### 目前分類：工作相關::working at sinica (32)

• Jun 14 Mon 2004 05:10
• ## 四分溪小生態--中研院區裡的小溪流 • Jun 10 Thu 2004 05:13
• ## [hypercube] Find all neighbors with a given distance

it's a problem similar to determine all possible combinations
One reason of why hypercube still interests computer science or applied mathematic people is its perfect correspondence between the binary system. For example, how many nodes in a d-dimensional hypercube? the answer is quite simple that 2 to the power of d.

• Jun 04 Fri 2004 05:24
• ## [hypercube] Minimum boundary edges b(x)

it is a beautiful curve.

To deal with nodes and edges of hypercubes is my recent work. We usaully use "aggegrate" A to denote a set of connected nodes, and the size of it |A| means the number of nodes included the set. Given a size, |A| = x of an aggregate, there could be many possible different forms. Here, we want to know the number of minimum boundary edges, b(x) for all possible forms. In previous researches, Leader (1991) proposed a formula that can exactly calculate the value of b(x).

• Jun 03 Thu 2004 05:26
• ## 今天中午吃什麼好呢? 當然是"30元自助餐"囉! • May 25 Tue 2004 03:46
• ## 我的工作環境簡介

• May 18 Tue 2004 03:55
• ## I got a new computer

I always use my notebook after I was in Acadamia Sinica from January 2004. Because my desktop computer in lab is too old to do most works. Finally I have a whole new computer now. Especially the new LCD monitor, it is very comfortable for long time working. Although I have to spend time for setting it up, I still feel very happy. • May 13 Thu 2004 04:04
• ## [bioinformatics] Genetic code in hypercube representation

Because the last effort of proof for diagnosability of hypercubes. I did not touch on anything about bioinformatics for a long time (about 2 months). Today I tried to search something interesting from Internet. So I typed "hypercube and bioinformatics" for a keywrod with google searching. Then I was surprised that there were not few results on the webpages. I picked one paper published in 1994 and read it immediately. • May 03 Mon 2004 04:09
• ## [hypercube] Boundary edges of aggregates

Before I discover the direct formula of partial sum of binomial coefficients, it is the best way to let computer handle this complex computation. Therefore I wrote two simple program (by javascript) on the webpage: program 1 and program 2. In the first webpage, one can input the dimension of hypercube (d) and number of partitions (m). Then it will output the result of the lower bound of diagnosability (t) of our algorithm and the number of boundary edges. In the second webpage, after one input d and m, the program will output the maximum t with the "isoperimetric inequality".

• Apr 30 Fri 2004 08:26
• ## Partial sum of binomial coefficients

is there any formula can calculate it directly?

• Apr 28 Wed 2004 08:29
• ## [hypercube] Circled a big round--go back to the origin again...

Last week, I tried to solve the problem by "edge isoperimetric inequality". But today I found it failed. It really depressed me...

I originally can't understand the proof of lower bound of diagnosability in hypercubes illustrated in the latest paper. So I buried my nose in calculating the relationship of degrees and size of connected component in hypercubes. After a week passing by, when I finally found out an great inequality of this two things, I found the result is exactly the same of the proof in that paper. Oh my godness! what a big round I circled these days. I would like to cry so much...

• Apr 23 Fri 2004 09:01
• ## [hypercube] Weekly Presentation

counting the boundary and internal edges of a connected component of hypercubes

If we obtain two values which represent the number of vertices and edges in hypercubes respectively, do we can determine the size of all possible connected components? For example, there are totlal 16 vertices and 32 edges in a 4-dimensional hypercube. Now we assume 10 vertices and 13 edges are remained in this hypercube. What are all possible cases?

• Apr 19 Mon 2004 09:10
• ## the Probabilistic Method--a powerful and modern tools in combinat

The "probabilistic method" is one of the most powerful and modern tools in combinatorics. The basic idea of this method is simple and elegant: In order to prove the existence of an object with a specific property, prove that a randomly chosen object satisfies that property with positive probability.

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