將錯就錯的knuth 河內塔
在這篇報告中，我們探索了「將錯就錯的Knuth 河內塔問題」。傳統河內塔問題在電腦科學上佔有重要的地位，是一個極具內涵的模型。由於這個模型的深厚數學內涵，使其和巴斯卡三角形建立了緊密的連結，且利用這個緊密的數學連結，設計出復原任意起始狀態的良好演算法。Knuth 河內塔起因於數學家Knuth 在論文[3]中，描述傳統的河內塔問題時所發生的一次筆誤。在這個新的規則之下，我們意外發現Knuth 河內塔存在著一個和傳統河內塔平行的模型，此模型在電腦科學及數學上有著完全不同於傳統河內塔的內涵。我們的研究主要如下：(分別為內文中的四大段)(一) 結構分析。移動環所需要的次數，如何移動環並分析每一次動作所動的環，及每個環何時被動到並給出演算法。(二) 正整數的分割。所有的移動步驟將正整數做了一個新的分割(Partition)；此分割模k之後有良好的循環性質。(三) 費波那契真分數的排序。這個正整數的分割形成一張表，這張表恰好就是分子分母皆為費波那契真分數之排序。(四) 隨意亂排的Knuth 河內塔復原演算法。在Knuth 河內塔的規定下將起始狀態改變，找出良好的復原演算法，並分析。 In this project we study the "Knuth Hanoi Tower", which is motivated by a typo in a paper of Knuth. This inadvertently typo leads to a new rule of moving the discs on the Hanoi Tower (see introduction below for definition). Although seemingly similar to the traditional Hanoi-Tower problem, it turns out that under this rule the "Knuth Hanoi Tower" problem consists of amazing properties, and is totally different from the traditional one. Our study focuses on the following directions: (1) Structure analyzing: We analysis the sequences recording the disc moving and offer enumeration results and recurrsive/non-recurrsive algorithms. (2) Partition of N: The moving sequence forms a partition (a table) of N, which has an amazing congruence property. (3) The order of Fibonacci proper fraction: The row/column of the partition table is, even more amazing, exactly the order when sorting the Fibonacci proper fraction with fixed denominator/numerator. (4) The Restoration of an arbitrary initial state: We offer an efficient algorithm for restoring any initial state of discs. We hope that our study on the "Knuth Hanoi Tower" offers a simple, neat, and new example on the theory of Algorithm, Number theory and Combinatorics.
Mechanisms of Tumor Cell Invasion: The Role of Stat3 in Squamous Cell Carcinoma
Skin cancer, including basal cell and squamous cell skin carcinoma, is known to\r be the most common cancer type. Skin cancer is thought to make up half of all known\r cancers. Over one million non-melanoma skin cancers (NMSC) are reported every year. \r Approximately 300,000 of these cases are squamous cell carcinoma (SCC). It is\r estimated that about 2,000 people die from NMSC each year. Of the two skin cancer\r types, SCC tends to be the more clinically aggressive and likely to spread and invade,\r typically by way of blood or lymphatic vessels. Understanding the signaling pathways\r in SCC cells that regulate invasion will be important for developing improved cancer\r treatments. The signal transducer and activator of transcription 3 (Stat3) protein is a\r central regulator of numerous cellular activities, including proliferation, survival, and\r motility. Stat3 also has enhanced activity in many cancers, including skin SCC. This\r study shows that Stat3 regulates several invasive properties in a human skin SCC cell culture model.\r HGF (hepatocyte growth factor)- induced cell schattering was assessed for\r SRB12-p9 cells (p9WT), a human skin SCC cell line, along with SRB12-p9 cells\r engineered to have reduced Stat3 activity. Next, a cell viability-based adhesion assay\r was performed with these cells. Finally, severe combined immunodeficient (SCID)\r mice were injected subcutaneously with P9WT and S3DN cells and tumors were\r measured twice weekly. Extracted tumors were analyzed by immunohistochemistry and Western blotting for expression of the invasion related enzyme, MMP-2 and MMP-9.\r The suppression of Stat3 activity in S3DN cell lines resulted in reduced motility,\r greater adhesion, and a less invasive phenotype in SCID mice. Immunohistochemistry and Western blotting indicated higher levels of MMPs in the P9WT cells with\r expression localization towards the outer perimeter of the tumors. This data suggests\r that Stat3 plays a role in skin SCC invasion and better understanding of Stat3 function\r could lead to improved treatment and prevention of the disease.
Asymmetric Total Synthesis of GlaxoSmithKline’s Potent Phosphodiesterase PDE IVb Inhibitor
Phosphodiestarase of subtype PDE IVb inhibitors are considered as perspective drugs for the treatment of the central nervous system disorders (depression, Alzheimer’s disease, Parkinson’s disease). Pyrrolizidinone Glaxo-1, proposed by GlaxoSmithKline, is a highly potent PDE IVb inhibitor (IC50 = 63 nM), then conventional phosphodiesterase inhibitors Ro-20-1724, Rolipram and Cilomilast. However the activity of the Glaxo-1 was studied on a racemic sample, since the asymmetric approach to its synthesis has not been developed. Therefore the purpose of this research was the development of an efficient synthetic scheme enabling enantioselective excess to both (-)- and (+)-Glaxo-1, which can be than subjected to biological studies. \r The key stage in proposed asymmetric synthesis (-)- and (+)-Glaxo-1 is stereoselective [4+2]-cycloaddition of the nitroolefin to an optically activity vinyl ethers, derived from (-)- or (+)-trans-2-phenylcyclohexanols. The resulting chiral cyclic nitronates are transformed into a functionalized cyclic oxime ethers using tandem sylilation-nucleophilic substitution procedure. Reduction and decarboxylation of these products lead to optically pure Glaxo-1 and the regeneration of chiral 2-phenylcyclohexanols (91%). \r Thus both enantiomers (+) and (-)-Glaxo-1 were obtained selectively in average yield 12% from isovaniline and nitroethane. The study of biological profiles of each enantiomer of Glaxo-1 will be conducted in near future.
Wind Power
My school requires year 13 students to complete a year long project of a topic of their choice, culminating in the presentation of a thesis, a display and speech to a public audience. Many different topics appealed, but in the end I decided to build a micro wind-turbine. I have always been fascinated with mechanics, mathematics, engineering, aerodynamics and electricity. A wind turbine is a mixture of these technologies, with the overall goal of electricity production. In a world that is starting to see the true costs of fossil fuels, renewable energy seems to be increasingly popular and the demand for electricity is always growing.\r I was aware that building a wind-turbine from the foundations up wouldn’t be easy. Many of the experts I contacted in the early days cautioned me against trying such a complex thing in one year, at the same time as completing a full Year 13 course. There were, however, people prepared to support me. Michael Lawley, who builds micro wind turbines in New Plymouth was very helpful, just full of priceless knowledge and gave me a few basic parts to start with. The knowledge gained from Doug Clark, who also builds his own 11 kW wind turbines, was such an inspiration. Later I had practical help from Wilson Springford and Darron Matthews.\r I investigated and documented the history of and current state of wind technology, as well as my own experience and learning in the design, construction and testing process. I thought it would be interesting to find out how the electrical and mechanical side works.\r The generator, a washing machine motor, needed to be completely rewired, and converted to DC (direct current) from AC (alternating current). I built my own 3-phase AC to DC converter.\r Other parts like the disc brakes and bearings had to be found. The rest was hand-made and every part, to a certain extent, had to be modified. Probably more than twenty braking system design attempts led to the final decision to incorporate the wind-activated hydraulic disc brake where the wind paddle starts to ease the brake on over a certain wind speed.\r I studied the dynamics of wind turbine blades, their shape, the material they were made from and how this affected their performance. The decision to make my own blades helped me gain a great sense of achievement and knowledge of blade design. I found some New Zealand made 100% recycled plastic pipe, an added bonus because I wanted to have minimal environmental impact. I designed the turbine with three blades to give better starting torque along with a lower top speed, perfect for how I wired the generator.\r I designed the swivel, the part of the wind turbine that enables the power cables to get from the turbine down the tower without twisting up and has the job of carrying the whole turbine, which is mostly made from recycled aluminium. The steel and bearings used to create the swivel were all second-hand parts and materials. The power from the turbine passes through the swivel into the cables and down the tower. The main mast of the tower is a little over 4.7 metres and pivots on two shorter supporting poles which go down around 2.6 metres to the bottom of the reinforced concrete foundation.\r I managed to, design and construct an operational prototype micro wind-turbine, incorporating recycled and recyclable materials as much as possible, with the end result surpassing all expectations.
吸〝氣〞大法-QCM 對有機氣體之吸附與偵測
中文摘要：\r 化學實驗中，常常會使用到各種具有揮發性的有機溶劑，如醇類、酸類、醛類及酮類等。\r 當吸入過量的揮發性有機溶劑時，將會對人體造成嚴重的傷害，故使用時格外需要留意。有\r 鑑於此，我們開始著手研究如何偵測氣相中的有機氣體分子。\r 本研究中，我們利用聚苯胺薄膜吸附氣體分子的特性並結合對質量變化極靈敏的石英晶\r 體微天平，自行設計了一套簡單、藥品用量少且不需昂貴儀器的實驗系統。藉由此系統，我\r 們有效的針對各種揮發性有機溶劑進行偵測，並進一步地探討不同氣體分子對於聚苯胺薄膜\r 的吸附現象。\r \r 英文摘要：\r Students usually use volatile organic solvent in laboratorys such as alcohols, carboxylic acids,\r aldehydes, ketones, etc. It will injure our body when we breathe in too much volatile organic\r solvent. For this purpose, we begin to study how to detect volatile organic compound in air.\r In this work, we combine polyaniline membrane which can adsorb gas molecules and quartz\r crystal microbalance which is highly sensitive to mass changes to design a simple and inexpensive\r system which needs only little chemicals. With this system, we can effectively detect different\r volatile organic compounds. Furthermore, we can also study the adsorption of polyaniline\r membrance for different volatile organic compounds.
一后多夫否？黑棘蟻(Polyrhachis dives)聚落生殖策略之研究
A vast amount of research has been conducted on various ant species such as Monomonum pharaonis, Formica rufa, and Lasius niger, demonstrating the coexistence of polygyny and monogyny colonies. In polygyny colony, the high heredity variability of filial generation could be expected, but what could the monogyny colony do to hold the high heredity variability in order to increase the fitness? I hope I can account the sex ratio in the colony of spiny weaver ants, Polyrhachis dives, and compare the different colony with different reproductive strategies. I also want to check by V8 that the colony can form a polygyny colony and virgin queens can mate with many males of the same colony in the artificial nest. The results suggest that in the colony of spiny weaver ants, the higher the number of the dealate queens, the lower the number of the male. In the monogyny colony, workers control the sex ratio. According to the observation, we can see the alate adult mate in the artificial nest, and multimating can be recorded for the first time. The following study was there for undertaken to examine what’s the aftereffect made by the Reproductive strategies of polygyny colony and monogyny colony.在多后聚落內，子代變異度高是可以預期的，但是單后聚落中，又如何維持遺傳的變異度以增加其對環境的適應力呢？我們希望能計算黑棘蟻聚落組成，比較不同生殖策略的聚落之各種性比，並且錄影證實黑棘蟻聚落可以為多后聚落並進行巢內自交。我們發現：黑棘蟻聚落內，蟻后數愈高，則雄蟻比例較低；單后聚落之性比決定於工蟻；而根據錄影觀察，聚落中的有翅生殖族可在人工蟻巢中完成交配，多次交配的現象首次被實地紀錄，並且佔所有交配新生蟻后的92.8%。本實驗可利用黑棘蟻來了解單后與多后聚落的生殖策略對其族群發展的影響。
蛙！到底發生了什麼事？探討溪谷生態系畸形蛙的發生原因及其生態學之研?
Our research started from June, 2003 to May, 2004. During these twelve months, we collected and discussed the basic ecology material of malformed “ Rana latouchii ”, which we call it frog in the following paragraphs . Thanks for the favorable geographical position, we collected the first-hand data in the area of Jin-Mian Mountain foothill gully situated in Taipei. Our investtigation project includes：the percentage of the malformed frogs in a whole race, the geographical distribution of dominant-abnormal frogs, the sexual distribution of dominant-abnormal forgs, and the possible roots for the generation of malformed frogs. We have altogether carried seventy-six times field investigations. In those investigations, we focused our research on the randomly-sampled 580 Rana latouchii. In these 580 sample, there are 190 female, 350 male, and 40 adolescent. We discovered seventy-six malformed frogs, constituteed by 21 female, 53 male and 2 adolescent. In another words, the occurance of malformed frog in a race is around 13.1. %. In our observation, we can classify dominant-abnormal frogs, “Rana latouchii”, into eight species. Here are the species: 1. the entire body is obviously malformed, 2. with only one eye, 3. in lack of appendage apod, 4. in lack of arms,5. in lack of palms, 6. with excess webbed toes, 7. the maltfromed of appendiculars, 8. the lack of toes on the palms. Within these 8 species, the last species has the highest occurance, 66.38% in aproximation. If we look at the classfication by sex, the ratio of female to male is around 1 to 2.52(1:2.52). However, the possibility of being maleformed is regarded as the same for female and male frogs in the same group. In statistical term, our research shows that the chi-square is 1.742 while our degree of freedom is 1 and confidence level is 95% (X2=1.742，df=1，p>0.05). During the research, we also observe that each malformed species affect different living activities of malformed frogs. In the worst situation, the malformed nature can result in shorter life. In our sampling area, malformed frogs mostly reside in high concealment and high humidity location. In our research data, within these area, our re-captured rate for malformed frogs is 25% and hirudin-parastical rate is 4.31%. As our research shows, the occurance of malformed “Rana latouchii” in our selected area results from 3 main causes： First, the parasitism of leeches or parasitic worm；Second, the agriculturally chemical contaminants；Third , the injured causes from escape from predator. 本研究自2003年6 月至2004年5月為止，共12個月的期間，於臺北市內湖區金面山南麓溪谷，對拉都希氏蛙(Rana latouchii)族群之畸形蛙個體進行基本生態資料的蒐集與探討，調查項目包括：族群中畸形蛙發生的比例、畸形蛙外部形質異常分佈的情形、族群中雌蛙與雄蛙發生外部形質異常之情況及可能造成畸形蛙產生的原因。 研究期間共進行了76次的野外調查，總紀錄了拉都希氏蛙580隻，雌蛙有190隻，雄蛙有350隻，幼蛙有40隻；畸形蛙個體共紀錄有76隻，雌性畸形蛙有21隻，雄性畸形蛙有53隻，幼體畸形蛙有2隻。族群中畸形蛙發生率約為：13.10％，外部形質異常的畸形拉都希氏蛙總計有八大類，包括：1.整隻個體形質畸形，2.單眼個體，3.附肢缺少，4.附肢缺臂，5.附肢缺掌，6.腳掌多趾，7.附肢腳掌畸形，8.附肢腳掌缺趾，其中以附肢腳掌缺趾類的66.38％發生率最高。畸形蛙中雌雄比約為1：2.52，族群中雌蛙與雄蛙發生畸形的比例並無顯著的差異（X2=1.742，df=1，p>0.05）。 不同部位形質畸形的發生，將會影響畸形蛙的個體活動，甚至可能降低畸形蛙的存活機率。研究調查樣區中，畸形蛙較常活動於濕度高且隱蔽度大的分樣區中，畸形蛙的重複捕捉率為25％，被水蛭寄生的比例則約是4.31％。 由調查研究結果顯示，造成內湖金面山區南麓溪谷拉都希氏蛙畸形蛙發生的主要原因，推測可能有下列幾種：(1)水蛭或是吸蟲類的寄生；(2)農作過程中的化學污染物；(3)逃脫掠食者捕食過程受傷。