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。

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.

Optimization of honey production by monitoring the behavior of bees based on studying their sounds

This is a first approach in the development of beekeeping and the preserving of bees, a crucial and important species in the balance of ecology on our planet. This project consists in designing and building a small affordable device that will help beekeepers keep an eye on their hives and prevent theft whenever and wherever they are by providing them with instant and continuous data and information about their beehive status through a mobile application. This IOT approach will rely on many physical variables especially the sound frequency of the bee buzz, which appears to be a way for the bees to communicate with each other in special circumstances. That is why; we aimed to analyze the sound frequencies of the bee buzz to detect beehive behavioral changes. Many other factors are also important for the keeping of a healthy beehive such us temperature, humidity, weight and fly activity. And as for security measures we are going to add a GPS tracker to the system to keep track of the hives and alert the beekeeper if there is any kind of danger. The development of this real time beehive monitoring system will not only help the beekeeper keep track of his hive and collect useful data but also increase the honey production and avoid many colony losses and thus preserve the bees and ensure their well-being.

以分子動力學模擬探討有機分子影響胰島類澱粉蛋白(IAPP)的聚集行為

近年來的研究指出:第二型糖尿病病徵與胰島類澱粉蛋白(islet amyloid polypeptide,簡稱IAPP)之聚集有關。如欲探討IAPP聚集機制以治療病症,需經多樣、多元的實驗條件進行試驗,這無疑是件耗時、耗費資源的大工程!本研究是以電腦軟體進行理論計算分析,採用分子動力學模擬系統,探討不同種類或官能基的有機分子對於IAPP作用之影響,再進一步觀察分子動態、統計系統能量,歸納出分子間的交互作用,釐清可能影響實驗結果的重要變因,期能達到提昇實驗設計、減少耗材浪費的綠色化學願景。本研究結果發現:在純水或稀薄食鹽水中,IAPP構形皆傾向摺疊結構;且具較高極性基團或易產生立障效應的有機分子會拉伸IAPP結構,使其分子間相互靠近聚集,形成β-sheet纖維;具較低極性基團的有機分子,易進入IAPP turn內,破壞引發聚集現象的疏水核心,進而抑制IAPP分子的積聚。

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.

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。

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。

DEVELOPMENT OF PAPER-BASED ORIGAMI BIOSENSOR PLATFORMS FOR COLORIMETRIC DETECTION OF BIOCONTAMINANTS

Infectious diseases caused by bacteria from biological pollutants pose a great burden in terms of diagnosis and treatment, and millions of people worldwide die from bacterial infections. Detection of bacteria plays a critical role in clinical diagnosis and control of contamination, but is not accessible due to the high cost, complex devices and equipment required. In the project, an alternative to existing methods, a paper-based biosensor for the detection of model organism E. coli bacteria, which is visible, low cost, easy to use, can be integrated with a smartphone, is based on rapid color change in the exposed environments, drinking and pool water, wastewater, beverage products. platforms were developed. For the specific detection of E.coli bacteria, two different biosensors have been developed that can perform colorimetric detection in a user-friendly origami design, minimizing microchip and processing steps based on antibody-bound PVDF membrane and filter paper-based immunological method. In the presence and absence of target bacteria E.coli, the lowest detection limit of the biosensors obtained by using paper-based platforms that create a distinctive color on them, depending on the concentration, was 0.9x103 bacteria/ml for origami biosensor, 2.7x103 bacteria/ml for microchip biosensor and the widest dynamic linear operating range was calculated as 103-107 bacteria/ml. With the biosensor platforms we have developed, the use of only one smartphone for both qualitative and quantitative, visible results and analysis within minutes constitutes the originality of our project. With these promising results, the biosensors we have developed can also be used for the detection of different biological pollutants, do not contain complex devices and can be easily produced in large scales. We believe that the biosensors we have developed for the detection of biological pollutants in water and beverages, especially in regions where test laboratory infrastructure is not available, will contribute to the literature, public health, health economy and sustainable development goals such as clean water and sanitation, health and quality life, and life in water.

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。

Forming Polygons with Broken Pick-up Chocolate Bars and Spaghetti Noodles

”The broken pick-up sticks problem” is proposed by T. Kyle Petersen and Bridget Eileen Tenner in 2020. We solve the problem by considering the discrete version using random variables, and the limit behaviour of the discrete version gives us a combinatorial solution to the original problem. We also evaluate the probabilities of the triangles formed by the broken/pick-up sticks satisfying some specific geometric conditions with various techniques, including calculus and elementary number theory.