組合學與離散模型

Abstract

在這個三年計畫中，我們主要的工作是要繼續研究新組合設計的建 構，圖的結構，以及它們在離散模型上的應用，這包含了複雜網路，小世 界網路以及計算分子生物學。 組合學的研究是我多年來一直不斷繼續做的工作；而它們的應用則是 近年來才吸引我的目光；在過去幾年，我們幸運地在網路、群試理論以及 計算分子生物學上有一些成果，然而我們更因為投入很多的心力才體會到 要有具體的卓越貢獻是一件非常困難的事，尤其是我們在前三年的計畫 中，很多預期有所貢獻的課題都只能有初步的構想或小成果；希望能在這 一期三年計畫中我們能有突破。 另外，我們也開始要利用在代數圖論及隨機圖上所得到的工具去研究 複雜網路，小世界網路；相信會有一些收穫。

This three years term proposal aims to study the construction of new combinatorial designs, the structure of graphs, and their applications in discrete modeling especially on complex networks, small world networks and some aspects(topics) in computational molecular biology. The part of developing more new tools in combinatorial theory is a long term project of my research, it has been the main focus of my research since I took this job 23 years ago in NCTU. Until quite recently I start to work on the application of combinatorics. After making several contributions on networks, group testings and coding theory, complex networks and computational biology are the topics which attract my attention. After three years practice, we did figure out why obtaining substantial works on problems of computational molecular biology is not an easy task, it takes a lot of effort. In order to a chieve the excellency, we just have to more forward and hopefully some smart ideas will be obtained through my own or my students. For complex networks, since they are close related to algebraic graph theory and random graph theory, we shall also look at the inside and see if we can make a substantial contribution in next three years.