全國中小學科展

三等獎

多維度空間中隨機漫步回到原點之方法數探討

隨機漫步是數學、物理學、化學、經濟學上常需要涉及和探討的問題,其中探討回到原點的方法數和機率是常見的研究方向。本研究嘗試列出不同維度之間回到原點的方法數遞迴關係,發現不同維度移動相同次數時,回到原點方法數為特定的多項式。 參考了文獻Counting Abelian Squares後,本研究證明了特殊的對應關係,得到了多維空間中回到原點方法數的漸近式。儘管並沒有直接以其他較困難的數學探討方法計算,但依據本研究之結論,已可算出多維度下回到原點之方法數 至於在有限空間中回到原點的方法數,本研究僅完成二維平面下,超出邊界不同次數各種情況的討論,並經由程式檢驗公式的正確性。

全向型風力發電機設計研究

本研究設計十個實驗討論風力發電部件的效率,首先探討垂直型風力發電扇葉(Vertical Axle Wind Turbine, VAWT)結構如何搭配外部全向型導風罩充分利用風能。我們研究全方位來風皆能產生正向力矩的VAWT,並設計出只要有風就可以正轉的VAWT,此外並設計扇葉副翼增強發電效能。並探討如何搭配外部導流板(Guide Vane, GV)裝置加強扇葉轉動以獲致最佳發電效能,我們整合水平和垂直型兩種導風裝置,可以將全向來風(Omni-Directional Wind)皆有效引導至推動VWAT之正向力矩,與用於發電。我們製作的風力發電機體積小效率高能利用各方來風,可將風力發電化整為零達成自主發電的目標,非常適合臺灣都會區風力有限以及建築物密集的環境。

探討組蛋白脫乙醯酶HDAC7對於癌細胞DNA損傷修復機制之影響

DNA損傷導致的基因體不穩定是癌症的共同特徵,而細胞依賴DNA損傷反應 (DDR) 來感知和修復受損的DNA,以維持基因體完整。DDR由DNA損傷傳感信號和修復網絡組成, DDR的活化可阻滯細胞週期並啟動DNA修復,是應對DNA損傷的關鍵步驟。其過程受許多因素調控,包括多種轉譯後修飾如乙醯化、脫乙醯化、小泛素化等。HDAC7是組蛋白脫乙醯酶,該家族成員有多個已被證實參與DDR且在多種癌細胞中常過量表現。最近研究發現HDAC7具小泛素蛋白E3連接酶活性,但相關研究甚少,因此欲探討HDAC7在DDR所扮演的角色。 本研究使用西方墨點法、免疫螢光染色、流式細胞儀分析、細胞存活率測試和細胞群落形成能力實驗,發現以RNAi技術將細胞的HDAC7基因沉默後會降低DNA損傷引起的ATR-Chk1及ATM-Chk2訊號強度,使不能有效率活化檢查點,並對DNA損傷藥物較敏感。由以上結果顯示,HDAC7有潛力做為抗癌藥物研發的新目標。

圓例覺醒

平面上,P點為△ABC內部任意一點,(AP) ⃡、(BP) ⃡、(CP) ⃡分別交△BPC、△CPA、△APB這三個三角形的外接圓於A'、B'、C'。若△ABC為銳角三角形,則¯(PA')/¯PA⋅¯(PB')/¯PB⋅¯(PC')/¯PC≥8,等號成立時若且唯若△ABC為正三角形,此外,並以三角形的三內角來表示P點為費馬點、外心、內心、垂心、重心時的確切比值;接下來推廣至n維空間,當P為任意n維n -單體A_1 A_2...A_(n+1)內任意一點,(A_1 P) ⃡、(A_2 P) ⃡、…、(A_(n+1) P) ⃡分別與n維n -單體P-A_2 A_3...A_(n+1)、P-A_1 A_3...A_(n+1)、…、P-A_1 A_2...A_n的外接n維球交於A_1'、A_2'、…、A_(n+1)',滿足∏_(k=1)^(n+1)▒¯(PA_k')/¯(PA_k )≥n^(n+1),等號成立時若且唯若¯(PA_k')/¯(PA_k )=n,k=1,2,...,n+1,其中n≥2。再藉由任意點的結論,可以應用於直接生成或快速解出許多特殊類型的三角函數不等式。此外,從主要的不等式還可以得到∑_(k=1)^(n+1)▒((A_k P)┴⃑)/(A_k A_k')┴⃑ =1,此時P點為n維空間中任意一點,最後,我們把圓改為圓錐曲線,再進行線段比值的探討。

強菌來襲!口腔大騷動!——食品中乳酸菌對牙齒保健的影響

乳酸菌(Lactic acid bacteria)是生活中常接觸到的菌種,除了製作食品,也有研究指出部分乳酸菌菌株可抑止造成齲齒的「變異鏈球菌」生長,目前已有牙膏等產品號稱添加乳酸菌。但乳酸菌發酵產生的乳酸,會分解牙齒的琺瑯質,所以我們從發酵乳食品中分離出9株乳酸菌,並進行氫氧基磷灰石的分解實驗與對變異鏈球菌的抑菌實驗。經過實驗,1號、5號、6號與8號乳酸菌株對氫氧基磷灰石的分解能力較弱,而6號、8號與15號對變異鏈球菌的抑制效果較明顯,實驗結果交互比較後,得出6號和8號菌作為牙齒保健的應用價值較高。未來若能進一步研究,可嘗試以離心將乳酸菌各部位分離,研究其真正有抑菌作用的物質,並加以純化,應用於保健食品中。

以SPH模擬螺旋星系旋轉軸角及其影響星系碰撞結構之關係探討

星系的碰撞機制屬星系演化中非常重要的過程,目前研究多以星系質量比、速度等變因如何影響碰撞後星系性質為主。而本研究認為星系旋轉軸角也是影響星系碰撞的重要因素之一,故以SPH模擬螺旋星系旋轉軸角度對星系碰撞結果的影響。分別模擬以角度單變因,以及搭配其他參數之多變因情形。 根據模擬結果,發現兩初始星系在直接碰撞(撞擊參數等於零)時,若以碰撞角、初始角差異近似於0度以及180度時搭配高速低值量比進行碰撞,較能形成低核盤比的橢圓星系。間接碰撞時,若旋轉軸貼近速度軸、兩初始旋轉軸夾角小,以及初始盤面平行等情形下,較能形成低核盤比的螺旋星系。 本研究也發現碰撞後星系長軸分佈聚集於0與180度區域,可用來探討橢圓星系軸向問題。最後,本研究以核盤比作為新式星系碰撞分類標準,建立螺旋星系演化機制的參考。

即時步態時空特性偵測的創新設計及其早期失能篩檢應用

預防醫學與健康管理是高齡社會的重要課題,生理或認知能力的退化皆會展現在步態變化上。本研究將利用步態參數的量測分析,以篩檢初期的老化。傳統的步態分析系統多為實驗室評估用,且需專人操作。為了可大量臨床與居家自行使用,本研究開發可攜式系統,搭配助步車硬體,利用(1)力敏電阻做成鞋墊型的足底開關,(2)加裝在鞋上之ToF測距模組,量測左右兩腳跨步的時空參數,並完成即時步態分析。本系統精簡且方便,可攜性佳而且不受環境光源干擾與誤測旁人。穿上鞋子走幾公尺即可得知使用者的步態特性。本研究發現透過受測者「空間不對稱步伐之自動恢復時間對稱」指標,應可用於初期老化篩檢。目前將邀請更多人使用本系統進行即時步態時空特性偵測,收集更多數據建立初老指標,促進預防醫學與優化健康管理。

Laying waste to Energy problems

This research aims at exploiting civil and pre-treated industrial wastewaters that go into the purifier and those that come out of it after various treatments in order to build a galvanic cell with the goal of producing clean electric energy. Our background hypothesis is that it is possible to exploit the existing potential difference between these two types of water to generate electricity. In fact, the water sent for purification contains elements (carbon, nitrogen, sulphur, phosphorus, etc.) in a predominantly "reduced" state and its oxygen level is scarce. On the other hand, the water coming out of the process contains the same elements in a mostly "oxidized" state and it is rich in oxygen. Those chemical discrepancies should get the job done. In order to simulate the two types of water, two different solutions were prepared. The first one is highly concentrated with pollutants and gaseous nitrogen is insufflated in it to reproduce its anoxic environment. The second one’s pollution level is based on the Italian legislative limits of chemical contaminants for superficial waters (Legislative Decree 152/2006) and the semi-cell is insufflated with gaseous oxygen.

蘭陽溪口溼地以及五十二甲溼地水質分析與比較

本研究區域為蘭陽溪口溼地與五十二甲溼地,各選擇5和6個採樣點,檢測水體中的溶氧度、pH值、導電度、總固體溶解量(TDS)、水溫以及濁度並記錄當時氣溫。 在蘭陽溪口溼地中我們發現越靠近出海口,導電度、TDS越高。採樣點4濁度為最高,猜想可能與位置有關。五十二甲溼地中則以採樣點6的導電度、TDS為最高,濁度、pH值及溶氧量則是採樣點3最高。我們還藉由五十二甲濕地分區使用圖,比較人為因素對水質的影響。採樣點3為遊客休憩區,測得的濁度、pH值皆較高,採樣點6為生態區,測值相對較小,推測人為因素與水質有關聯。最後,在10月10日的數據中,發現蘭陽溪口溼地的導電度特別高,推測潮汐現象為可能造成此現象的因素,也是未來研究的方向。

Adversarial Attacks Against Detecting Bot Generated Text

With the introduction of the transformer architecture by Vaswani et al. (2017), contemporary Text Generation Models (TGMs) have shown incredible capabilities in generating neural text that, for humans, is nearly indistinguishable from human text (Radford et al., 2019; Zellers et al., 2019; Keskar et al., 2019). Although TGMs have many potential positive uses in writing, entertainment and software development (Solaiman et al., 2019), there is also a significant threat of these models being misused by malicious actors to generate fake news (Uchendu et al., 2020; Zellers et al., 2019), fake product reviews (Adelani et al., 2020), or extremist content (McGuffie & Newhouse, 2020). TGMs like GPT-2 generate text based on a given prompt, which limits the degree of control over the topic and sentiment of the neural text (Radford et al., 2019). However, other TGMs like GROVER and CTRL allow for greater control of the content and style of generated text, which increases its potential for misuse by malicious actors (Zellers et al., 2019; Keskar et al., 2019). Additionally, many state-of-the-art pre-trained TGMs are available freely online and can be deployed by low-skilled individuals with minimal resources (Solaiman et al., 2019). There is therefore an immediate and substantial need to develop methods that can detect misuse of TGMs on vulnerable platforms like social media or e-commerce websites. Several methods have been explored in detecting neural text. Gehrmann et al. (2019) developed the GLTR tool which highlights distributional differences in GPT-2 generated text and human text, and assists humans in identifying a piece of neural text. The other approach is to formulate the problem as a classification task to distinguish between neural text and human text and train a classifier model (henceforth a ‘detector’). Simple linear classifiers on TF-IDF vectors or topology of attention maps have also achieved moderate performance (Solaiman et al., 2019; Kushnareva et al., 2021). Zellers et al. (2019) propose a detector of GROVER generated text based on a linear classifier on top of the GROVER model and argue that the best TGMs are also the best detectors. However, later results by Uchendu et al. (2020) and Solaiman et al. (2019) show that this claim does not hold true for all TGMs. Consistent through most research thus far is that fine-tuning the BERT or RoBERTa language model for the detection task achieves state-of-the-art performance (Radford et al., 2019; Uchendu et al., 2020; Adelani et al., 2020; Fagni et al., 2021). I will therefore be focussing on attacks against a fine-tuned RoBERTa model. Although extensive research has been conducted on detecting generated text, there is a significant lack of research in adversarial attacks against such detectors (Jawahar et al., 2020). However, the present research that does exist preliminarily suggests that neural text detectors are not robust, meaning that the output can change drastically even for small changes in the text input and thus that these detectors are vulnerable to adversarial attacks (Wolff, 2020). In this paper, I extend on Wolff’s (2020) work on adversarial attacks on neural text detectors by proposing a series of attacks designed to counter detectors as well as an algorithm to optimally select for these attacks without compromising on the fluency of generated text. I do this with reference to a fine-tuned RoBERTa detector and on two datasets: (1) the GPT-2 WebText dataset (Radford et al., 2019) and (2) the Tweepfake dataset (Fagni et al., 2021). Additionally, I experiment with possible defences against these attacks, including (1) using count-based features, (2) stylometric features and (3) adversarial training.