| [ QuizWit ] in KIDS 글 쓴 이(By): pinkrose (Wenger) 날 짜 (Date): 1999년 2월 9일 화요일 오전 03시 42분 33초 제 목(Title): Computational Geometry 2. While I was sitting in a lecture, I was keep thinking about E.C. and finally had an inspiration. ^^ NEW PROBLEM: Let C be a cube of size N^3. C consists of N^3 unit cubes C_i. Each C_i is 0 with a probability p and 1 with a probability q=1-p. If C_i = 0 then it is empty otherwise it is closed simply connected set. Find the expected Euler characteristic of C as a function of N and p. NOTE: C_i is distributed as Bernoulli random variable. (just like a tossing a coin) There are 2^(N^3) possible configurations for C. You have to find the average E.C. of all possible configurations. This problem is not that hard. Let's solve together. I haven't even solved it yet myself. Such C is mathematically called "Random Fields" They said "What sign can you give us to see, so that we may believe you?" |