2025年

在這篇作品中，主要研究Repunit數列=在模n之下的餘數數列循環性質。我們探討了Repunit餘數數列在什麼條件下 為純循環週期數列、混循環週期數列和完全純循環週期數列，同時給出了循環週期的公式及上界。接著我們發現一階非齊次線性遞迴數列在模n之下的循環週期與c進制Repunit數列在模 n/gcd(n,c)之下的循環週期相同，並且進一步探討餘數數列在什麼條件下為純循環數列、混循環循環數列和完全純循環數列。

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。

睡眠相關問題常見於現代緊張的社會，傳統睡眠分析方法需要腦電圖（EEG）、肌電圖（EMG）、眼電圖（EOG）等信號，量測複雜度高。本研究透過 Python 程式語言以深度學習和階層式投票機器學習方法，開發一套自動分析程式，僅透過心電圖（ECG）信號分析睡眠階段。並結合睡眠評估標準，製訂一可量化的睡眠品質評估表，提供臨床醫師判讀睡眠品質的指標。本研究的優點是僅透過一種信號便能準確、客觀、快速分析，且操作介面簡易。研究結果顯示，本研究清醒和睡眠狀態之辨識準確率高達約90%，與其他類似睡眠品質評估研究的論文比較，準確率高出10～17%，整體睡眠階段分析準確度高達87%。本研究方法未來可應用於臨床醫療，協助醫師做精準的患者睡眠品質診斷。

克雷伯氏肺炎菌（Klebsiella pneumoniae）近年來於亞洲盛行，其除了傷害健康外，亦對於醫療經濟造成一定程度的影響。隨著時間發展，此細菌也逐漸獲得了抗藥性，使早期使用之抗生素不再有效，因此，尋找治療此疾病的替代療法成為近年來持續被關注的議題。由於其對細菌具高度專一性，噬菌體之莢膜多醣分解酶被認為極具開發抗生素替代療法之潛力。 本研究陸續於污水中分離純化出1212P2、H-P7、H-P8、0505P5、0505P6、05052P5、0505Kp3等噬菌體，並藉由一系列實驗，篩選出可能具有莢膜多醣分解酶的噬菌體。最後將候選噬菌體1212P2、0505Kp3進行全基因定序。 未來，將進行全基因序列分析，若成功比對並找到具有莢膜多醣分解酶潛力之基因，我們將對其加以表現並測試活性。並進一步進行體內試驗檢驗此噬菌體或其莢膜多醣分解酶的效力，探討其是否能作為開發藥物的工具，為對抗克雷伯氏肺炎菌盡一份努力。

An exploration of Pachyrhizus erosus as an option for plant-based milk in the 印尼n market for people with lactose intolerance. With its prevalence in tropical climates, Pachyrhizus erosus is an affordable crop in 印尼. Pachyrhizus erosus is a root vegetable containing a calcium content of 15.6 mg per cup (130g) in its unprocessed form, concentrated in its white flesh. Based on its affordability and calcium content, Pachyrhizus erosus can be transformed into a beverage product with nutritional qualities on par with existing plant-based milk, therefore being a solution for calcium sustenance that is more accessible due to its high capability to be locally grown in 印尼. However, this may be a partial case as Pachyrhizus erosus only thrives in regions with long warm seasons. In this research, three trials of Pachyrhizus erosus-based milk recipe have been conducted Trial 1 consists of a 1:1 ratio of Pachyrhizus erosus to water, Trial 2 consists of a 2:1 ratio of Pachyrhizus erosus to water, and Trial 3 consisting of a 10:10:1 ratio of Pachyrhizus erosus to water, and to a small amount of soybean. Based on the results of 14 organoleptic test respondents, it is concluded that the best ratio of ingredients is 10:10:1 (water: Pachyrhizus erosus: soybean) due to an overall preference of the third trial with this ratio, in terms of taste, aroma, color, and consistency. Pachyrhizus erosus is the dominant ingredient in developing alternate plant-based milk. However, findings from the most preferred trial in the organoleptic test suggest that implementing a minor amount of soybean would stabilize the milk-like consistency and flavor. Pachyrhizus erosus’ ability to retain calcium in its water content has been additionally proven in a calcium test using a reagent solution of ammonium oxalate, as even with the trials’ step of straining the liquid content of Pachyrhizus erosus that had been blended with added water, all three trials tested positive based on the high level of the precipitate. Other tests that tackle the quality of each trial include In Silico Testing, biuret protein test, alcohol test, COB test, and pH level testing.

現今醫療中，黃疸的早期偵測對肝臟疾病的預防與治療至關重要，但多數人難以在症狀輕微時察覺。我們希望藉由智慧手機影像結合機器學習進行黃疸檢測，提升民眾自我監測的能力。Su 等人（2021）曾使用深度學習和機器學習進行黃疸預測，但其方法依賴專業色卡進行色彩校正，成本高且限制應用範圍。本研究提出以白平衡演算法中的白色補丁法與灰界演算法，搭配深度學習模型 DCCNM1和2 取代色卡，提升黃疸檢測的普及性與便利性。經黃疸偵測效果評估顯示，DCCNM2 在無色卡模型中表現最佳，雖然各指標略低於色卡校正，但其展現出優異的穩定性和準確性，證明其作為無色卡黃疸篩檢方案的可行性。本方法將能提供便捷的居家黃疸檢測途徑，尤其對偏鄉地區居民而言，不僅提升早期發現的機會，還能有效減輕醫護人員的負擔，推動大眾健康管理。

背景：預測分子性質如溶解度、毒性及熔沸點對於基礎科學至關重要。然而，實驗測量這些性質耗時且昂貴，因此本研究使用多種機器學習模型藉由調整變相來準確預測熔、沸點。 方法：本研究使用超過一萬筆數據及兩種類型的機器學習方法：淺度與深度學習。淺度學習由 PyCaret實現，並以Mordred作為分子描述器；深度學習使用圖神經網路，包括（CMPNN和GCN），並調整隱藏層參數。 結果：CMPNN在目前嘗試的模型中表現最佳。發現影響沸點預測的關鍵特徵是piPC1，與鍵級相關；熔點則是AATS0d，與σ電子的 Moreau-Broto自相關有關。 結論：CMPNN模型在沸點與熔點預測中均表現最佳。沸點中深度學習模型優於淺度學習模型（p<0.05）。此外，使用SHAP成功找出piPC1和AATS0d對最關鍵。本研究不僅得出了高準確性的模型，還發現了影響分子性質的關鍵特徵，且可擴展至其他預測。

「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。

Wibrazz is a wearable communication tool that allows the teacher, the therapist, the parent to communicate information to the child remotely using the device. Haptic (vibrationbased) feedback is becoming increasingly important in everyday life. A vibrating device that transmits information through clothing can help people with disabilities who have no or limited sensory use to live an integrated life in society without barriers.

An actuator [7,22,28,29] is a motion control mechanism. Depending on the type of actuator, it can convert one type of energy (e.g. chemical, electromagnetic, thermal) into mechanical energy. The field that laid the foundations for the realization of actuators is the field of electromechanics, whose evolution was common with that of actuators. Thus, a periodization of the electromechanics paradigm includes 3 major stages [7,6,25,28,29]: I.1830-1950 Old electromechanics. It is the period when the development of electric cars is significant, which imposed the appearance of classical or primary electromechanical drives. It was a generous nineteenth century, dominated by the scientific results of the triumvirate: Michel Faraday (initiator of fundamental empirical experiments in the history of electricity; the law of induction, of the principle of electric motor, of the magnetic circuit, initiator of electro-chemistry), James Clerk Maxwell, (the genius theorist who put into mathematical form the equations of electric and magnetic fields, as well as the connection between them), and Werner Siemens (engineer and capitalist genius manager who managed to exploit and validate the relationship research-technology-economic development), triumvirate that can be disputed in the sense that other scientists also made outstanding contributions to the history of electricity: Edison, Ampere, Ohm (to name but a few who do not exhaust a significant list). Industrial production of electric machines also appeared and the first signs that will announce the emergence of electromechanical actuators as a basis for military applications. II.1950-1970, Traditional electromechanics, in which electrical power drives appear, a theoretical and experimental development on the emergence of new material and electromechanical principles. Much military research (such as missile control or ship and torpedo control) influences and produces the transfer of applications in ordinary life, including the actuator subfield. III. 1970-2020, Avant-garde electromechanics, representing according to Thomas Kuhn's theory, a paradigm forcing [30]. It is worth noting the contributions of the new scientific revolution. - Specific technologies of miniaturization, by material deposition. - Elastomeric polymeric materials with the help of which it was possible to make electrostrictive actuators, - Very special means of investigation, mainly the development of microscopy, - Gradient of applications in the field of medical engineering, with outstanding contributions both in investigation and microsurgery, applications of actuators in biological micropumps, etc. [25,27,28,29].