全國中小學科展

三等獎

矩形密鋪及其應用

「在格狀平面中用矩形以互不重疊的方式鋪滿(2D rectangle tiling problem)」為一NP-complete問題(Dani`ele Beauquier et al ,1995),目前多項式時間只能求出盡可能覆蓋最大面積的近似解。本研究所創的階梯演算法 stair algorithm 透過改變動態規劃紀錄狀態的方式,使狀態數大幅減少,進而改善求準確解的時間複雜度,也成功證明此演算法的正確性。本研究的演算法可被應用於平行計算中的負載平衡、積體電路設計等方面。隨後,本研究寫了一個互動展示品清楚呈現此演算法的功能。且以階梯演算法成功檢驗並比較 RTILE PROBLEM 的 7/3-approximation algorithm (Krzysztof Lorys and Katarzyna E. Paluch,2000 [4]) 與 11/5-approximation algorithm (Piotr Berman et al,2001[7])進行比較與分析。

語音模型逆向攻擊架構分析與防禦策略探討

本研究中,我們對模型逆向攻擊在語音辨識系統中的影響及風險進行深入分析。隨著Siri、Google Home等智能助理設備在日常生活中的廣泛使用,其語者辨識系統的安全隱患引起了我們的注意。本研究目的在於深入理解模型逆向攻擊的運作機制,並探討其對語音辨識系統的攻擊效果。我們透過實施多樣化的攻擊策略,對不同的模型架構和數據處理方法進行了評估,並對人聲與非人聲的數據集進行了攻擊效果的比較。此外,我們亦實現了基於差分隱私的防禦算法,在多數模型架構下達到接近50%的防禦效果,顯著提高攻擊代價。研究整體揭示了語音辨識系統在面對模型逆向攻擊時的脆弱性,並藉由實驗分析推論出可能的防禦策略,期待能通過策略來增強模型的安全性。

探討手性有機硒催化劑合成與性質

研究指出⼿性有機硫催化劑能催化反應合成出⾼立體選擇性的產物,並有相關的研究指出以同族的硒取代⽽成的催化劑也有類似的性質,我們好奇兩者之間催化能⼒的差異處。本研究探討⼿性有機硒催化劑THSeOBn的合成,並將其應用催化形成氮環丙烷化物及環氧化物以探討其性質。本研究發現相較⼿性有機硫催化劑THTOBn催化,其催化形成氮環丙烷反應的dr 值及反應速率皆有顯著的上升,但其催化形成環氧化物的反應儘管反應速率有上升,但是dr值卻下降。最後本研究提出了關於THSeOBn催化形成氮環丙烷及環氧化物的反應機構。

Development and Comparison of a Small-Scale Toroidal Horizontal-Axis Wind Turbine to a Conventional HAWT Design

Wind energy is one of the most promising and rapidly growing sources of renewable energy, although maximizing its efficiency while minimizing noise remains a challenge and limits its widespread adoption. The emergence of toroidal propellers, which have gained popularity for producing comparable thrust levels to traditional drone propellers while producing less noise, could mitigate this. This study aimed to develop a small-scale toroidal HAWT and compare its power and noise output to a conventional rotor design under similar wind velocity conditions. 15-centimeter diameter models of the toroidal and conventional rotors were created in Fusion 360 and simulated using Ansys Fluent to identify the significant aerodynamic characteristics that positively affect the blades’ power coefficient. The toroidal design with the greatest simulated power output at low tip speed ratios (TSRs) was then 3D printed and physically tested in a wind tunnel against the control rotor. The experimental results confirmed that the toroidal design had greater power coefficients at lower TSRs compared to the control rotor. The toroidal rotor started operating at a wind velocity of 3 m/s compared to the control rotor’s 6 m/s, which indicates superior start-up characteristics. While the toroidal rotor produced half the power output of the control at the highest tested wind speed of 7 m/s, it emitted 18 decibels less noise and showed a reduction in discernible noise between frequencies of two to five kilohertz. The results from this study show its potential in low-noise wind turbines within low-wind velocity environments.

「旋」機妙策—探討颱風與季風互動之螺旋式風場變化

本研究主旨是在探討颱風與季風互動對颱風風場不對稱性變化的影響,分析了2013至2024年9月期間的颱風數據,結果顯示,季風是影響颱風風場形狀的關鍵因素。在東亞特有的季風氣候中,84%的颱風受到季風共伴的影響,我們發現,在季風共伴下,颱風的七級風場會呈現螺旋形,東北季風影響下多呈「6」形,西南季風影響下多呈「9」形,這些形狀可用「等角螺線」來描述,對於季風影響不明顯的颱風,風場形狀則更接近橢圓。我們進一步計算集合重合率以驗證形狀描述的準確性。 此外,本研究將颱風生活史的流型演變分為五類,結果顯示,環境條件相似的颱風,在流型變化上具有相似性。我們還利用颱風氣流場裝置模擬颱風風場,測量風速和風向,深入探討環境風場對颱風不對稱性的影響。

基於LSTM行為與活動力之樂齡關懷系統

本研究開發基於RNN和LSTM的獨居者居家行為監控系統,利用樹莓派、多種無侵入式感測器及鏡頭實現獨居者日常活動的實時監控與情緒評估。系統收集各感應器數據,透過 LSTM 進行學習與預測,並使用隨機森林演算法分析行為狀態,提供客製化數據處理與預測性能優化。 長期數據收集可觀察獨居者的活動力及情緒變化,早期發現健康風險,針對現有求救設備頻繁異常通知的問題,我們開發了能夠識別長期身心狀況變化的監測系統,並整合人體紅外線感應器、都卜勒雷達感應器、日夜感測器等技術,透過Python程式及MQTT進行數據收集與處理。模型訓練使用SQLite資料庫數據,經過多次測試選擇最佳參數以提高預測準確度,隨機 森林演算法也強化決策準確性。 通過長期的數據收集和分析,本系統能夠觀察並預測獨居者的活動力和情緒的變化,早期發現獨居者的身心健康是否有風險。

Utilizing Sparse Optimal Linear Feedback Control to Design Targeted Therapeutic Strategies for Enhancing Gut Microbiome Stability

According to the 2024 American Cancer Risk Survey, one in 24 individuals is at high risk of developing colon cancer. This condition is linked to gut microbiome instability. Consequently, there is a pressing need for a more effective and precise approach to maintaining gut microbiome stability, which this research aims to solve by finding the most crucial bacteria species in maintaining the stability of the gut microbiome through the application of Optimal Linear Feedback Control. Two of its variants being applied in this research are Sparsity Promoting Linear Quadratic Regulator (LQRSP) with a variety range of  (0.05, 44.58, and 49.84) and Linear Quadratic Regulator (LQR) ( = 0) along with other supporting methods; Controllability Gramian and Network Theory (graph analysis). The finding in this research shows that bacteria species Bacteroides hydrogenotrophica, Bacteroides uniformis, Bacteroides vulgaris, Bacteroides thetaiotaomicron, Escherichia lenta, and Dorea formicigenerans have an important role for preventing and medicating a variety of gut-related diseases. This conclusion is reinforced by the analysis conducted using the Controllability Gramian, displaying five of the chosen bacteria with the highest controllability index, which demonstrates that the system can be effectively controlled. This finding suggests a potential for enhancing therapeutic strategies, rendering them more precise and systematic. To gain deeper insights into the relationship between each bacteria and the rationale behind the selection of these bacteria by LQRSP, this study also employs network theory, which successfully elucidates the choice of Bacteroides uniformis despite its low controllability index. Additionally, to further validate the efficacy of these bacteria, the research develops a simulation that compares the controlled system with the uncontrolled system, utilizing two types of disturbances. The results indicate a significant difference in robustness against disturbances between the controlled and uncontrolled systems. The findings from this research can be used as a foundation for a more efficient and systematic intervention strategy findings. By researching gut microbiome composition regulation using a mathematical approach, it opens new opportunities for new method discoveries aiming to increase the health of the gut microbiome which is beneficial for the medical field and prevention of gut related diseases.

The conspiracy mentality: its relationship with absurdity and ostracism

Conspiracy theories are generally perceived as irrational, absurd and as having a negative effect on our reputation. Yet some people do not see them as such. This may lead us to wonder why and how an individual would come to believe or support such statements. In this work, the primary goal is to obtain the level of absurdity of various conspiracy theories so that they can be used in experiments designed to test Williams' “Strategic Absurdity Hypothesis”. In addition, this study attempts to demonstrate the link between conspiracy mentality and feelings of ostracism. In this research, I analyzed a group of 47 participants recruited via social networks in May 2023. The survey collected their demographic information, their conspiracy mentality, their feeling of ostracism, their knowledge of conspiracy theories and their perception of absurdity toward them. The results were analyzed using correlations and linear regressions. The results show a negative correlation between conspiracy mentality and the perception of absurdity for most theories. In other words, the higher a participant's conspiracy mentality, the less absurd the theory is perceived to be. Therefore, hypothesis (I) is partially supported. On the other hand, hypothesis (II), which says that ostracism predicts conspiracy mentality, is not supported by the results. These results are in line with Williams' “Strategic Absurdity Hypothesis” and Sterelny's signaling theory, explaining that an individual, by expressing agreement with a conspiracy theory typically perceived as absurd, damages their reputation in the eyes of others to show that they belong to the group. However, for the theories relating to COVID-19 and climate change, the conspiracy mentality does not predict the vision of absurdity, suggesting that their currentness and media coverage influence whether they are used as signals. The literature does not fully agree with our results and still presents very divergent opinions regarding the links between feelings of ostracism and conspiracy mentality. Indeed, it remains difficult to determine whether conspiracy mentality influences ostracism or vice versa. In conclusion, this study provides new ideas for future research on the origins and impact of the conspiracy theories.

Autonomous Ecosystem Surveillance Vehicle

As of 2021, there are 368 harmful algae blooms and over 6000 invasive species in the United States of America. Furthermore, it is reported that the United States spends more than 11.1 billion dollars per year on clean-up methods for marine debris. However, there currently isn’t a method to monitor aquatic problems simultaneously, autonomously, and efficiently, creating a capability in the aquatic biosecurity sector. To combat this, we have created an autonomous vehicle that can conduct long-term monitoring of freshwater bodies for up to 60 hours.

Revolutionizing Metabolic Health: The Therapeutic Potential of Next-Generation Probiotic Akkermansia Strains (Z62, IR119) for Metabolic Syndromes

The human gut microbiome is integral to digestion, overall health, and metabolic disorder imbalances. Recent advancements in fecal microbiota transplantation (FMT) have highlighted the therapeutic promise of restoring healthy gut microbiota in populations with high incidences of diseases. Focusing on fecal DNA samples from healthy Asian individuals, this study examines the potential of novel Akkermansia strains, specifically Akkermansia muciniphila (Z62) and Akkermansia massiliensis (IR119), as next-generation probiotics for mitigating metabolic syndrome. A key aspect of the study is the investigation of short-chain fatty acids (SCFAs), which are produced and play a crucial role in regulating metabolic processes. SCFAs such as butyrate, acetate, and propionate are essential for energy provision to colon cells and exerting anti-inflammatory effects. The methodology involves selecting two Akkermansia strains, analyzing them through 16S rRNA and WGS, evaluating their growth and survival rates under acidic and bile-salt conditions, alongside their cell adhesion capabilities. The study focuses on the production of key short-chain fatty acids (SCFAs) and tryptophan derivatives by bacteria in regulating metabolic processes, as well as their anti-inflammatory effects on colon cells. Through in vitro assays, both strains exhibited survival in acidic/bile-rich conditions, though Z62 demonstrated superior adhesion to Caco-2 cells, suggesting a higher colonization potential. Metabolomic analysis revealed both strains produce SCFAs, including propionic and acetic acids, and indole metabolites, such as indole-3-propionic acid and indole-3-acetic acid, which are known to influence lipid metabolism and insulin sensitivity. In adipocyte cell models, IR119 significantly reduced lipid accumulation, while Z62 increased lipid presence. Furthermore, IR119 reduced pro-inflammatory cytokine levels, including IL-6 and TNF-α, suggesting potential for inflammation mitigation. The future potential of IR119 as a therapeutic probiotic is extraordinary in addressing complex metabolic and inflammatory diseases, which open new avenues for managing chronic inflammatory conditions like type 2 diabetes and cardiovascular disease. Future clinical trials could refine IR119’s efficacy, positioning it as a leading probiotic in preventive and therapeutic contexts.