 一 1 品系生物時鐘之特性
我們成功的用溶氣計偵測到了聚球藻 RF-1 在 28℃下光合作用的概日韻律。和傳統的研究方法比起來，這個方法具有連續偵測的優點，減少因不斷取樣所造成的影響，此實驗可觀察到聚球藻 RF-1 溶氣量之變化圖與一般藻類（如單殼縫藻）不同.在光 /暗條件下 RF-1 之溶氣量的增加與減少均呈週期性變化，而且此變化現象在進入連續照光後仍然可以維持兩個循環以上，這些結果顯示以溶氣計連續偵測聚球藻 RF -1之概日韻律是可行的，而且所得到的變化圖形遠比傳統方法（於不同時間取樣）所得者自然。本實驗同時發現含聚球藻之培養液的溫度，在進入黑暗週期時會有明顯的上升，由於其變化程度比其他藻類明顯，如加以探討應有助於對此藻以及其韻律特性之瞭解。We successfully detected the photosynthesis circadian rhythm of the prokaryote Synechococcus RF-1 under 28℃ by a DO (Dissolved-Oxygen) meter. The advantage of this method, comparing with the traditional methods, is that it can detect signals continuously, reduce the influence of discrete sampling. The DO curves of the Synechococcus RF-1 are different from that of other algae. Under Light/Dark conditions, the DO values of RF-i increased and decreased periodically. The periodic phenomena progressed over two cycles under constant lighting conditions. These results revealed the feasibility of using DO meter to continuous detect the circadian rhythm of the Synechococcus RF-1 The detected DO curves looked more natural than those obtained in the traditional discrete-sampling method. We also found that the temperature of the culture increased in dark cycle. Since the variation is clearer than that of other algae, further investigation will benefit the understanding of the Synechcoccus RF-i and its circadian rhythm.
影像的色偏校正
The human eyes can adjust automatically the color of object under different illuminants. But digital camera does not have such mechanism, must join the white balance to simulate the color constancy of human eyes. There are many existing white balance methods. They can be categorized into two types. The first type utilizes the widespread assumption on the dealing natural scenery, which has the advantage of simplicity. Another type explores knowledge of the semantic content, which has the advantage of accuracy. In this study we modify and enhance the widespread assumption methods that can adopt the advantage of the simplicity and accuracy. Our proposed method is structured in two main parts: a color cast detector and a color cast remover. The detector first analyzes the color distribution of the image with simple statistical tools to determine whether or not the image has color cast. The remover, a modified and enhanced version of the widespread assumption methods ( gray world and max RGB ), is then applied on the color cast image. From the experiment results, it demonstrates the efficacy and performance of the proposed method.人類的視覺能夠自動修正因光線變化而改變的物體顏色，但是數位取像設備的感光元件卻不具有這樣的功能，必須加入白平衡的功能，才可模擬人眼維持色彩恆常的特性。現有的白平衡演算法可分為兩大類型，第一類型為廣泛假設型，具有運算速度快、與取像設備無關的特性，但是平均誤差會較大；另一類型為預知特性型，其特徵為準確性較高，但是運算較速度較慢、建立色彩特性資訊時所需的成本較高，本篇研究針對廣泛假設型的演算法做些修正與增強，使其具有較小的平均誤差以獲得較佳色彩品質的影像。我們將影像的色偏校正分為色偏偵測與色偏移除等兩個階段來進行，由於僅有被偵測出有色偏的影像才需要進行色偏的移除，所以可以避開將無色偏或固有色偏的影像做錯誤的修正，由實驗的結果看來，我們的方法確實有效，除了具有運算速度快、與取像設備無關的優點外，其色偏校正能力也較現有的方法好，使得影像色彩更能與人眼所見相近。
Molecular and Cellular Responses under Hypoxic Stress among Rice Cultivars with Different Flooding T
全球暖化造成水災頻繁，嚴重威脅植物生存。看似耐淹水的水稻，在完全淹水下亦有其生存危機。水稻FR13A 因耐水性極佳而常用於分子育種，IR64 產量高卻不耐水。是那些特質使稻種間有不同耐水機制？我們觀察其幼苗淹水24 小時後生長情形、通氣組織 (aerenchyma) 變化及應用即時反轉錄聚合?鏈反應 (real time RT-PCR)，研究酒精醱酵的主要蛋白質：乙醇脫氫? (alcohol dehydrogenase, ADH1, 2) 及丙酮酸脫羧? (pyruvate decarboxylase, PDC2) 基因之表現量。兩種水稻的胚鞘及根都因淹水減緩生長，以FR13A 減緩最明顯。通氣組織在淹水期間都有增加，FR13A 中的形成近似於對照組，IR64 則明顯較差。FR13A 中ADH1 及ADH2 在淹水一小時後迅速增加60 至100 倍，IR64 僅增加10 至20 倍。PDC2 在IR64 中表現量的增加幅度較大，但最大值仍小於FR13A 之基礎表現量。由此可知，FR13A 在完全淹水時成長減緩而原有通氣組織則持續生長，且酒精醱酵中的基因有獨特誘導反應，因此耐水性較佳。藉由此研究揭開水稻細胞及分子生物學上的耐水反應策略，將可更精準地改良稻作使其對抗淹水逆境，解決未來因環境造成的糧食危機。Global warming increases the frequency of flooding, which drastically reduces the growth and survival of plants. Although rice (Oryza sativa) appears well-adapted to flooding of roots as it is often farmed in paddies, problems arise when the whole plant is submerged in water. I am interested in the structural and molecular responses that result in different submergence tolerances in rice cultivars. Indica rice FR13A is submergence-tolerant and frequently used in molecular breeding for this trait, while IR64 is a high-yield but submergence-intolerant cultivar. In this study, I monitored the growth rate, aerenchyma formation, and gene expressions of the carbohydrate metabolism in FR13A and IR64 seedlings subjected to submergence for 24 hours, by means of real time RT-PCR and microarray. FR13A had prominently inhibited coleoptile growth and sustained levels of aerenchyma formation whereas IR64 did not. The mRNA levels of alcohol dehydrogenase 1 (ADH1) in FR13A was induced prominently, while ADH2 was induced in IR64 during early hours of submergence. The induction of pyruvate decarboxylase 2 in FR13A was stronger than IR64. The expression of sucrose synthase was similar in both strains. Expressions of the genes involved in anaerobic carbohydrate metabolism were also studied by analyses of microarray data. My findings demonstrate that elongation quiescence, persistent aerenchyma formation and shifts in anaerobic carbohydrate metabolism gene expressions are beneficial strategies of FR13A towards submergence. Through elucidating the molecular basis of coordinating submergence tolerance genes as this study provided, it will be possible to discover multiple traits associated; hence crop improvement for flooding tolerance could be achieved.
台灣和東亞地區的氣候變遷
由人類活動造成的溫室效應可能導致地球溫度升高,聖嬰現象加劇等現象與災害,本文利用個氣候中心發展出的模式,推估台灣和東亞地區未來氣候變遷的情況,我們發現當大氣中的二氧化碳濃度增加為現在的1.9倍時,台灣地區的年平均溫度將升高0.85-2.50度C而東亞地區將會升高1.46-4.07度C,在同條件下個模式的平均推估量也顯示,台灣地區將每天增加0.10公厘的降水，而東亞地區每天將增加0.08公哩,我們希望這個研究結果可以做為其他相關研究的基礎,使大家提早因應未來氣候變遷所可能引發的種種變化;Greenhouse effect, incurred mainly by human activities may result in lots of phenomenon and damages such as the increasing of the world's average temperature and he aggravation f the "ElNino" effect. In this research, we simulate future metrological values by employing several simulation modes developed by different climate centers and predict future climate changes in Taiwan and East Asia area. We found that when the concentration of carbon dioxide exceeds 1.9 times than current value, the estimated range of the increased year-average temperature are0.85-2.5℃ and 1.46-4.07℃ for Taiwan and East Asia, respectively. Under the same condition, the ensemble mean reveals that the precipitation raises will be 0.1 and 0.08mm per day, for Taiwan and East Asia respectively. We hope our work can be the foundation of other related researches, and all the researches together can help for coping with possible damages caused by future climate changes.