2019年

本研究為一迷宮遊戲和旋轉方塊所組合成的問題。在給定行列數的可旋轉方塊上，置入「路」和「橋」，指定起點，並透過方塊的旋轉改變路徑，探討所有可能到達的終點以及抵達各終點的最短路線數。 此研究中，首先透過問題簡化和圖形討論，發現旋轉方塊以迴圈和無法繞行的路線（構造S）交錯形成，得到所有可能的終點位置。接著，整理所有簡化圖形的規律，利用加法原理推算出最短路線數。透過找出圖形對稱特性，得到不同終點之最短路徑數的關係。而後將不同規格的旋轉方塊的最短路線數關係，以遞迴關係式表示，並且找出其生成函數，希望透過生成函數得到最短路徑數的一般式。研究時，我們不僅發現不同規格之最短路線數生成函數的關係，從而能探討每一規格的最短路線數。更進一步發現無論方塊行數取至極限時或方塊行列數相同時，其最短路徑數的數列與卡特蘭數列（the Catalan numbers）有關。

本研究旨在對費馬多邊形數定理(任意非負整數皆可表成n個n邊形數的和)進行更進一步的延伸探討，更精確地說，即是：對於給定的二次式an2+bn+c，定義一數列〈an 〉n=-1∞=〈a-1=0,an=an2+bn+c, ∀n≥0〉，而若存在一最小正整數γ，使得對於所有非負整數x，可由數列〈a_n 〉_(n=-1)^∞中取出共γ項，滿足x恰為這γ項之和。這時，我們稱正整數γ為二次式an^2+bn+c的指標值，定義函數Yi使得γ=Yi(an2+bn+c)。 在本研究中，首先先行探討函數Yi的一些基本性質，再藉由電腦以暴力法算出一些二次式指標值的下界，從這些指標值中找出規律，將其推廣至所有我們所討論的二次式，並證明之，至於再探討二次式指標值的上界的部分，我將數學家MelvynB.Nathanson證明費馬多邊形數定理的證明技巧，稍作改寫，使其能夠應用至更為一般的情況，藉此系統性的求得二次式指標值的可能上界。最後，經由不斷的優化上界與下界，即可求得二次式的指標值。

Even as a child, I was fascinated by the colors in nature, such as rainbows, butterflies and flowers. This fascination developed into curiosity with age, and as my school studies developed, I became particularly interested in the scientific aspects of the origin and development of colors. I wanted to answer the question: How are the different colors of the butterfly wings related to the nanostructures of scales and pigments? The color on the butterfly wings results either from the pigmentation (chemical color) or from the structure (physical color) of the wing scales. Colors such as yellow, black, red and brown are mainly created by pigments. The interaction of light and structures in and on the surface of butterfly wings, often the size of the wavelength of the light, results in physical colors. These colors are usually bright and dependent on the viewing angle (unlike chemical pigments that spread light diffusely). The colors produced here are usually golden, green, purple and blue. But, where do these colors come from and why do certain species dazzle more than others? To get to the heart of the matter, I identified two key questions: • How are the different colors of the butterfly wings related to the nanostructures of scales and to the pigments? • Using the nanostructure, can you find out the wavelength of the reflected light? In this work, I focus on the structural colors of butterflies and study the physics behind them. This includes parachuting in areas such as diffraction gratings, scattering of light, interference in thin films, and multilayer interference. In order to experience the greatest possible diversity, I selected butterflies from different species for the measurements. Using the spectrometer, I measured the light reflected from butterflies. High-resolution microscopes such as the laser microscope and the scanning electron microscope gave me the opportunity to study the detailed nanostructures of the wing. In addition, I was able to analyze and evaluate my results using existing physical models and MATLAB simulations (Maxwell equations).

Cancer is the second leading cause of death today[1], accounting for nearly 1 in 6 deaths worldwide. Despite this, diagnosis and treatment models for cancer are limited and as such, new methods to identify and treat susceptible patients are required urgently. HLAF- adjacent transcript 10 (FAT10) is an oncogene that is strongly implicated in the development of inflammation-associated cancers[2]. Previous research on this highly polymorphic gene has identified 2 haplotypes – the reference haplotype, which is found in both cancer patients and healthy individuals, as well as an additional haplotype that is occurs at higher frequency in cancer patients and is associated with higher odds of cancer. In this study, it was hypothesised that the cancer-associated FAT10 haplotype can better promote tumorigenicity and could thereby serve as a useful biomarker for cancer. Here, we functionally characterize the 2 FAT10 haplotypes to understand how they influence some of the hallmarks of cancer. The cancer-exclusive haplotype was observed to enhance hallmarks of cancer, namely uncontrolled cell growth, resisting cell death and anchorage-independent growth as compared to the reference haplotype. Moreover, we uncovered the differential gene expression patterns induced by each haplotype. Molecules involved in cell adhesion and proliferation, as well as transcription were upregulated by the cancer-associated haplotype and hence could have contributed to the increased tumourigenic potential of the cancer haplotype.

In recent years, the ticks have reached the valley of Poschiavo and so far no study has been done to determine their diffusion. Recently, this presence has become a much discussed topic as these ticks can be carriers of pathogenes and represent a danger to humans. The goal of this work is to analyze the current situation in the valley of Poschiavo to understand in which areas the ticks are widespread, if they are carriers of pathogens and which factors could have an influence on their expansion. Several methods have been used for data collection. Ticks were found on ungulates killed during the high hunt in autumn 2016. In spring 2017, ticks were collected in various areas of the valley using the flag method that involves dragging a cotton cloth onto the ground. Some of the collected ticks were sent to a laboratory to identify the presence of the Borrelia burgdorferi, the pathogen responsible for Lyme borreliosis. To understand the evolution of the presence of ticks in the valley, the doctors and veterinarians were interviewed. Finally, to identify any climate changes related to the diffusion of ticks, the evolution of the tem-perature and relative humidity measured by two meteorological stations in the valley of Poschiavo since 1980 have been analyzed. Thanks to this study it was possible to highlight for the first time the presence in the valley of Poschiavo of ticks wich are bearer of the Borrelia burgdorferi. In fact, the bacterium was present in 26% of the analyzed ticks. Currently, the thicks populate the southern part of the valley, from the lake of Poschiavo to Campocologno, a small area in the central part of the valley and the area around Poschiavo and San Carlo. The interviews carried out showed that in recent years the ticks in the valley have increased and that the climate change could be a possible cause. In fact, since 1980 the temperature measured on the bottom of the valley has increased on average by 1.5 ° C and also the relative humidity has risen slightly. These changes could affect the diffusion of ticks in the valley of Poschiavo. In the future the temperatures will rise further and consequently the climate of the Poschiavo valley will most likely be more suited to the life of the ticks favoring their in-crease.

一個裝有水的玻璃杯，用喇叭撥出大聲的聲音，便能觀察到共振的現象發生，玻璃杯將會不停的震動，甚至導致破裂。本研究將會藉由傅立葉轉換(Fourier transform)來分析玻璃杯的振動的本徵頻率，並進一步探討頻譜的峰值。另外我們也研究了不同水位的高低以及液體密度對於共振頻率的影響，並以能量守恆的觀點進一步推導出玻璃杯的震動方程式。最後我們也近一步討論higher harmonic，並且發現non-linear dispersion relation的現象，有別於我們對於f∝n的觀念。

Nowadays Electric energy is the most useful in the world because we use it every day for lightening, work, entertainment ext … but electric energy also can be expensive and it will pollute the air plus we all know that the air pollution is getting worse. Our world consumes a huge amount of electric energy . Also we know that the homelessness is getting higher all around the globe and it reached a high percentage. The high price and the sudden cut of the electric energy and with it the air pollution makes a big problem. That’s why we created this project named TURN ON which is a friend of the environment and a friend of the humans. Our product will help us to produce and create strong, clean and renewable energy plus it will help the homeless to have free food and free transport tickets. After doing a lot of researches we found that our new method of producing energy gives a great electric energy and limit pollution. The kinetic energy is produced using rotations. That’s why we used the rotations of motorbikes, bicycles, cars wheels and turn that mechanical energy (wm) into electrical energy (we) that we can easily use in our daily life plus we can help homeless by giving them food widgets… in exchange with the electrical energy that they produced while using bicycles…After performing several tests and taking notes, we are able to conclude that our apparatus is indeed efficient as it is able to convert the rotation into electronic energy that we can store and use in emergencies to solve this big problem and in the same time to limit air pollution with using bicycles and reducing hunger regarding homeless. This machine should be easy to implement, cheap, does not depend on any other parameters such as the wind. Any rotation in any place can be a source of Electrical Energy. To facilitate the use of this new device, A START UP will be launched to rent electric bikes for “free”, distribute free food, snacks, tickets to homeless regarding to the energy production.

The cost of damage caused by hurricanes in 2017 is estimated to be over 200 billion dollars. Quick and accurate prediction of the path of a hurricane and its strength would be very valuable in alleviating these losses. Machine learning based prediction models, in contrast to models based on physics, have been developed successfully in many problem domains. A machine learning system infers the modeling function from a training dataset. This project developed machine learning based prediction models to forecast the path and strength of hurricanes in the North Atlantic basin. Feature analysis was performed on the HURDAT2 dataset, which contains paths and strengths of past hurricanes. Artificial Neural Networks (ANNs) and Generalized Linear Model (GLM) approaches such as Tikhonov regularization were investigated to develop nine hurricane prediction models. Prediction accuracy of these models was compared using a testing dataset, disjoint from the training dataset. The coefficient of determination and the mean squared error were used as performance metrics. Post-processing metrics, such as geodesic error in path prediction and the mean wind speed error, were also used to compare different models. TLS linear regression model performed the best of out the nine models for one and two time steps, while the ANNs made more accurate predictions for longer periods. All models predicted location and strength with greater than .95 coefficient of determination for up to two days. My models predicted hurricane path in under a second with accuracy comparable to that of current models.

此研究在探討「給定一圓及多個已知點，求作各邊或其延長線上恰含有前述已知點中之一點的圓內接多邊形」之作圖方法及圖形的性質。 研究當中，以反演的幾何變換結合代數方程式並透過遞迴關係，除了找到該問題之解的個數與條件外，並求得有唯一解之點的軌跡方程式，從中發現其軌跡圖形為一圓錐曲線，且隨著給定點在圓外個數的奇偶性，會有或為橢圓或為雙曲線之不同的圖形變化。同時也發現給定點本身使得滿足條件的圓內接多邊形存在之個數將決定該軌跡圖形與給定圓間之切點個數等的有趣性質。

I built a robot that is able to improve safety in mines. The robot takes a series of sensor readings, do 3D mapping to compare deteriorating physical conditions in time, detect CO and CH4 levels and record video footage. All of this information is then sent back to the user. The project aims to build a robot that could decrease the amount of casualties in mines due to gas or instability. A strict engineering process, which comprised researching different features on a robot, was followed. A prototype robot was built, tested and improvements made. Some of the challenges faced, while building the prototype robot, included manoeuvrability over any type of terrain, even rough and rocky terrain. Choosing the correct driving mechanism (wheels, tracks, suspension and steering) also proved to be a very important feature that had to be kept in mind. The sensors used included, a temperature, humidity, carbon monoxide gas, as well as a methane gas sensor. A Gyro, Accelerometer and compass for easier navigation were also used. Two cameras which included a front camera for navigation and 3D mapping as well as a back camera for navigation were installed. The robot was tested over various terrains, it was able to retrieve sensor data and all of the engineering goals were reached. After the robot was built it was tested on various terrains. The robot achieved all of the engineering goals. The sensors was able to give readings, the robot 3D mapped an area and was also able to manoeuvre over rough terrain.