Monte Carlo methods are non-parametric algorithms that use random numbers and theorems of probability theory to approximate values that are not random. The purpose of my research was to approximate the surface of different geographical areas that can be easily approximated to polygons (e.g. lakes, glaciers, deserts) with Monte Carlo simulations starting from either Cartesian coordinates or pictures. Computer science would not exist without math, and this research project showed me the importance of a deep understanding of probability theory in the world of simulations and, more generally, the importance of developing new theorems and algorithms. The results of my research could be developed in different ways: it would be interesting to produce software that allows one to approximate areas from pictures taken from a smartphone; as well, the theorem I found has to be proven, and also Monte Carlo methods as a means of random number generation can always be improved. There are still many possibilities.

This project was inspired by a tournament call the International Young Physicist’ Tournament (IYPT). The problem could be broken into two aims: ‘Investigate the forces that cause a ball to levitate in a titled airstream’ and ‘optimize the system for the maximum angle of tilt that results in a supported ball’. The first stage of the investigation was research and learning. Two fluid mechanics courses online were used to build a basic of knowledge of the subject. Next a force diagram was created to model the forces acting on the ball. The diagram identified a force called the lift force that must be acting on the ball to be supported. There were three contending theories that could explain the lift force: The Bernoulli theory, the Coanda theory and the Magnus theory. A practical investigation was then instigated to differentiate between these three theories. Since the Magnus theory is only applicable if the ball is spinning in the airstream, this theory was isolated by changing the center of mass of the ball but keep everything else constant (this allowed control of how much the ball spun in the airstream). Changing the center of mass didn’t impact on the maximum angle of tilt at all, proving that the spinning of the ball isn’t producing a significant amount of lift, and therefore the Magnus theory couldn’t be a cause for lift. Because further testing couldn’t isolate the Coanda and Bernoulli theories, a solution was developed to explain why the two remaining theories might co-exist. Further testing methods have been designed to investigate this possibility in more depth. To meet the second aim of this project, an investigation was launched to see how parameters affected the maximum angle that the ball could be supported at. The parameters investigated were: Ball radius, ball mass, ball surface, air speed and airstream diameter. A lot of time was spent creating a reliable experimental method. The method could be used to support a ball in an air stream, slowly tilt the air stream, and then measure the angle of tilt the moment that the ball fell out. After experimentation, a table was created to describe how the listed parameters affect the maximum angle of tilt that a ball can be supported at. Explanations were proposed for why each parameter affected this angle. Future experiments have been devised to build a deeper understanding of the effects of a wider range of parameters.

The aim was to determine whether there is an amount of gyroscopic force that keeps a bicycle wheel upright and stable. Two hypotheses were used, the first being as the mass of a wheel increases so does the force required to tilt the wheel by thirty degrees and the second that as the speed at which the wheel is spun increases so does the force required to tilt the wheel.

為探討青少年壓力對生活的影響，我們在網路上進行問卷調查，調查12~18歲的青少年對自身所感受到的壓力所進行的自我評估。 統整後，決定以青少年時期之小鼠作為模型，探討睡眠剝奪對青少年學習的影響，並討論男女差異。生理狀態方面得知睡眠剝奪會使體重成長較緩慢，且由曠野實驗發現睡眠剝奪不會大幅影響自主活動量。 學習與記憶方面利用新奇事物測驗測量短期記憶，在公鼠身上可以看到睡眠剝奪會影響公鼠的短期記憶；母鼠在此實驗中控制組與操作組無顯著差異。長期記憶與空間記憶部分利用巴恩斯迷宮測試，發現性別間無顯著差異，各性別控制組與睡眠剝奪組間亦無顯著差異。

基因陷阱(Gene trap)和增強子陷阱(enhancer trap)在近年來被廣泛應用於斑馬魚的研究上。 因此，本實驗利用實驗室現有的增強子陷阱，包含熱休克蛋白（Hsp-70）促進子和綠螢光蛋白基因(GFP)及兩端的Tol2重複序列，得到不同位置發亮的斑馬魚。其中，本實驗選用側線細胞之套細胞（mantle cell）和中間神經肥大細胞（Interneuromast cell）表現綠色螢光蛋白的斑馬魚（HG7L）進行研究，推測sortilin-related VPS10 domain containing receptor 3 (sorcs3)為部份的被取代基因。另外，將HG7L互相交配後，進行被取代基因對側線組織再生之功能的實驗，發現雙股皆被取代的斑馬魚的毛細胞（hair cell）再生較遲緩且排列凌亂，推測被取代基因對側線發育有影響。再者，藉由被標定的套細胞觀察側線組織的發育，並模仿前人的實驗方法，觀察得知側線的發育過程不只與套細胞更和中間神經肥大細胞有關。

This science project is designed to answer a question of whether or not a chemical reaction is needed to produce industrial quantities of carbon nanostructures by exposing dry ice to a high temperature that is at least 3100°C. A small carbon arc furnace powered by an electric welder is used to produce the high temperature. During control runs, the carbon arc furnace is energized for a predetermined time, after which the carbon arc furnace is de-energized and any carbon particles within the furnace are collected. During carbon nanostructures synthesis runs, dry ice is placed within the carbon arc furnace. The carbon arc furnace is energized and the dry ice is consumed for the predetermined time. Carbon nanostructures synthesized during the synthesis runs are collected once the carbon arc furnace is de-energized and allowed to cool. The volume of the carbon particles collected during the control runs is compared to the volume of the carbon nanostructures produced by the synthesis runs. This science project has discovered that on average at least 16 times more carbon nanostructures are produced during synthesis runs consuming dry ice as opposed to the control runs. Moreover, the synthesis runs did not rely on chemical reactions. Further still, samples of the synthesized carbon nanostructures were imaged using a transmission electron microscope (TEM). The TEM images clearly show high-quality carbon nanostructures that include carbon nanotubes, faceted carbon nanospheres, and the super-material graphene.

Ferrers diagram是指在n個小方格中填入數字的圖表，且必須有： (1)方格緊密堆積在一個矩形的左上角 (2)每個方格的值分別定義為：(正右方的方格數)+(正下方的方格數)+1 (Hook length) 而所感興趣的問題是：如果有一個Ferrers diagram，那麼至少需要知道多少幾個格子的位置與它們的值，則整個Ferrers diagram就可以被唯一的確定下來。 我們稱具有上述性值的格子所構成的“子圖”為特徵圖，顯然整個diagram也是一個特徵圖；那麼，特徵圖至少又需要有幾個格子呢？於是定義特徵圖中格子個數最少的為最小特徵圖，因此問題轉變成探討最小特徵圖的大小(即格子個數)。 我們的研究結果是最小特徵圖的大小跟原本diagram中值為“1”的方格數(文內一般以K來表示值為“1”的方格數)有密切關係，關係如下： (1)最小特徵圖的大小≦K+1 (2)廣義最小特徵圖的大小 (3)狹義最小特徵圖的大小 同時，我們也有實例說明以上不等式的等號是可以成立的；換言之最小特徵圖的格子數之最小上界為K+1，廣義最小特徵圖的格子數之最大下界為，而狹義最小特徵圖的格子數之最大下界為 。