本研究由布拉美古塔定理(Brahmagupta theory)的圓內接四邊形的布拉美古塔線，找出二種具有內切圓性質的新衍生四邊形，此特定條件下的圓內接四邊形，會呈現是等腰梯形結構。將特定條件下的圓內接四邊形推廣至特定圓內接五、六、七、八、……、等n邊形中，可發現在多組正交對角線條件下，這些特定圓內接n邊形間具有遞迴關係數量的內切圓，其半徑之間、各自的圓面積與原外接圓面積都有特殊的比例關係。上述衍生多邊形的頂點、內切圓圓心、原圓內接多邊形的對角線與其交點，這些元素間也具有多點共圓的性質。

我們利用遞迴式求n個不同球放入k個相同箱子的方法數，得到形如巴斯卡三角的數值表，並發現在遞迴關係裡求得的數與落階乘多項式的係數恰好相同。 接著我們將形如巴斯卡三角的數值表轉換成矩陣表示，求出其反方陣，此反方陣竟然是Stirling numbers of the first kind；再將反方陣中的元素取絕對值得Stirling numbers of the second kind；Stirling numbers of the second kind表中的第n列第x行的元素，竟是將n個人分成x圈的方法數。 接著我們找出: Stirling numbers of the first kind與調和級數的關係式、Stirling numbers of the second kind與Pmn的關係式、Stirling numbers of the second kind與Cmn的關係式及Stirling numbers of the second kind與Hmn的關係式，並利用數學歸納法與gamma函數證明上述關係式；並尋找到響鈴數字與n個不同球放入k個相同箱子的方法數的連結。

We are conducting research for the purpose of treating contaminated water generated by the nuclear accident with C.moliniferum. In previous research, the school seniors examined whether there is a difference in absorption by changing the wavelength of the LED to establish efficient Sr2+ absorption conditions. As a result, the red wavelength was found to be effective for the efficient Sr2+ absorption of C. moniliferum. Therefore, in this study, in order to verify how much Sr is actually absorbed into the cell, the amount of Sr absorption using an atomic absorption photometer is quantified, and the previous research has shown that red is effective for the efficient Sr2+ absorption. The wavelength was considered to be effective because of photosynthesis, and was observed with a scanning electron microscope (SEM) using the photosynthesis inhibitor (DCMU). As a result, it was clarified that C. moniliferum absorbs Sr intracellularly, and photosynthesis was related to absorption.

Cancer is responsible for an estimated 9.6 million deaths in 2018. Deaths from cancer worldwide are projected to reach over 13 million in 2030. Thus, developing a device that has the capability to solve today’s toughest global challenge is crucial by utilizing a simple yet robust approach - “SEEING THE UNSEEABLE” through bold innovation. Although removing cancer is much more effective than either radiation or chemotherapy, when unseen residual cancer cells remain, they could grow back into tumour overtime. The reoccurrence of cancer contributes to a greater risk of death. Hence, launching a system that is able to distinguish between the cancerous cell and normal cell is ultimately essential to make sure no cancer is left behind during surgery. This robust optical system is established with quantitative approach by exploring the integration of an algorithm into the developed software. The end result of this device has the capability to provide users an accurate numerical pH value. The developed system is integrated with the smart IoT gateway capability whereby this powerful analytical device is incorporated with the real-time monitoring, data transformation and data analyzer. Harnessing the power of technology lets us fight cancer better. Each time a pathologist analyzes tissue after operation, it can take up 2 to 3 days because the tissue has to be frozen, thinly sliced, and stained so it can be viewed under the microscope during the process of biopsy. Thus, it is crucial to invent this Surgeons’ VisionMetric device which has an IoT-based microcontroller that is capable of providing real-time numerical value on-site.

This report includes the design and prototyping of a portable automatic bag-valve mask (BVM), or commonly known as the Ambu bag. This development is for use in emergency transport, resource-poor environments, and mass casualty cases like the COVID-19 pandemic. This device replaces the need for human operators whose job is to squeeze the BVMs for extended periods of time. The prototype is made from a stainless-steel skeleton, measuring 470 x 240 x 230 mm, with the addition of acrylic coverings. A repurposed motor from a car is used to drive the squeezing arm. The speed of the arm for inspiration and expiration along with the pausing time between each breath can be adjusted with this prototype. It also features an LCD screen to display the arm speed, along with real-time pressure graph displayed on both phones and computer monitors. For future versions, an app is to be developed to enable the control of the automatic bag-valve mask from phones and tablets, further creating ease for users and increasing portability. Additionally, important requirements will be added: alarm system for over pressurization, control for inspiration to expiration ratio, number of breaths per minute, control for tidal volume, pressure relief valve, and assist-control mode. The cost of this prototype is approximately $430. With this design of an automatic BVM, it allows for the production of a ventilator-like technology that will be able to perform main functions of basic ventilators at a fraction of the current cost.

In all experiments for detection of WIMP dark matter, it is essential to develop a classifier that can distinguish potential WIMP events from background radiation. Most often, clas- sifiers are developed manually, via physical modeling and empirical optimization. This is problematic for two reasons: it takes a great deal of time and effort away from developing the experiment, and the resulting classifiers often perform suboptimally (which means that a greater amount of expensive run time is required to obtain a confident experimental result). Machine learning has the potential to automate this and accelerate experimentation, and also to detect patterns that humans cannot. However, two major challenges, which are shared among several dark matter experiments, stand in the way: impure calibration data, which hinders training of models, and unpredictable physical dynamics within the detector itself. My objective was to develop a set of machine learning techniques that address these two problems, and thus more efficiently generate highly accurate classifiers. I was able to obtain raw data for two dark matter experiments which exhibit these challenges: the PICO-60 bubble chamber [2], and the DEAP-3600 liquid argon scintillator [1]. For each experiment, I developed and compared three general-purpose algorithms intended to resolve its inherent challenge (impurity and unpredictable dynamics, respectively). In PICO-60, background alpha and WIMP-like neutron calibration datasets are used for training; however, there is an impurity of 10% alphas in the neutron set. While a conventional classifier was developed (and is believed to be 100% accurate), machine learning in the form of a supervised neural network (NN) has also been previously explored, because of the benefits of automation. Unfortunately, it achieved a mean accuracy of only 80.2% – not usable as a practical replacement for conventional methods in future iterations of the experiment. In DEAP-3600, photons are absorbed by a wavelength shifting medium and re-emitted in an unpredictable direction, before being detected by one of 255 photomultiplier tubes (PMTs) around the spherical detector. The randomness severely limits the accuracy of conventional classifiers; in a simulation, the best so far removes 99.6% of alpha background, while also (undesirably) removing 91.0% of WIMP events. Because of physical limitations, simulated data is used for calibration, with 30 real-world experimental events available for testing. I have written a research paper [11] about my work on PICO-60, which has been approved by the PICO collaboration and pre-published at https://arxiv.org/abs/1811.11308. It is currently undergoing peer review for publication in Computer Physics Communications. All PICO researchers are listed on my paper for their work on the original PICO-60 experi- ment. They did not contribute to this study; I completed and documented it independently.

尿酸氧化酶參與嘌呤代謝，然人類尿酸氧化酶基因已退化，易使過量尿酸沉積於關節造成痛風，近年來微生物源尿酸氧化酶之酵素工程改良，逐漸被應用於尿酸檢測與降解藥物，因此具極高研發價值。 本研究針對微生物源尿酸氧化酶進行基因體探勘，篩選出抗輻射奇異球菌(Deinococcus radiodurans)及耐熱雙球桿菌(Thermobispora bispora)源尿酸氧化酶基因，以蛋白質異源表現與金屬螯合層析法純化取得重組尿酸氧化酶，進行酵素動力學、熱穩定分析、結構解析、金屬離子耐受性分析與尿酸檢測應用。在最佳反應條件下，抗輻射奇異球菌源酵素於30 ℃之Km與Kcat為679.03 μM, 30.33 s-1；耐熱雙球桿菌源酵素於70 ℃之Km與Kcat為191.31 μM, 12.85 s-1。此外，我們已解析耐熱雙球桿菌源尿酸氧化酶結構，發現其羧基端之特異性構型可能與熱穩定性有關。本研究以此兩種尿酸氧化酶為酵素工程改良標的，盼未來能研發作為快速篩檢與臨床治療之生物替代藥物。

The main goal of this study was to address a variety of topics concerning the role of the Ih current in HCN channels of SHANK Wild-Type and Knock-Out Thalamus Neurons (as described further below). This research explored the cellular effects of sedation (like Dexmedetomidine) and laser light stimulations on the Ih current of neurons, as well as discovering novel biomarkers for detecting Autism Spectrum Disorder. This study also showed that methods (like utilizing laser therapy with and without various photosensitizers) have the potential in raising depressed Ih currents of SHANK Knock-Out neurons.

This research project focuses on developing a web-based multi-platform solution for augmenting prognostic strategies to diagnose breast cancer (BC), from a variety of different tests, including histology, mammography, cytopathology, and fine-needle aspiration cytology, all in an automated fashion. The respective application utilizes tensor-based data representations and deep learning architectural algorithms, to produce optimized models for the prediction of novel instances against each of these medical tests. This system has been designed in a way that all of its computation can be integrated seamlessly into a clinical setting, without posing any disruption to a clinician’s productivity or workflow, but rather an enhancement of their capabilities. This software can make the diagnostic process automated, standardized, faster, and even more accurate than current benchmarks achieved by both pathologists, and radiologists, which makes it invaluable from a clinical standpoint to make well-informed diagnostic decisions with nominal resources.

Sustainable mobility concepts are playing an increasingly important part in today's social developments. As a promising mode of future transportation, quadcopters play a special role, and their further development and optimization is being advanced along many disciplines. Even in my hometown of Zurich this trend has not passed by without leaving its marks. Since 2019, the Swiss National Postal Service has been testing autonomous means of transport together with the Zurich University Hospital as part of a pilot project. However, quadcopters are not exclusively used for transportation purposes. Geologists use them for landscape modeling and the insurance industry utilizes them for damage assessment. Quadcopters have also become an integral part of photography and agriculture, where they are used for pest control, for example [2]. I first became intensively involved with quadcopters in 2017, when I received a hobby model for my birthday in the form of the Mavic Pro from the Chinese company Da-Jiang Innovations Science and Technology Co., Ltd (DJI). In October of the same year, I completed an internship in the biofluid mechanics department of the Institute for ImplantTechnology and Biomaterials e.V., where I studied the aerodynamics of airfoils. With my Mavic Pro in my backpack, I had the idea to develop and prototype my own functional rotor for my quadcopter as part of my upcoming Swiss Matura thesis paper. The rotor would be considered functional if it generates enough lift to keep the quadcopter hovering. The focus of this project was the investigation of aerodynamic properties. The influence of other factors, such as the material used, was not the primary focus of the work and therefore not investigated in detail.

Colorants are used in many industries, especially in the textile industry. These substances both cause visual pollution and create an anaerobic environment for aquatic creatures. In this study, it is aimed to examine the usability of activated carbon synthesized from waste polyethylene terephthalate (PET) bottles, which is an important environmental problem, in removing the pollution caused by the colorants caused by industrial activities in water resources.

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.