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。

費馬多邊形數定理之延伸探討

本研究旨在對費馬多邊形數定理(任意非負整數皆可表成n個n邊形數的和)進行更進一步的延伸探討,更精確地說,即是:對於給定的二次式an2+bn+c,定義一數列〈an 〉n=-1∞=〈a-1=0,an=an2+bn+c, ∀n≥0〉,而若存在一最小正整數γ,使得對於所有非負整數x,可由數列〈a_n 〉_(n=-1)^∞中取出共γ項,滿足x恰為這γ項之和。這時,我們稱正整數γ為二次式an^2+bn+c的指標值,定義函數Yi使得γ=Yi(an2+bn+c)。 在本研究中,首先先行探討函數Yi的一些基本性質,再藉由電腦以暴力法算出一些二次式指標值的下界,從這些指標值中找出規律,將其推廣至所有我們所討論的二次式,並證明之,至於再探討二次式指標值的上界的部分,我將數學家MelvynB.Nathanson證明費馬多邊形數定理的證明技巧,稍作改寫,使其能夠應用至更為一般的情況,藉此系統性的求得二次式指標值的可能上界。最後,經由不斷的優化上界與下界,即可求得二次式的指標值。

上皮細胞黏著分子(EpCAM)促進大腸癌細胞中對於艾瑞莎(Gefitinib)之抗藥性研究 EpCAM enhances Gefitinib-induced drug resistance in colon cancer cells

上皮生長因子受體 (EGFR) 已被確認在人類上皮惡性腫瘤扮演重要角色,因此臨床上開發出許多針對EGFR之大腸癌、肺癌等的小分子標靶藥物,但治療期間所產生的抗藥性仍是一大瓶頸。 過去上皮細胞黏著分子(EpCAM)只被認為是胞間連接分子,現今則在癌幹細胞 (cancer stem cells,CSCs)等領域被研究。然而從文獻與先前實驗室的試驗,可以看見EpCAM促進癌症抗藥性的可能。 本研究發現在大腸癌中,艾瑞莎 (Gefitinib) 會透過轉錄因子FOXO3a促進細胞凋亡,而EpEX會經由抑制FOXO3a所促進的凋亡路徑,導致癌細胞產生Gefitinib抗藥性,且此抗藥性,也與EpICD下游之誘導性多能幹細胞相關基因 ( iPS-related genes )的表現有關,但其分子機制尚不清楚。 本研究以大腸癌與Gefitinib做為癌症與EGFR小分子藥物的模型,找出EpCAM可能造成的抗藥路徑,未來可應用在各類癌症之聯合治療 (Combination therapy) ,以克服癌症治療所產生的EGFR小分子藥物抗藥性。

A 100% Solar Electric Vehicle: Applying high efficiency solar modules in sustainable transport

As our planet suffers the effects of climate change, it is only a matter of time before society will have to centre all aspects of development around sustainability. In the past, clean solutions for transportation have been dismissed due to the higher cost, and lower efficiency than fossil fuels. However, in the past few decades, there has been a steep decline in solar module cost, and and a steady climb towards higher efficiency. From my findings in this project, I have concluded that we are now at a point where we can embrace the clean, renewable potential which our sun offers. I have created and tested a proof-of concept electric vehicle (Solar EV), which can run indefinitely during daylight hours, provided sunny conditions. There are several mechanical features of my project which highlight the potential that renewable energy in transportation can have. Firstly the vehicle’s 500W motor is powered by 3 100W solar modules, and 3 50W modules, for a total of 450W or power generation. This means that when driving at anything less than 90% throttle, the Solar EV can run continuously without needing to stop to charge or refuel. Another design mechanism installed in the vehicle are three 12V lead acid batteries. These batteries allow the Solar EV to be powered for over 1.5 hours, which is useful during cloudy conditions, night, and most importantly, when driving through areas of shade. A unique efficiency component designed into my vehicle is the linear actuator I installed into the module racking system. This design element allows the tilt of the modules to be altered, to maximize the efficiency of the solar module array. At early or late hours of the day, it can be heavily tilted with the press toggle switch, or kept at a relatively flat level when the sun is the highest in the sky. I ran a series of trials to figure out whether or not the theoretical data matches up with the experimental results. After my series of trials, the bike was yet to run out of power. The solar vehicle reaches speeds up to 32 km/h, however comfortably glides at around 25 km/h. The linear actuator I installed allows the solar modules’ tilt to change . During different times of day or year, the sun is at different heights in the sky, however it is very important to maximize the solar potential. With the press of a switch, the module can be actuated to account for this. Lastly, regenerative braking captures the energy from braking. Using the reversible nature of a DC motor with a specialized motor controller responding to feedback from the brake actuators allows the vehicle to reuse energy that would otherwise be wasted as heat.

運用GAN實現字體風格轉換

本研究以實作字體風格轉換的生成對抗網路模型為動機,將Conditional GAN當作模型的基礎,探討pix2pix模型及其他研究的一些方法對模型會產生甚麼影響,以得出能最優化預測成效的深度學習模型。 首先進行的是前處理的步驟,將字體的truetype檔案轉換成模型輸入的jpeg檔,再以生成器(Generator)和判別器(Discriminator)建立Condional GAN的基礎模型,然後探討加入U-Net、Category Embedding等方法,以及訓練資料集大小對模型造成的影響,最後實作整合的pix2pix模型和CycleGAN模型進行比較。 經過實驗後發現,U-Net和Category Embedding都對模型的預測成果有所幫助。另外,對相似的字體而言,pix2pix的效果較好,而對兩種風格差異較大的字體則需用Category Embedding的方式,融入更多字體進行訓練以達到更好的成效。

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。

Satellite Modeling of Wildfire Susceptibility in California Using Artificial Neural Networking

Wildfires have become increasingly frequent and severe due to global climatic change, demanding improved methodologies for wildfire modeling. Traditionally, wildfire severities are assessed through post-event, in-situ measurements. However, developing a reliable wildfire susceptibility model has been difficult due to failures in accounting for the dynamic components of wildfires (e.g. excessive winds). This study examined the feasibility of employing satellite observation technology in conjunction with artificial neural networking to devise a wildfire susceptibility modeling technique for two regions in California. Timeframes of investigation were July 16 to August 24, 2017, and June 25 to December 8, 2017, for the Detwiler and Salmon August Complex wildfires, respectively. NASA’s MODIS imagery was utilized to compute NDVI (Normalized Difference Vegetation Index), NDWI (Normalized Difference Water Index), land surface temperature, net evapotranspiration, and elevation values. Neural network and linear regression modeling were then conducted between these variables and ∆NBR (Normalized Burn Ratio), a measure of wildfire burn severity. The neural network model generated from the Detwiler wildfire region was subsequently applied to the Salmon August Complex wildfire. Results suggest that a significant degree of variability in ∆NBR can be attributed to variation in the tested environmental factors. Neural networking also proved to be significantly superior in modeling accuracy as compared to the linear regression. Furthermore, the neural network model generated from the Detwiler data predicted ∆NBR for the Salmon August Complex with high accuracy, suggesting that if fires share similar environmental conditions, one fire’s model can be applied to others without the need for localized training.

TCA cycle perturbation induces renal mitochondrial dysfunction and enhanced oxidative stress in diabetic nephropathy-1H NMR-based untargeted metabolomics analysis for potential biomarkers and the effe

本研究藉由基因誘導之第二型糖尿病小鼠(Male B6.BKS-Leprdb mice; db/db mice)做為動物模型,並利用氫質譜儀與代謝體學之平台(1H NMR-based untargeted metabolomics)了解第二型糖尿病所導致的腎病變之疾病進程中的代謝途徑變化,及白胺酸的介入對於疾病進程的影響。研究發現,三羧酸循環及支鍊胺基酸代謝途徑中的代謝物,在基因誘導之第二型糖尿病小鼠尿液中有顯著下降,此發現指出糖尿病腎病變所造成的粒線體能量代謝功能下降。在肝臟組織萃取中,脂化膽固醇(esterified cholesterol)的上升及 β-胡蘿蔔素(β-carotene)、維生素A(vitamin A)及維生素A酸(retinoic acid)的下降顯示肝臟產生脂肪肝及其氧化壓力之上升。白胺酸的介入對於減緩腎臟粒線體受損及降低脂肪肝與氧化壓力並無顯著功效,此現象可歸因於支鍊胺基酸啟動mTORC1代謝途徑。本研究所標定之代謝物可被應用於第二型糖尿病及其所導致之腎病變的生物指標。

電池養魔豆──自製環保電池

本研究在於製造出一顆環保並可回收利用的電池,在顧及環保的同時,也要有更多經濟與日常的考量。 在電解液方面:藉由添加植物肥料中常見的含氮、磷元素之化合物,及金屬離子以產生氧化還原反應來獲得電動勢,如此一來,電池使用完畢後,還能將剩餘的電解液做為肥料來為植物施肥。 在電極方面:在政府教育的推廣下,使用後的乾電池都必須要進行回收以免破壞生態。據此,我們進一步從廢棄乾電池中取出電極部分並作為環保電池的電極運用,如此一來便能使廢棄乾電池重獲新生。 在外殼方面:我們利用可生物分解的甘蔗渣吸管為包覆材質。 我們已自製成功可產生約1.5 V的環保電池,後續將發完電的電池做為肥料並用來使植物茁壯成長,未來若能取代現有乾電池,那麼對於廢棄電池造成的環境汙染,將具有極大的改善效益。

微生物發酵法運用於蚓糞處理與雞場除臭之研究

本研究以不同微生物發酵方式(EM菌(Effective Microerganisms)、枯草桿菌(Bacillus subtilis)、蔡十八菌、木黴菌(Trichoderma))養殖蚯蚓,並固定牛糞、紙污泥與太空包與其他輔料(米糠、蔗渣、果皮、腐葉)成分(原料來自雲林縣工、農業廢棄物),並用本土種的掘穴環爪蚓(Perionyx excavates)分解,以室內分層式堆肥採收蚓糞,再用機械篩選出高純度蚓糞;以雲林縣農作物:小白菜(西螺鎮)、香瓜(二崙鄉)、番茄(口湖鄉)為實驗作物,探討蚓糞當有機肥,作物生長與甜度變化;並將蚓糞與剩料(純度較低)運用於雞場除臭功能,經實驗結果顯示,蚓糞用於農作物與除臭皆有顯著的效果呈現。