本研究首度發現人類肺癌A549細胞會促進其所浸潤的樹突細胞分泌Resistin，而更深入地探究獲悉Resistin會透過活化WHSC1/Twist途徑促進肺癌A549細胞惡化，此惡化過程包括誘導癌細胞上皮間質轉化(epithelial-to-mesenchymal transition; EMT)及提升癌細胞的移行(migration)和入侵(invasion)能力。為確認Resistin在臨床的重要性，透過肺癌病患檢體分析發現，相較於健康捐贈者，肺癌病人的血清可測的較高濃度的Resistin；更甚之，比較非腫瘤組織部位之CD11c+樹突細胞，浸潤於腫瘤組織部位之CD11c+樹突細胞會呈現高量的Resistin。接續探討Resistin對肺癌細胞的影響機制，實驗結果發現Resistin會增加A549細胞表現histone methyltransferase WHSC1的表現，而WHSC1在Twist啟動子的H3組蛋白lysine 36位置進行dimethylation修飾，並降低H3組蛋白lysine 27位置的trimethylation進而促進Twist的表現，促使A549細胞進行EMT和增加癌細胞移行和入侵。因此，Resistin可作為肺癌診斷分子及藥物發展的重要標靶。

Inflammatory Bowel Disease (IBD) is a prevalent disease of the West which pathogenesis is driven by a combination interaction between bacteria and inflammatory cells. In this study, two Kazal domain peptide from Palythoa Caribaeorum were identified. They were found to exhibit serine protease inhibitory, anti-bacterial effects and low toxicity, making them ideal candidates for IBD treatment due to their ability to inhibit inflammatory cell migration and bacterial load. We amplified their coding DNA sequences via PCR and ligated the resulting PCR product into pGEX-4T3 vector. The recombinant plasmid was verified by sequencing, and restriction digest before being transformed into competent E.coli cells. Following transformation, we induced target peptides expression by IPTG to confirmed successful transformation and peptide production. Selected transformed bacterial colonies were expanded in LB broth before mixing with glycerol and frozen in -80°C freezer to complete the process of cell bank production.

Despite the multitude of biomedical scans conducted, there is still relatively low accuracy and standardization of diagnoses from these images. In both the fields of computer science and medicine there is very strong interest in developing personalized treatment policies for patients who have variable responses to treatments. The aim of my research was automatic segmentation of brain MRI scans to better analyze patients with tumors, multiple sclerosis, ALS, or Alzheimer’s. In particular, I aim to use this information, along with novel artificial intelligence algorithms, to find an optimal personalized treatment policy which is a non-deterministic function of the patient specific covariate data that maximizes the expected survival time or clinical outcome. The result of the research was IlluminaMed, a biomedical image analysis toolkit that relies on the development of new artificial neural networks and training algorithms and novel research in fuzzy logic. The networks can detect patterns more complex than humans can identify and create patterns over long periods of time. IlluminaMed was trained by a dataset of professionally and manually segmented MRI scans from several prestigious hospitals and universities. I then developed an algorithmic framework to solve multistage decision problem with a varying number of stages that are subject to censoring in which the “rewards” are expected survival times. In specific, I developed a novel Q-learning algorithm that dynamically adjusts for these parameters. Furthermore, I found finite upper bounds on the generalized error of the treatment paths constructed by this algorithm. I have also shown that when the optimal Q-function is an element of the approximation space, the anticipated survival times for the treatment regime constructed by the algorithm will converge to the optimal treatment path. I demonstrated the performance of the proposed algorithmic framework via simulation studies and through the analysis of chronic depression data and a hypothetical clinical trial. IlluminaMed can automatically segment the scans with 98% accuracy, find tumors with 96% accuracy and approximate their volume within a 2% margin of error. It can also find lesions in MS and ALS, distinguishing them from tumors with 94% accuracy. IlluminaMed can, in addition, determine the tendency of a patient to develop Alzheimer’s several months before patients develop symptoms correlating the brain structure and its fluctuations. Lastly, the censored Q-learning algorithm I developed is more effective than the state of the art clinical decision support systems and is able to operate in environments when many covariate parameters may be unobtainable or censored. IlluminaMed is the only fully automatic biomedical image analysis toolkit and personalized medicine engine. The personalized medicine engine runs at a level that is comparable to the best physicians. It is less computationally complex than similar software and is unique in the fact that it can find new patterns in the brain with possible future diagnoses. IlluminaMed’s implications are not only great in terms of the biomedical field, but also in the field of artificial intelligence with new findings in neural networks and the relationships of fuzzy extensional subsets.

本實驗將小型塑膠圓片置於水中釋放模擬落葉的運動模式，發現圓片與水平之夾角呈現週期性變化，變化範圍會隨著時間改變。在運動幾個週期後，變化範圍會被限制，此時為穩定狀態。在水中加入鋁粉以觀察圓片運動時流場的變化，提出分流模型與最短時間原理，發現此模型可以解釋圓片的轉動機制。

對於轉向次數K→∞且轉向角ɵ為任意角時，各收斂點P於坐標平面上恰形成圓C：。已知U為x軸上任一點且坐標為(u,0)，當ɵ改變時，p1p2與UP之交點S的軌跡為圓錐曲線（點、直線、拋物線、橢圓、雙曲線）。當U=c 時，交點S的軌跡為橢圓，此橢圓的長軸長為圓C半徑（r/1-r2 ），且焦點為P1(1,0)與C(1/1-r2,0)。各轉向點Pn(nÎN)位於一個方程式為，定角為之等角螺線上；同時繪出轉向次數k在不同值時，瓢蟲行進終點之軌跡，以驗證當k愈來愈大時，各終點形成的軌跡會趨近於一個圓。當k=2時，圖形為蚶線並證明其經平移後之極坐標方程式為R=r+2r2cosɵ。最後我們展示行進公比 r→1-，r=1 ， r→1+ 時所呈現的終點軌跡，並對此軌跡所呈現出的意象與自然界連結，而其實質關聯性則有待未來研究。

這份研究是關於一個「數形合一」的問題，研究的主要目的是找出同時具有兩種圖形數身分以上的數。研究結果發現雙重多角數必定存在，但個數可能有限個也可能無限多個，有些雙重中心多角數是有限多個，有些雙重中心多角數是無限多個，但令人意外的是同時是K角數和中心K角數的數卻皆是永遠是無限多個，我對其模式進行了探究並加以具體分類，並說明原因。研究過程中發現遞推關係可以大大簡化計算的步驟，可簡潔快速的求出這些數。我也證明了同時是三、四、五角數的數只有 1。此外，我將研究應用在熱門的平衡數(balancing numbers)和NSW數(NSW numbers)等上面，應用多角數的研究解決一些熱門的問題和找出了圖形上不證自明的結果。

Data and records show accidents caused by loose bolts or nuts often occur in building or mechanical structures all over the world. They may be train derailments, parts falling off amusement rides, escalator breakdowns or wheels coming off automobiles. These incidents can often cause serious casualties and should not be ignored. At present, the only devices used to prevent screws loose are spring washer and nylon locking nuts, but they are not readily detectable with the naked eye when they failed to tighten. Based on simple mechanics and spring principled, our “Smart Washer” has been designed to detect loosen screws. Whenever the bolt or nut gets even slightly loose, the lower part of the washer will spring up, this is a sign to alert and remind the user to carry out maintenance and re-tighten the loosen screw before serious accidents occur.

本實驗主要是透過及程式模擬分析，探討變形之阿特午機 在一般狀況下及過渡期 的運動過 程。透實驗，我們找出不同的初始條件對於運動結果影響 ，如質量比、繩長 等。我們透過實驗和數值分析建構變形之阿特午機的模型 。因為 摩擦力和空氣阻對於運動 的影響皆不可忽略，因此 我們 也設計阿特午機和鉛直圓周運動的 實驗以求出兩個影響因素參數， 並將其結果統整於理論分析中。這份研究有助我們了解力學的過程目前我們 也正在進行更詳細的數值分析， 我們也希望能在之 後將變形之阿特午機的理論與實驗結 果合，預測不同變因的實驗結果。