我在中研院的日子

當初會選擇中研院成為國防役服務單位的主要原因就是這裡豐富的學術資源。因為不想當兩年大頭兵的緣故，從大學畢業後就一直找機會唸書，從碩士念到了博士班，跟我一樣已屆"而立之年"還沒有入伍的人實在是不多了，眼看博士班畢業遙遙無期，又有國防役這個機會，所以便想到這個兩全其美的方式：博士班休學，進入研究單位服役，然後運用這裡的資源與環境一邊工作一邊寫論文，運氣好的話還可以同時完成兩項任務(服完兵役+博士學位)...老實說，這裡的學術資源確實比一般大學還要豐富許多，光是具博士學位的人口密度就可能是全國之冠，許多頂尖的國家計畫也都跟這裡相關，不過跟我目前工作最為相關的應該是"網路上的學術資源"吧！

還記得剛念碩士班時，時常都為了找paper研讀而必須跑到圖書館翻著一本本相關的學術期刊，相對於現在的線上期刊資料庫(IEEE、ACM、Elsvier等...)， 真的是相當的沒有效率(當時還有許多同學會利用「找不到相關paper」當作偷懶的藉口)，這些資料庫大部分都提供非常清楚友善的查詢介面，除了有讓使用者直接輸入關鍵字(keyword)的傻瓜查詢法，也有提供類似圖書館系統的作者、年份等進階搜尋技巧。

四分溪是一條穿過中研院區的小溪，我不知道他原始的面貌如何，不過以目前看來他已經經過一番人工的改造，河床由水泥構成，河道兩旁也以搭上了護欄。第一次撇見此溪流時只當它是條大水溝，但隨著相處的日子越久(沿著四分溪散步兩次是我每天的行程，因為這條路是停車場通往資訊所的必經之路)，漸漸發現了它的有趣。

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.

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).

中研院院址在台北市的南港區，與北縣的汐止與深坑交界處附近，周邊大部分是住宅區，所以環境算是相當清幽。不過也因此生活機能並不佳，方圓一公里之內連一家7-11都沒有...

來中研院資科所服務(服國防役)已經快要五個月了，雖然對大部分早在這裡工作的人員來說我還是個菜鳥中的菜鳥，卻也已經開始適應這裡的工作模式。這裡的工作時間非常彈性(標準的朝九晚五)，而且我的老闆給我的工作內容也非常彈性，說穿了也就是「作研究」三個字，研究的題目不限(當然最好要跟自己的興趣與專長相關)，而終極目標就是在學術期刊上"發表論文"。

我所屬的Lab並不大(應該說是非常小)，一間大約三坪大的正方形辦公室擠了三個人，扣掉一個角落留給門口之外，每個人可以分到一個角落，在擺上桌子之後就成了L形的工作空間，算是蠻不錯了的，照了一張相片給大家一點感覺囉...

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.

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.

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".

is there any formula can calculate it directly?

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...

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?

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.