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    政大機構典藏 > 理學院 > 應用數學系 > 學位論文 >  Item 140.119/52633
    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/52633


    Title: 熱帶格雷斯曼的計算及其應用
    Tropical Grassmannian computing and its application
    Authors: 許瑜芳
    Contributors: 蔡炎龍
    許瑜芳
    Keywords: 熱帶幾何
    熱帶格雷斯曼
    演化樹
    tropical mathematics
    tropical Grassmannian
    phylogenetic tree
    Date: 2011
    Issue Date: 2012-04-12 14:11:56 (UTC+8)
    Abstract: 這一篇論文是說明矩陣中的元素如果滿足熱帶格雷斯曼就可以將它用樹型圖表示。第二章簡述熱帶數學的基本運算和介紹超曲面,作為熱帶格雷斯曼的先備知識。第三章介紹演化樹,在第二節中用兩種方法重建演化樹,第一種方法UPGMA是要在特定的條件下所建造的演化樹才會正確,第二種方法是利用矩陣中兩個物種間的距離假設的樹型配置圖,解聯立方程組得到各段距離,第三節中先介紹代數幾何中的格雷斯曼再聯結到熱帶幾何中的格雷斯曼。第四章是將第二種方法寫成Python程式,輸入矩陣中的元素,如果滿足熱帶格雷斯曼,就可以顯示它可能的樹型圖以及算出距離。
    第一章 緒論 ...............................3
    第二章 理論背景 .............................5
    2.1 基本運算 .............................5
    2.2 多項式 .............................7
    2.3 超曲面 ............................9
    第三章 演化樹和熱帶格雷斯曼的關係.............11
    3.1 演化樹空間 .........................11
    3.2 如何建立演化樹 ........................18
    3.3 代數曲體以及格雷斯曼 ..................25
    3.4 熱帶格雷斯曼 ....................33
    第四章 利用Python程式畫出演化樹 ............35
    4.1 Pthon程式樹圖表示法 ...........35
    4.2 當n=4時,演化樹的畫法 ...........37
    4.3 當n=5時,演化樹的畫法 ...........44
    第五章 結論 ...........57
    Reference: [1]Billera, L. J.; Holmes, S. P. & Vogtmann, K. Geometry of the space of phylogenetic trees Adv. in Appl. Math., 2001, 27, 733-767
    [2]Buneman, P. A note on the metric properties of trees J. Combinatorial Theory Ser. B, 1974, 17, 48-50
    [3]Kleiman, S. L. & Laksov, D. Schubert calculus Amer. Math. Monthly, 1972, 79, 1061-1082
    [4]Maclagan, D. AARMS Tropical Geometry 2008
    [5]Schröder, E. Vier combinatorische probleme Zeit. für Math. Phys., 1870, 15, 361-376
    [6]Speyer, D. & Sturmfels, B. Tropical mathematics Math. Mag., 2009, 82, 163-173
    [7]Speyer, D. & Sturmfels, B. The tropical Grassmannian Adv. Geom., 2004, 4, 389-411
    [8]Stanley, R. Enumerative Combinatorics Cambridge University Press, 1999, 14
    [9]Adams, W. W. & Loustaunau, P. An introduction to Gröbner bases American Mathematical Society, 1994,3, xiv+289
    [10]Fraleigh, J. B. A first course in abstract algebra Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1967, xvi+447
    [11]Gusfield, D. Algorithms on strings, trees, and sequences Cambridge University Press, 1997, xviii+534
    [12]Harris, J. Algebraic geometry Springer-Verlag, 1992, 133, xx+328
    [13]Lutz, M. Programming Python Sebastopol, Calif. : O`Reilly, 1996
    [14]Steven Bird, Ewan Klein & Loper, E. Natural language processing with Python Sebastopol, Calif. : O`Reilly, 2009
    Description: 碩士
    國立政治大學
    應用數學系數學教學碩士在職專班
    98972008
    100
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0098972008
    Data Type: thesis
    Appears in Collections:[應用數學系] 學位論文

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