The Transformed View - Part I

During my travel during the last few days, a lot of discussions happened about the KTU and its impact on the technical education. Many people from the teaching community feel that it is a ill-planned set up and exists only in news and hype. Let us not build a discussion here, but take some useful positives from the idea of unifying the local universities.

Many philosophers agree to the fact that the universe exists on a absolute "truth" and everything that we deal with are just its manifestation. Even the partitions that we build on religion, science, arts or any such streams actually are the same. In a united approach we see them as one. The learning in one stream does not in any way contradict the other.

Imagine you are in front of a white board and are gazing at it. Now you look the same screen with a yellow glass. The entire screen now becomes yellow. In reality the screen has remained white, and only the glass had made a difference. So are the different things that happen around us. Let us take this discussion to the subject of signal processing. Most of us are familiar with the natural time domain for the electrical signal. We are also aware that the power line signal that provides electricity has a sinusoidal fundamental frequency. We express the same thing here in different viewpoint. One viewpoint is the time and the other is the frequency. Nature imposes duality in the time-frequency, which brings about a conflict. Engineering solutions are nothing but a compromise on this duality. We shall build some interesting compromises in part II of this post.

Dynamic Programming Decision Making

All of us set certain goals and try to achieve them. What is the best way to keep track if you have taken the right decision?  Here is a quick method to keep track of your progress. Consider that you set a goal today, and you are trying to optimize all the actions in order to reduce the total cost. The cost here can be due to time, money, effort, social costs and others.

The idea is to incorporate a method to reach the optimum in a step by step manner that uses only the local information. We query that : "If I assume that I am optimal in the future, what action needs to be taken today to ensure a global optimum". This leads us to the answer that, the best way is to determine the best that you can do today, with the assumption that from tomorrow we are going to be optimal. This seems to be very suited to our current practice also. While we drive a car we put the gear to the right speed, so that we can endure the local roads and the nearby traffic. The goal might be distant but we always have to act optimally to reach there.  While spending we ensure that the basic needs for today is met. The savings also are done accordingly. Take the simple game of tic-tac-toe, here we are trying to see the local information in the game and trying to win or in most situations stop the opponent from winning !

Courtesy : http://experimental.designforfun.com

This approach of dynamic policy is widely employed in control systems and  communication. There are two things that we consider in this optimization problem, one is the value or the cost that is incurred due to our decision (actions)  and the second is the policy that we have come up with. So remember at the beginning of each day try to see that you are going to be optimum for 'today', because tomorrow will "take care for itself".

[Topic Courtesy :  Introduction to Stochastic Optimization, IITB]