You are currently browsing the monthly archive for December 2010.
This topic may have been discussed and debated a thousand times. I remember seeing one such report, not so long ago in EE times. The Economist has just placed a new one as well. The title is ” Why doing a PhD is often a waste of time”. Pretty interesting nevertheless. Anyway, I personally do not think that it is all waste. On the other hand there are a lot of things out to learn in the process. Eventually it is a matter of personal choice!
On the Christmas day, out of blue I bumped across an old archive of Robert Fanos’s interview (oral history). Beautiful one.
Henri Padé wrote his PhD thesis in 1867 at the École Normale Supérieure in Paris. The dissertation was on what we know today as the Pade approximant. Come to think if it today, it is really remarkable that 100 years ago, mathematicians had thought about function approximations using rational polynomials. Now it may appear all too simple, but without the aid of a serious computing machine, one would have to rely on the mathematical rigour on every small argument. In comparison, these days, we can quickly check the validity using some computer program before venturing into a formal proof.
Anyway, the sudden recollection of this French mathematician happened, as I was looking for a good curve fit for a problem I need as part of my work. I needed to minimize the maximum error than the average or squared error. I thought about Legendre polynomial fit, which gave me the minimum root mean squared error and Chebychev who minimized the worst case error. The order of the polynomial and the number of sample points seemed to have dependency. Pade approximant is a cool technique which reduces the polynomial order while using a rational polynomial. I am not too convinced about the statistical properties of this method. The data points I have at disposal may have some measurement error attributed. I need to investigate a bit more before taking a decision on the potential optimality for the given problem! Happy knowing this scheme though. In retrospect, I remember hearing it in my statistical signal processing books, but never paid any serious attention then! Silly.
Official call on the world cup soccer hosts for 2018 and 2022 came out couple of days ago. It is going to be the beautiful Russia in 2018 and the Arab land gets the lot for 2022. One in eastern Europe and the other truly middle east Asia. Both these announcements created ripples and expected controversies, but I personally liked both the choices. My liking is bound from the fact that, these are two new hosts and the world deserve it see a global event occurring in 4 year gap to be held at different countries. So much to see and so much to learn. Why restrict only to a selected few countries. Afterall, there are 8 and 12 years to prepare. Unless the country is seriously deprived of money, then go ahead. Qatar with oil reserve have no shortage of bucks. Russia will never have a dearth, looking at the sheer volume of natural resources they have.
One of the major criticism against Qatar was that, it is hot. So what?It is really glad to hear that Qatar is planning eco friendly stadiums for the super event to be held in 2022.
And the Worldcup 2018 bid by Russia in Zurich was a fabulous one.
After all, there are trees on earth’s terrain. Why not on Google earth? Google just don’t delay it any further. Now we can see trees with Google earth 6. Amazing view of SFO, right here. As they say, it is here as it is there. Now we truly have the world in front of our eyes. The beautiful 3D world is now ready.
Lipschitz continuity is a stronger property than continuity. First, when I heard this (through Ruediger’s treatment on expectation analysis of codes), it was all haze. For the second time, I made some sense during the Applied Stochastic process course. Anyway, a final appreciation of this concept kicked my brain only when I started working on a problem. Recently, I came across this again and hence thought of penning a few easy lines on this.
Here is a beautiful explanation of this concept.