September 17, 2010

Back to Reality, Back to Math

This was the plan: Linear Algebra --> Linear Programming --> Convex Programming (Semi-definite programming) --> Optimization, Error Bound Analysis     Especially in Graphs!

Thanks PatrickJMT for the hard work and easy and quick math reminders. L’Hospital’s Rule was just fun!

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PS:
After starting to read the book "Convex Optimization" by Stephen Boyd and Lieven Vandenberghe; I realized that convex optimization has lots of uses data mining, statistics, control theory, etc apart from the graph analysis topic that I am reading it for. It makes it even more exciting!

September 14, 2010

Keep my eyes in the sky, but my feet on the ground

Reality is we want to be there, but where we are, we have a number of steps before we can overcome all the limitations. Gustavo Stolovitzky (IBM Research)

http://www.youtube.com/watch?v=pKi30ai35mU

September 10, 2010

This did inspire me!

Virtual-Real Rehabiliation!

Rank Reduction

One of the interesting topics in linear algebra is matrix rank. It outlines ways that columns of a matrix correlate to each other. There are basic and free columns. and you can define free columns in terms of linear combination of basic columns. It highlighted a matter of data redundancy to me. So if you can define a column based on other columns, you won't need the content of those columns any more; just keep the coefficients that should be applied to basic columns and you are good to go! It seemed to be highly useful in matrix compression. An image which is a big matrix could be compressed like this by some matter of rank incrementation.

I succeeded in getting an algorithm to alter the rank. Unfortunately as it is not the current topic of my research, I was prohibited to work on this, deviate less and concentrate more on my research area. Anyway I found interesting relevant researches on matrix rank reduction, this is at the back of my mind for sometime to be used.

September 4, 2010

Rashomon

Rashomon: One of the best movies I have seen in my life. Whose story is true? Which is to trust? How can you judge?

What would you do if you were involved in the case? If you were the samurai, or the samurai's wife or even the bandit Taj┼Źmaru, or even the farmer witeness? That is a hard situation for each of these characters. Tell me what would you do.

I keep my faith in the man.

September 1, 2010

Achilles Heel!

When Achilles was a baby, it was foretold that he would die in battle from an arrow. Naturally, his mother Thetis did not want her son to die. So she took Achilles to the River Styx which was supposed to offer powers of invincibility and dipped his body into the water. But as Thetis had held Achilles by the heel, his heel was not washed over by the water of the magical river. Achilles grew up to be a man of war who survived many great battles. But one day, an arrow shot at him was lodged in his heel, killing him instantly.

I had heard Achilles heel several times but never knew what it was about.