全國中小學科展

2019年

以狀態有向圖探討跳躍數列方法數

本篇研究針對跳躍進行數列本身意義的探討,用新的數列V表示跳躍數列的接球狀況,接著利用狀態有向圖定義出表示跳躍數列球在空中狀況的「頂點」以及表示跳躍數列內數值的「邊」,而迴圈狀況即為跳躍數列的情況下我們利用鄰接矩陣的想法進行探討,並且最後利用跡數的方式進行跳躍數列形式的討論。不同於文獻中僅針對用球數b和跳躍數列字串長度n做為討論,本篇研究增加了代表著跳躍數列中數值可達到的最大數值s(也代表著表示跳躍數列球在空中狀況的「頂點」長度),針對用球數為1顆的情況下為k階盧卡斯數的數值,而在其他用球數也有好的結果,並且針對不同情況下的跳躍數列整理出遞迴關係式以及生成函數。最後,在本篇研究中也找到許多在OEIS上所沒有的數列,並且給予這些數列有不同的解釋。

旋轉方塊路橋問題之探討

本研究為一迷宮遊戲和旋轉方塊所組合成的問題。在給定行列數的可旋轉方塊上,置入「路」和「橋」,指定起點,並透過方塊的旋轉改變路徑,探討所有可能到達的終點以及抵達各終點的最短路線數。 此研究中,首先透過問題簡化和圖形討論,發現旋轉方塊以迴圈和無法繞行的路線(構造S)交錯形成,得到所有可能的終點位置。接著,整理所有簡化圖形的規律,利用加法原理推算出最短路線數。透過找出圖形對稱特性,得到不同終點之最短路徑數的關係。而後將不同規格的旋轉方塊的最短路線數關係,以遞迴關係式表示,並且找出其生成函數,希望透過生成函數得到最短路徑數的一般式。研究時,我們不僅發現不同規格之最短路線數生成函數的關係,從而能探討每一規格的最短路線數。更進一步發現無論方塊行數取至極限時或方塊行列數相同時,其最短路徑數的數列與卡特蘭數列(the Catalan numbers)有關。

眼位變變變-蝌蚪變態前後眼睛型態轉變之研究

兩棲類是一群可以在水域及陸域棲息生活的動物,幼體期蝌蚪生活在水中,具尾巴可四處游動,多數為濾食或刮食,但變態後的成體青蛙主要生活在陸地,吐出長舌捕食會動的生物。因此蝌蚪變態前後不僅生存環境大為改變,攝食行為也從被動取食轉為主動攻擊,所以推測牠們在變態過程中,眼睛位置會有所變化,形成更大的雙眼(立體)視覺區,適應變態前後的劇烈改變。本研究運用向量幾何作圖方式,將頭部眼睛位置座標數值化後,分析不同蝌蚪變態前後眼睛位置與雙眼視覺的變化情形,試著找出變化趨勢與棲地、行為或演化之間的關聯性。結果發現不同眼睛類型的蝌蚪在變態過程中,眼睛位置會有不同的轉變過程,但變態之後,眼睛皆會往頭部兩側移動,眼睛至吻端的距離變短,導致雙眼視覺區變大,更具立體視覺,可精準判斷獵物位置。此外也發現蝌蚪視野範圍主要受水層高低影響,高水層蝌蚪眼睛位於頭兩側,低水層蝌蚪眼睛則生長在背部。成蛙視野範圍影響因素有棲地、行為及親緣關係,棲地分析結果顯示會在水陸兩邊活動的成蛙視野範圍最大。水棲型的福建大頭蛙具有強領域行為,陸棲性黑眶蟾蜍具瞄準捕食行為,故雙眼視覺都較大。同屬於樹蛙科的蛙類雙眼視覺大小的影響因素主要與為活動高度有關,樹棲型樹蛙因需在樹林活動,演化出較大的雙眼視覺,以利判斷空間位置。艾氏、王氏與碧眼樹蛙等親緣關係接近的姊妹種因生殖行為類似,蝌蚪與成蛙都演化出具有相似的眼睛型態。

水稻根表鐵膜對植體營養元素吸收的影響

鐵是植物生長的必要營養元素之一,土壤中的鐵含量雖然不低,但受限於含鐵礦物的溶解度使得鐵的有效性低,植物對鐵的吸收因此受限,進而影響人類的鐵攝取量並造成相關的健康問題。欲提高植物對鐵的利用效率,必須先了解植物對其吸收之相關機制,主要關鍵之一為植物根如何改變根圈環境以控制鐵吸收的有效性。 本研究以水稻為對象,探討水稻不同根部泌氧能力,對水稻根部鐵膜組成、鐵吸收效率,及其對其他營養元素吸收的影響。我們藉由遺傳篩選方法,選殖出較不易生成鐵膜之突變株(#878),透過比較野生型與突變株 (#878)水稻生理性狀之差異,發現通氣組織的生成為控制根系泌氧的影響因子;此泌氧能力會使根系周圍的鐵氧化,並於根表形成一層含有鐵氧化物的沉澱 (即鐵膜);而鐵膜的生成會影響水稻營養元素的吸收,其中鐵膜對陽離子型態的營養元素有較好吸持效果。

從「圓」「點」出發—過定點的圓內接多邊形之研究

此研究在探討「給定一圓及多個已知點,求作各邊或其延長線上恰含有前述已知點中之一點的圓內接多邊形」之作圖方法及圖形的性質。 研究當中,以反演的幾何變換結合代數方程式並透過遞迴關係,除了找到該問題之解的個數與條件外,並求得有唯一解之點的軌跡方程式,從中發現其軌跡圖形為一圓錐曲線,且隨著給定點在圓外個數的奇偶性,會有或為橢圓或為雙曲線之不同的圖形變化。同時也發現給定點本身使得滿足條件的圓內接多邊形存在之個數將決定該軌跡圖形與給定圓間之切點個數等的有趣性質。

Improving Communication for the Visually Impaired Through an Innovative Arabic Writing System

Visual impairment is a major global health problem. In 2017, WHO estimated that there were 253 million people worldwide with this ailment. According to the journal of the American Medical association, the prevalence of visual impairment in the Saudi population is 9.3%. Learning Braille by families of students with visual impairments remains a major obstacle, which precipitates several communication issues. Moreover, difficulties for the students themselves lie in learning braille with languages that include diacritical marks; consequently, affecting their academic progress. My main objective of this project is to help improving life quality of these individuals, and the focus is to advance their social productivity and adaptation. This was accomplished through creating a new simpler Arabic writing system using geometrical shapes. As a part of this project, fifteen participants with visual impairments were interviewed and tried this new writing system; two of them are adults between 25 and 40 years old while the rest are students from 9 to 17 years old. Additionally, 100 participants with visual impairments completed a survey. The data showed that students learned this system in two hours in comparison with students that mastered braille in a few months. This shows that this system is easier to learn and subsequently saves time and effort. The most important value added to this project is that diacritical marks were combined with the alphabet, thereby considerably reducing book sizes compared to Braille-written books. This project presents a novel system that helps people with visual impairments to increase their confidence and independence.

Improving Spinal Fusions: Redesigning the Pedicle Probe to Prevent Vertebral Breaches

Pedicle probes are medical devices used by surgeons during spinal fusions for patients with conditions such as scoliosis and spinal fractures. The probe creates pilot holes to guide the placement of pedicle screws in vertebrae. The screws are then connected with a metal rod to stabilize the spine. Twenty-nine percent of patients who undergo spinal fusions suffer from vertebral breaches – accidental damage to the spinal cord – which cause complications such as infection, motor defects, and in many cases paralysis. My goal was to make spinal fusions safer by redesigning the pedicle probe to provide surgeons with instantaneous feedback on the probe’s location, enabling them to more accurately place pedicle screws. The pedicle probe I developed takes advantage of the difference in density between the inner cancellous (spongy) bone and the outer cortical (compact) bone found in vertebrae. Cortical bone is avoided by monitoring the cannulation force – the force required to insert the probe. When the probe contacts denser cortical tissue, it warns the user by providing tactile and visual feedback through a vibration motor and an LED. This enables the surgeon to redirect the probe and advance down the optimum path, preventing a possible breach. It proved successful in preventing breaches on lamb vertebrae, which closely resemble human vertebrae. This novel device improves feedback to the surgeon and eliminates the need for costly and potentially harmful ionizing radiation exposure. Furthermore, it does not depend on, or require, any preoperative imaging. The cost of manufacturing the improved probe is less than $42 USD (NT$1297). Results of patent searches for 加拿大, the 美國, and Europe suggest that the redesigned probe is unique in predicting and preventing breaches in spinal fusions based on predetermined force threshold values. The probe is also unique in enabling personalized procedures in spinal fusions for those with complications, through calibrating a control (force) limit based on tissue samples prior to the procedure. Enhancing a surgeon’s ability to determine an appropriate path for pedicle screws through a sensor-enabled probe has the potential to significantly reduce the incidence of vertebral breaches during spinal fusion surgery.

藉由雙硫化物交聯製成的植物核酸奈米粒子可當作穀胱甘肽誘發的抗癌藥物載體

由於人工合成的化學材料在包覆藥物進行人體醫療測試時,不可分解性會帶來體內累積的毒性,搜尋各類化合物的結構後,發現核酸上的含氮鹼基具有一級胺結構,可和天然交聯劑京尼平或DTSSP進行反應,因此,本研究抽取水果的核酸進行實驗,利用界面活性劑乳化的過程中將阿黴素(DOX),包覆進入交聯後的核酸水膠,穿透式顯微鏡的結果顯示交聯後的水膠結構是球狀,平均粒徑大約是120奈米,核酸本身帶負電,水膠有包覆藥物的界面電位稍微減少負電,利用人類正常肺上皮細胞進行水膠共同培養,2毫克/毫升的水膠溶液在連續培養48小時後,並不會造成細胞死亡,奈米水膠在pH值5.5釋放DOX的量比pH值7.4還要高出27%,有奈米水膠包覆DOX的情況下,更能有效率進入癌細胞內與引起癌細胞毒性,本水果核酸製成的奈米水膠在生物體可分解的無毒包覆材料上,於未來可提供一個新的藥物載體參考。

Convert pixel image into paths saves in XYZ format to use in CNC machines using innovative algorithms.

CNC machines use vector graphics or vector image programs that take time and effort on hobbyists. Therefore, it is important to provide accurate techniques for converting ordinary images available on the Internet or can be designed with easy programs. In order to have precise drill paths read by CNC machines directly and produce a product that does not contain rattles at the edges. This depends on the accuracy of processing the extracted paths. The development of algorithms has been completed Transforms Pixel image into Paths with XYZ extension, which is used to drill material and cut it through CNC machines. And the algorithms are based on transfer images with low quality. And Its Advantage that it can create high Paths with as few points as possible. The program can convert the pixel image into paths, and then converted into g-code, and use it in CNC machines directly.

BA-ADA based ROS-responsive nanoparticles for selective drug delivery in cancer cells

Current medical intervention in cancer therapeutic methods has shown risks and side effects with normal tissues. This includes incomplete cancer eradication. In reference to numerous studies and literature reviews, a stimuli-responsive drug delivery system is selected as an innovative, safe and more assured treatment due to its site-specific release ability. This allows specific intervention upon the given stimulus which response to the presenting disease symptoms. Hence, we designed a ROS(Reactive Oxygen Species)-responsive BA-ADA(4-Hydroxyphenylboronic acid pinacol ester and 1-Adamantanecarboxylic acid bonded molecule) nanoparticle delivery system. In our study, ROS-responsive nanoparticle was designed and prepared based on a synthetic molecule from BA and ADA. A therapeutic payload, Doxorubicin, can be loaded into the nanoparticles and it can be selectively released within cancerous tissues whereby ROS level is over-expressed. This will enhance both therapeutic efficiency and reduce side effects. The stability and ROS-responsiveness of the particle were proven in a series of evidence-based experiments. The results showed a significant difference in cell viability during the experiments with healthy and cancerous cell samples. Further research will be required to extend the experiment in vivo.