2021年

前作「建構邊長為整數的圓內接多邊形」[2]中，我建構了多類兩種相異整數邊長的圓內接多邊形的一般式。本研究利用n倍角公式，建構三種以上相異整數邊長且外接圓半徑與所有對角線長均為整數的圓內接多邊形。 我依正整數的分割數將圓內接多邊形分類。除了正多邊形之外，6類圓內接五邊形、10類圓內接六邊形、14類圓內接七邊形。取畢氏三元數做變數變換，做出所有類型相異且有不同邊長的圓內接多邊形。另外在建構圓內接八邊形、九邊形與十邊形時，我考慮建構邊長相異且其中一邊為外接圓直徑的圓內接四邊形、圓內接五邊形與圓內接六邊形...等，將上述圖形做適當的伸縮與組合，即可以建構邊長皆為相異的整數的圓內接n邊形。研究過程也發現可用同一組一般式可建構不同的圓內接多邊形。最後推得各類非等邊長且外接圓半徑亦為整數的圓內接多邊形皆可尺規作圖。

In 2016, the population of people over the age of 65 in Macau was 11.2%. This means that Macau has already become an aging society. As such, more younger generations are needed to look after the elderly. According to statistics, falls are the primary cause of injury or death for the elderly over 65 years old. About 30% of the elderly over 65 years old fall every year. Along with the increase in the elderly population, it is urgent to find a fast and effective way to ensure the safety of the elderly. As there is a lot more danger besides falling in an elderly life, we aim to build a robot collocated with its danger detection system to ensure the safety of the elderly at home. The reason we decided to use robots is that we want to have larger flexibility and mobility, for example, we can give elderly rescue materials when they need help. Moreover, more home robots will be used in the future, they can just apply our system to theirs and ensure the safety of elderlies. In this research, we mainly used cameras with the Openpose model to detect dangers such as falling, potential human action danger, and environmental danger. Innovative ways are used to detect fall action, collocated with our home robot, it is a foreseeing project that could ensure the safety of the elderly in a home environment.

Research Question or Engineering Problem A stroke continues to be the most important medical and social problem of the modern world. Stroke is a type of acute cerebrovascular accident (ACVA) and is characterised by a sudden (within minutes, less often - hours) appearance of focal neurological symptoms (motor, speech, sensory, coordinating, visual and other disorders) and / or general brain disorders (depression of consciousness, headache, vomiting, etc.) that persist for more than 24 hours or lead to death of the patient in a short period of time due to a cause of cerebrovascular origin. There are two clinical and pathogenetic forms of stroke: ishemic stroke (cerebral infarction) is caused by acute focal cerebral ischemia, leading to infarction (zone of ischemic necrosis) of the brain; hemorrhagic stroke (non-traumatic intracerebral hemorrhage) is caused by rupture of an intracerebral vessel and blood penetration into the brain parenchyma or rupture of an arterial aneurysm with subarachnoid hemorrhage (SAH). ACVA also includes transient disorders of cerebral circulation, characterised by the sudden occurrence of focal neurological symptoms that develop in a patient with cardiovascular disease (arterial hypertension, atherosclerosis, atrial fibrillation, vasculitis, etc.), last for several minutes, less often hours, but no more than 24 hours, and ends with a full restoration of the impaired brain functions. Transient disorders of cerebral circulation include: transient ischemic attack (TIA), which develops as a result of short-term local cerebral ischemia and is characterised by sudden transient neurological disorders with focal symptoms; hypertensive cerebral emergency, which is a condition associated with an acute (usually significant) rise in blood pressure (BP) and accompanied by the appearance of general cerebral (less often focal) neurological symptoms secondary to hypertension. The most severe form of hypertensive crisis is acute hypertensive encephalopathy, the basis of pathogenesis of which is cerebral edema. Cerebral infarction generally is the result of the interaction of many etiopathogenetic factors, which can be subdivided into local and systemic ones. Local factors include: morphological changes in the brachiocephalic or intracerebral arteries (pathological tortuosity, etc.), atherosclerotic lesions of the vessels of the aortic arch and cerebral arteries, cardiac lesions as a source of thromboembolic cerebral infarctions, fibromuscular dysplasias of the walls of the brachiocephalic and cerebral arteries, brachiocephalic artery dissection, vasculitis (arteritis), changes in the cervical spine with the formation of extravasal compression of the vertebral arteries, anomalies in the structure of the vessels of the neck and brain (hypoplasia of the vertebral artery, trifurcation of the internal carotid artery), etc. Systemic factors include: disorders of central and cerebral hemodynamics (a sharp change in BP or a decrease in cardiac output, etc.), hereditary and acquired coagulopathies, polycythemia, certain forms of leukemia, hypovolemia, psychoemotional stress / distress, etc., hypercoagulative / hyperaggregatory side effects of a number of medications (oral contraceptives, etc.). In the 俄羅斯n Federation, more than 500 thousand people have a stroke every year. About 25,000 new cases of stroke occur in St. Petersburg every year. The incidence of stroke in the 俄羅斯n Federation is 3.48 ± 0.21 cases per 1000 people. The incidence of various types of ACVA varies widely, in particular, cerebral infarctions account for 65–75%, hemorrhages (including subarachnoid hemorrhages) – 15–20%, transient cerebral circulation disorders account for 10–15%. The frequency of cerebral strokes in the population over 50–55 years old increases by 1.8–2 times in each subsequent decade of life. Medical and socio-economic consequences of ACVA are very significant, in particular, death in the acute period of stroke occurs in 34.6% cases, during the first year after the end of the acute period in 13.4% cases; severe disability with the need for constant care is present in 20.0% of stroke patients; 56.0% have limited working capacity and only 8.0% return to their previous work activity. Disability due to stroke (the national average is 56–81%) in our country ranks first among all causes of primary disability, amounting to 3.2 per 10 thousand people. Stroke mortality among working-age population has increased in the 俄羅斯n Federation by more than 30% over the past 10 years. The annual death rate from stroke in our country is 175 per 100 thousand people. Stroke annually becomes the main cause of disability: 85% of victims experience a decrease in strength or a complete lack of ability to control the muscles of half of the body and only half of them recover limb functions partially or completely; the rest of those who have suffered a stroke remain paralysed and require care, since they are not able to completely independent existence. In this regard, recently, in the process of rehabilitation, the technology of brain-computer interfaces (BCI) has begun to be actively used. on the basis of this technology exercise machines are created. These exercise machines are controlled directly by the patient himself. This feature of the technology increases the effect of the procedure by providing a direct connection between the patient's desire and effort with the work of the simulator. The greatest development of this technology is observed in the field of medicine, where BCIs are used as a means of communication or as one of the tools of neurorehabilitation. In this regard, it seems very promising to develop the most optimal brain-computer interfaces. The goal of our project was to create an automated training complex in the form of a neuro-controlled glove with tactile feedback, designed to simplify access to rehabilitation means.

在實體店鋪進行限時搶購活動 (Flash Sale)，近年來已逐步在世界各地快速散播。在這樣的閃購活動期間，商場往往會宣傳銷售商品的巨幅折扣，吸引消費者。消費者在閃購的活動期間，爭先恐後的進入商場，過程中，除了可能造成消費者的傷害外，亦有可能造成商品本身的損傷。 本研究發想自第六屆數學建模挑戰賽之國際賽題。首先，本研究分析了商品損壞的各種方式。第二，本研究用虛擬的商品列表，與一個虛擬的商場平面配置圖作為規劃範例。第三，繪製並配對完貨架與商品後，運用賽題中的專家評分、剩餘數量等數據，寫出了每個商品的平均歡迎指數。第四，建立數學函式，計算路徑風險值，並藉由定量分析預測，成功地判斷哪一個以及哪一些商品的受歡迎程度會較高。最後，提出了優化於賽題給予的平面配置圖方式。

本研究試圖找出一些策略，以了解在mxn的格狀街道中，最少應該放入幾個吸螞蟻的裝置，便保證能抓到所有螞蟻。這問題等價於在圖G(m,n)中，最少應放入幾個紅點後，便能使G中的所有環都能碰到至少一個紅點。更等價於在圖G(m,n)中，最少應扣除幾個點後，便可形成一森林。 我們將這些點數記作k(m,n)。特別地，當m=n時記作k(n) 。本文推得：k(m,n)≧[mn+1/3]，並將等號成立時的k(m,n) 稱為完美的。經過構造後發現k(2n)、k(3,n)、 k(3n,m)、k(2+6m,2+6n),k(4+6m,4+6n) , 亦為完美的，並且將k(m,n)壓到只剩兩種可能。也得知了在無限擴張的格子圖中被移除點的密度為1/3。

Tissue engineering has developed novel therapies such as many types of wound dressings, bio-pads, scaffolds and bandages, in order to reduce the effects of deep and extensive skin wounds. Here, we have produced an electrospun nanofiber scaffold, based on biodegradable materials such as gelatin (as a natural and hydrophilic polymer) and cellulose diacetate (with optimal biodegradability), in order to increase wound healing using nanotechnology. We also used green tea extract for its anti-oxidant and anti-bacterial effect, to improve the biological properties of the scaffold. In the fabrication process, two polymer solutions: 1. Gelatin (with acetic acid solvent) and 2. Cellulose Diacetate (with acetone solvent) mixed with green tea extract, were prepared. Then they were spun using a two-nozzle electrospinner to produce a hybrid nanofiber scaffold. SEM images showed enough finesse and uniformity of the produced scaffold to simulate the extracellular matrix. Further, measuring the contact angle of water droplet and the web surface, indicated optimal hydrophilicity of the nanofiber scaffold, which controls the level of scaffold degradability and cell adhesion. Also, the results of antibacterial tests for two bacterial strains (E. coli and S. aureus) showed the antibacterial characteristics of the extract-containing scaffold. In addition to previous tests, evaluation of fibroblast morphology on the nanofiber scaffolds, indicated appropriate cell adhesion and expansion, that confirms the biocompatibility of this produced scaffold.

Revealing fascinating and educating concepts in a field of astronomy usually requires expensive equipment. Therefore, most schools have very little practical equipment to teach astronomy. I wanted to investigate the Sun’s track using a simple apparatus that can be afforded by many schools instead of using an expensive one.

強化學習為當前AI領域的熱門話題，其特點是在環境的獎勵與懲罰下，進行學習。強化學習雖然較為困難，但其成功的項目都非常有名，其中最著名的例子有: AlphoGo、AlphaZero等等。 深度強化學習(DRL)是深度學習與強化學習的結合體，本專題透過DRL實現近端優化策略演算法，來使BipedalWalker環境中的二足模型學會行走，並調適超參數與神經網路來讓模型訓練擁有更好的結果。 經過實驗後發現，適當的降低獎勵折扣衰減率能有效的提升學習速度以及學習上限，同時可以避免分數落差過大導致的Dead relu問題。最終的結果能讓平均分數達到302分，成功達成了BipedalWalker環境要求(平均分數>=300分)。 為了使智能體擁有更好的探索能力，本專題加入了ICM(Intrinsic Curiosity Module)，成功提升了最終的平均分數至316分，將不摔倒的機率提升至99%，最高分數則到了320分，使得雙足模型能以更快的速度向前移動並保持穩定。

正常細胞的 C-terminal tensin-like (CTEN) 蛋白質位於細胞質且含量低，但研究發現 CTEN 在大腸癌細胞中會大量表現並累積於細胞核內，進而提升癌細胞遷移與侵襲的能力；而 Wnt 訊息傳遞路徑在癌細胞中常有過度活化的現象。因此本研究主要探討 CTEN 於細胞核內的累積和 Wnt 訊息傳遞路徑的互動關係，進而調控細胞癌化的機制。分析 CTEN 分布有差異之細胞株的轉錄體發現，在較多 CTEN 累積於細胞核的大腸癌細胞株中，其 Wnt6、Wnt11 兩基因的表現量上升，研究指出 Wnt6、Wnt11 皆會影響大腸癌細胞的遷移與侵襲。另外，CTEN 會與 Wnt 訊息傳遞路徑中的 β-catenin 結合，因此本實驗利用啟動子帶有 Wnt 訊息下游轉錄因子結合位的質體，測定其下游 β-catenin/TCF/LEF 轉錄因子的轉錄活性。結果顯示 CTEN 累積於細胞核中會提高 β-catenin/TCF/LEF 之轉錄活性，進而增加 Wnt6、Wnt11 等下游基因的表現量，影響大腸癌細胞的遷移與侵襲。

It is known that copper foil undergoes a color change in heating by oxide thin layer formation. Therefore, we focused on the color change by the oxidation of brass foil. Brass foil (Akaguchi (Cu87%Zn13% alloy) and Aoguchi (Cu85%Zn15% alloy)) also undergoes color change by oxidation, and it shows heating time and temperature dependence. Brass foil need longer heating time to appear color change than copper foil, and we can visually confirm that the brass has corrosion resistant. In addition, color change of brass foil depends on the percentage of copper in the brass, and Aoguchi shows rapidly color change in same heating condition. We show that brass has different physical properties than copper, even with a high percentage of copper in brass, and this was verified through comparison using diffusion length and RGB data in Aoguchi and Akaguchi. We demonstrate these colored brass foils are used as art materials, and our results expanded material using possibility of brass foil.