Chronic kidney disease (CKD) represents a significant public health challenge, often referred to as a “silent disease” due to its asymptomatic progression during early stages (1–2). Consequently, most diagnoses occur during advanced stages (3 and beyond), where treatment options are more complex and outcomes are less favorable. Globally, CKD affects over 850 million individuals, with 434.3 million cases in Asia alone. Despite its prevalence, early-stage awareness remains alarmingly low, with only 5% of affected individuals aware of their condition. Existing screening methods are predominantly hospital-based, expensive, and time-intensive, limiting their accessibility, particularly in resource-constrained settings. This underscores an urgent need for more accessible and efficient diagnostic tools to enable early intervention. In response to this critical problem, we developed KidneyLifePlus+, an AI-powered platform that leverages advanced machine learning models, including U-net, ResNet-50, and YOLO v8, to analyze retinal images for early CKD detection. These models are integrated to ensure high screening accuracy by identifying subtle biomarkers indicative of CKD progression. Complementing the software, we designed proprietary hardware capable of capturing high-resolution retinal images, delivering performance comparable to hospital-grade equipment. By ensuring affordability and ease of use, the system extends screening capabilities beyond clinical environments, making it suitable for deployment in community healthcare settings. KidneyLifePlus+ addresses key limitations of traditional methods by offering a rapid, cost-effective, and highly accurate diagnostic solution. The platform’s potential to enhance early detection rates could significantly improve clinical outcomes and quality of life for CKD patients. Furthermore, this innovation contributes to global efforts to reduce the burden of CKD by promoting equitable access to diagnostic services, particularly in underserved regions.

The quantum mechanical description of the four fundamental forces of nature is very important for the decryption of the rules which underlie our world. While Quantum Electrodynamics (QED) describes the electromagnetic force in great detail, it also uses complex mathematical techniques and advanced physical concepts. In the following, I will analyze to what extent a quantum mechanical two-state model can be used to describe the Coulomb interaction between two charged particles. To do so, I will exclusively focus on the electrostatic interaction, leaving dynamics aside. Furthermore, the analysis is nonrelativistic and does not consider the spin of the particles. Finally, using discrete state theory allows to explore the strength of the basic concepts of early quantum mechanics. In this sense, I will try to develop a simpli ed model for the quantum mechanical description of the electrostatic force. However, the analysis is not simplistic, since the traditional formalism of quantum mechanics will be used, including Dirac's Bra-ket notation, probability amplitudes, the Hamiltonian matrix as well as the Schrödinger equation. To understand the framework of my project, it may be helpful to take a look at the source of inspiration for my analysis: In Chapter 10 of the third volume of the well-known textbook series The Feynman Lectures on Physics[4], the force holding the hydrogen molecular ion together is explained in terms of a two-state system. The electron of the molecular ion can be either at the rst proton or at the second one. The exchange of the electron between both protons leads to an attractive force between them. It is known from QED that the electrostatic interaction between two charged particles is due to the exchange of a virtual photon which acts as force carrier. The idea of my work is to explore whether the electrostatic force can be described by a very similar model, replacing the electron acting as force carrier in the molecular ion by a virtual photon for the description of the electrostatic force between two charged particles. To describe a system consisting of charged particles, I will make the assumption that a charged particle can appear in two states. Either it is in state e where it can emit a photon or it is in state a which enables it to absorb a photon. Upon emission or absorption of a photon the charged particle transitions to the respective other state. This makes the approach analyzed in my work an element of discrete state theory, since two di erent states of the particle are used to store information about it. Of course such a model cannot be compared to the sophisticated theory of Quantum Electrodynamics. The point is, however, that it is interesting to explore the power of the most fundamental concepts of quantum mechanics and to show that such an analysis can lead to inspiring results.

工業環境中揮發性有機化合物(VOCs)的洩漏不僅危害人體健康，更可能導致工安事故。現有氣體感測器常存在選擇性低、反應時間長等限制。本研究開發高選擇性與快速反應的奈米材料導電式氣體感測器，以實現即時監測。 研究中合成並測試六種銀奈米 (Ag-MPC)材料：Ag@C6、Ag@C12、Ag@C16、Ag@MCP、Ag@C12/MCP及Ag@C12/MBT複合材料。在500-5000 ppm濃度範圍內偵測1-丁醇、正辛烷及間二甲苯等目標氣體的電阻變化。實驗結果顯示，Ag@C12經官能基修飾後，對1-丁醇具有明顯的選擇性。我們開發基於Arduino微控制器的即時監測系統，透過運算放大器電路實現高精度的電阻變化檢測。可以在工業環境中持續監測VOCs濃度並即時示警。未來將著重於優化訊號放大電路、開發新型官能基修飾材料、實現複雜氣體混合物的組分分析。開發成本低、反應快、選擇性好的感測系統，為工業安全監測領域提供實際應用價值。

The equation of an ellipse and quadratic residues are well-known concepts in elementary geometry and number theory, respectively. While the properties of ellipse equations in Euclidean space have been extensively studied, many characteristics of quadratic residues, such as consecutive quadratic residues, have also been explored in past research. In this study, we discovered the characteristic polynomial of the equation of an ellipse over finite fields Fp, a single-variable polynomial that shares the same roots as the ellipse. Furthermore, by examining the parallels between the equation of an ellipse and the pairs of residues and nonresidues, we derived a characteristic polynomial for this concept and demonstrated its connection to the Catalan number, a significant sequence in combinatorics. This research was conducted through the following steps. First, the power sums of the roots of the ellipse in Fp were calculated using the Legendre symbol and Euler’s criterion. Next, the characteristic polynomial of the ellipse was determined using Newton’s identity, generating functions, and Vieta’s theorem. Finally, leveraging the equivalence between the equation of the ellipse and the pairs of residues and nonresidues, we established the main results connecting these two concepts with Catalan numbers.

光柵作為常見的分光元件，應用於許多光學儀器中。然而，傳統光柵彈性較差且硬度較高，限制了其應用範圍。本研究利用具有高彈性和易形變特性的 PDMS 作為柔性光柵的材料，對不同厚度和彎曲程度的光柵進行一系列測試。為了探討厚度和彎曲曲率對繞射效果的影響，進行了不同厚度柔性光柵的繞射點分析實驗。實驗結果顯示，增加柔性光柵的厚度會提升其彎曲時第一亮紋的變化率；相反，減少厚度則會降低該變化率。隨後的研究進一步探討不同施力方式是否會影響柔性光柵的分光效果。通過拉伸和壓縮光柵，發現拉伸會使光柵的軌距變大，而壓縮則會使軌距變小。此外，研究還探討了利用 PDMS 複製類似光柵的結構是否具有分光效果。實驗結果顯示，複製的指紋確實展現了類似特性，期望未來能夠將這些特性實際應用於相關領域。

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。

Road safety remains a global concern, with driver-related factors like distraction, drowsiness, and medical conditions such as stroke being leading causes of accidents. In this paper, we propose a real-time ensemble learning framework that leverages transfer learning for the detection of stroke, drowsiness, and distracted driving. Our model integrates multiple Convolutional Neural Networks (CNNs) fine-tuned for each specific task, and employs a stacking method to combine the predictions of these models using a meta-classifier. Notably, the model is optimized to enhance stroke detection, minimizing false negatives— an essential aspect for timely medical intervention. Experimental evaluations on diverse datasets demonstrate the efficacy of our approach, achieving an overall accuracy of 92.5%. The results emphasize the model’s potential for real-time driver monitoring, offering critical safety features that could reduce accidents and save lives.

本研究探討在一場圓桌會議中，n人逐一亂序入場找尋各自對應的名牌編號(1~n號)入座，其中1號第一個入場並坐到了k號位，此後入場的人們若發現與自己編號相同的位置是空的，就直接入座；若與自己編號相同的位置被占走了，就以逆時針方向尋找空位入座。在上述的規則下，若共有n 人，且 1 號坐到 k號位的情況，給予與問題相關統計量的組合證明。後續本研究將規則改為1 ~ p號 按照順序進場且皆想坐到 k 號位的前提下，探討了坐錯的人們是怎麼樣的循環和坐錯人數的次數分佈。並多數的研究結果皆與 stirling numbers of the first kind 有相關。 本研究還 探討了共有 n 人，且 1 號坐到 k號位的情況下， 坐錯人數的標準差函數的遞增情況 與對數函數完全曲線相關。

植物進化成陸生植物的過程中，氣孔和角質層是關鍵特徵。氣孔由保衛細胞調控，負責二氧化碳進入和水分蒸發；角質層則保護植物免受水分流失及環境壓力。調控這些特徵的基因尚不明確。本研究利用全基因組關聯分析（GWAS）探討阿拉伯芥的角質層和氣孔發育。GWAS結果顯示，與角質層厚度相關的基因位於第二條染色體，而與二氧化碳吸收效率相關的基因位於第五條染色體。氣孔導度和水分吸收效率的調控基因可能在第一、三、四條染色體上。角質層變薄時，氣孔密度下降，導致氣孔導度和水分蒸散率上升；而當角質層通透性增加到一定程度時，二氧化碳固定效率達飽和。此外，透過反向遺傳學篩選候選基因，研究特定基因對角質層合成及光合作用效率的影響。突變株分析顯示，抑制控制角質層或氣孔的基因會促進另一性狀的表現，未來可進一步探討自然族群中相關基因的功能。

抗癌藥物的研究一直受到重視，吲哚(indole)衍生物可助抵擋自由基，而二吲哚(Di-indole)衍生物已成為抗癌劑。鈣離子/鈣調蛋白依賴性蛋白激酶 (Ca2+/calmodulin-dependent protein kinase II，CaMKII)之抑制劑為癌症標靶藥物重要研究方向之一，抑制CaMKII可降低各種癌細胞增殖和存活，但目前尚無CaMKII抑制劑藥物。本研究以三吲哚為主架構，發展衍生物作為CaMKII抑制劑，期望可應用於抗癌劑。電腦軟體Discovery Studio2016模擬各種三吲哚衍生物分子模型與CaMKII α(PDB: 2VZ6)之結合能，選出結合能較大之化合物3，並延伸結構/活性(SAR)最佳化，進行一系列高效率藥物合成純化工作。經由送測生物細胞活性，其中先導化合物(lead compound) 3-1對癌細胞之毒性高且對CaMKIIα的抑制效果佳，符合癌症治療上的需求，將繼續最佳化此結構，並進行細胞訊號傳送途徑及動物實驗。

本作品由2023年IMO的第五題出發，希望探索在忍者通道中的其他性質，首先思考改變每排中放入的球數並觀察規律，進而推廣到三維圓圈塔中的性質，最後使用hyper-cube(超立方體)的情況進行一般化的推廣與構造的優化，完成最小值問題的求解，另外也對於特例部分探索解的總數。

本研究設計與合成一系列的電子供體分子，以研究分子單體的化學結構對於所形成的激發複合體光物理性質的影響。 五個所設計的供體分子已被成功的合成並確定均具有分子內電子轉移的性質 其躍遷偶級距變化分布範圍在17.6-28.6D之間。 將此五個供體分子分別與兩種電子受體分子在溶液聚集在一起，利用在長波長處所新生的螢光發光，推測激發複合體的形成。研究的成果並顯示，具有類似三角形結構的供體分子將更容易形成激發複合體，而具有棒狀結構的分子則較不易形成之。此成果有效的提供有關於單體分子結構的設計對於所需激發複合體光物理性質的影響，形成可快速地提供各式不同發光波長的材料，將可作為在發光二極體發光層材料、螢光感測器、生物成像等領域需求時的分子設計藍圖與指引。