How not to slack off ?

Living in US sure has way too many distractions. For a easy going graduate student, who wants to experience everything his university provides, life seems like an adventurous journey of Indiana Jones. But its usually not very late until you realize that Mike Slackenerny used to feel the same way when he was in his first year.

How not to get distracted is the big question. But do not get excited, I am not giving out the answer in public. At least, if I knew it. Since I too am a grad student who gets distracted by every little video that comes out on stage6.divx I can kill to know the answer (kill mosquitoes not homo-sapiens). In theory one could find millions of books and sites which claim that they know the answer. But as Morpheus one said, knowing the path is different (and boring) than walking the path. So I am going to try out something different this time.

1. Using Google calender, I have put up milestones for the entire month. For example, finish reading with Network Coding till March 7, start searching for wireless project ideas on March 10 and so on.
   
2. It is very important to make realistic targets. I remember one of my friends, whose plans for the final exam read like: 'Finish entire syllabus of Physics and Chemistry till Monday, redo all the 15 assignments on Monday night, do all the practice problems in the book on Tuesday morning, etc'. Trying to poke a hole in the sky might make you a better archer but eventually you will get frustrated with constant failure. You might take consolation in the fact that you have done good work and the aim was just too high anyway. But this is when you make failing a habit and lower your confidence. You start taking challenges which are either too easy (so that you are sure of completing them) or too difficult (since failing it is already your second nature). Again, from experience, if targets are constantly on the higher side and you happen to achieve one of them, it does feel great at first. But the victorious feeling tends to persist longer than it should and starts affecting the next target.
   
3. I think if targets are spaced out properly, I will be able to take out time and be guilt free at the same time.

Let us see how this one goes.

Update (3/5): Here is now my calender looks now. The brown entries correspond to day-to-day activities and commitments. The blue entries correspond to the milestones set by me. It seems to work out well so far since I am able to achieve my goals and do even low priority tasks (such as going to the gymnasium).
By the way, the cool photo is from Google calender. And it seems DivX Inc. took my comment to heart and shut down stage6.divx - God bless them.

Doing Better Research

I have been slacking off a lot recently. I think it is time for a little retrospection.

1. Listening to presentations: This is something I am very bad at. Usually most presentations are not in my exact area and the presenters are not always very good ones. They always begin well by giving a broader picture and the motivation for their work. This part usually interests me. But soon I start getting lost into the mathematics and eventually loose interest. Trying to take in information like a sink is neither interesting nor recommended.
• The mathematics part usually involves description of some tools or techniques the author has employed. Since my work also involves use of such tools, it is a good idea to try to make a note of these.
  
• To benefit fully from a seminar/presentation, I think it is necessary to know atleast the basics of that area. Thus it might be a good idea to do a google search on that topic before hand, and spend about 15 minutes reading the basics to get started, before the presentation.
• Whenever there is a waning of interest because of too much mathematical details, it might be a good idea to stop listening to the presenter and go up one level. Remind oneself of the point the presenter is trying to make by doing this proof. Try to think beyond the presenter (what he might have done in his later slides, what should be the natural extension of the work and what could be some practical issues with the presenters implementation ?)
2. Reading papers: Depends upon if the paper is in my area or not.
   
• If it is, I must spend atleast half an hour contemplating what the author could have done after just reading the abstract. Since I have been doing research in that area, understanding what the author is proposing simply after reading the abstract may not be that difficult. Of course, later that paper has to be read in detail and possible extensions should be thought of.
  
• If, on the other hand it is something that I have to learn, it might be a good idea to read the abstract, introduction and conclusion. Write down what is being proposed and what could be the possible extensions. Then move to the system model. A research journal entry should follow.
  
• If it is something I am just using as a look-up for use in my research, glossing over it should be fine. But do not look up unless you are absolutely sure you can not solve the problem by yourself. Simply Googling whenever in doubt is NOT recommended.
  
3. Attending classes: This of course have many caveats.
• Mathematical details cause loss of interest: Follow the same strategy as presentaions; try to think of possible implications and applications of the course material in your research.
• Mathematical details are too trivial: try to find shortcuts. Correlate with other non-trivial parts.
  
• Class is a bouncer: try asking more general questions (such as the intuition behind the results). Create analogies and ask if they make sense. Do not let the instructor think that you are able to understand.
• Class itself is quite trivial: fall asleep and make sure to snore as loudly as possible.
  
4. Keeping up the motivation: try reviewing what has been achieved in the last week. Compare it to a more productive week you have had in the past.
   

Exam Time and Emma

Exam time is usually the most imaginative time for me. It is when I am completely burdened with ToDos, that I tend to loose my concentration and wander into reveries. I imagine things that I would do after the exams, things that should be done in general, future planning or simply a plot for a blockbuster movie.
It was Monday night and I had to submit a project by Tuesday midnight. I was unable to make the simulations run and the report was not even half complete. I decided to stay in the lab for the night hoping to finish things till dawn have a sweet morning sleep. At approximately 2am, I ventured into the story of how Emma tried to take over the internet.

Of course, Emma was not a girl that I was fantasizing about; instead she was an artificially intelligent program, written by a graduate student in midwest, which employed human like memory structure consisting of nodes containing concepts linked to each other in virtual hyper space. I spent approximately two hours working on the story and amount of creativity I had generated is enough to make two movies. On the downside, I had to stay in the lab for the next 23 hours and went home next day at 1am. Unfortunately, I still have my last exam tomorrow which means I will be telling you the story some other (exam) day.

Approximate Square Root

Unlike most of my friends who simply dove into the JEE preparation after announcement of their tenth results, I spent my summers reading Asimov and playing with numbers. In fact more than half the time of my class XI was spent just playing with Mathematics, rather than solving problems of the correspondence courses and joining coaching classes. I remember the thrill and excitement that came from exploring the woods of numbers and the freedom to choose my own direction. In fact my interest in mathematics could largely be attributed to that period alone.

I discovered this formula way back in the starting of class XI. The formula is startlingly simple and gives good results in most cases. Furthermore, I barely knew enough calculus at that time to actually prove it and I am always amazed at how useful it has been.

Given a number x, choose any a such that a^2 is the closest to x (and you remember the 'a and a^2' pair; that usually happens with integers). The approximate square root of x is simply (x+a^2)/2a. One could alternatively express it as a+(x-a^2)/2a if that sounds easier. The proof is a simple class XI exercise in calculus.

Around that time I read another approximate formula for square root in Mathematics Today. Comparing the two, I found that their formula was much less accurate and had a smaller domain of applicability. I remember that I was very encouraged by this fact and even wrote to them, though they did not publish my work.

Visualizing Complex Signals

Since I have been in third year, I have been dealing with complex signals. Now real signals are always easy to visualize but the same is not the case with complex signals. Since a large portion of my work involves getting a feeling of what is going on, trying to see the signals from an engineer's eye is always considered a better approach than simply doing algebraic juggling.

The most logical method that comes to mind is expanding of the real axis into an entire plane facing the time axis. A complex exponential like exp(jwt) will then appear to be a spiraling staircase. An extremely useful matlab program which takes in a complex signal and outputs a 3D complex plot is given below:

function complexplot(x,t,connect)
% This function plots complex sequences in 3D line format
% x is the given complex sequence (1D)
% t is the optional time axis. By default t = 1:length(x)
% put connect = 1 if you want to connect the plot with the axis

%% Input validation
if (nargin <>
connect = 0;
end
if (nargin <2)
t = 1:length(x);
end

%% plotting 3D
x1 = real(x);
y1 = imag(x);
axisline = zeros(size(t));
plot3(axisline,t,axisline,'k');
hold on
plot3(x1,t,y1);

%% Connect lines
if(connect ==1)
for k = 1:length(t)
plot3([x1(k) 0],[t(k) t(k)],[y1(k) 0],'r')
end
end

view([90 0])
hold off

Gbps Internet

The fourth generation mobile systems claim to achieve few Gbps of data rates on short ranges. This means that you can download an entire movie in less than a second. There is a lot of research going on ad hoc networks.

Idea : Imagine an environment where you have wireless connection to Gbps internet all the time. This can be achieved by carefully placing small 4G devices distributed throughout the place. These devices cooperate among themselves similar to sensor motes do. They are finally connected to a central server that connects you to internet.

Challenges : 4G is still in embryonic stage. Routing in sensor nets is largely at theoretical level. At least 10-20 years are required to make a commercial system, though test systems can be made with current technology.

Animations

With increasing technology, it is possible to make images in photoshop that look almost real. If you don't believe me, just have a look at this http://www.bertmonroy.com/fineart/text/fineart_damen.htm.

Idea : Imagine animated movies that look as real as normal movies. And normal movies putting in a lot of special effects looking as unreal as animated ones. Soon the two will be indistinguishable. And you can see all your favorite actors again - imagine seeing movies of Kishore Kumar or Charlie Chaplin using mobile phones and computers. Since normal filmaking is a costly project involving a lot of people management, the industry will gradually move to animations until finally all you see will be animations stuffed with all your favorite actors looking as real.

Challenges : The pace at which technology in film industry moves seems to be really slow. Increasing realism in animations is a very difficult task. Also the best animations available like Final Fantasy and Animatrix (first story) are actually far from real. Atleast 10 years till they start looking real and another 5 till industry actually accepts this as a cheaper form of production - maybe more.

Some more di : 3 LOTR movies incurred a production cost of $300 million. Compare with a huge company having 2000 animation engineers @ $10000 per month for an year (a rather overpaid and hence dedicated team; salary of $240m), 100 managers @ $15000 pm ($18m), hi-fi computers @10000 for each employee and 500 extra machines ($25m, not considering the fact that most computer parts do not become outdated in an year) plus overheads(marketing etc) of as much as $25m, totalling to $300m, can produce a superb movie, atleast 10 yrs down the line if not earlier (figures ignore the inflation rate).

Update in Apr 2009: Looks like this one is coming true. For one, the number of animated movies has increased tenfold in just 4-5 years. Further, digitally engineered characters are no longer a fantasy. The movie "X-men Origins: Wolverine" shows a young Charles Xavier, a digitally modified Jean-Luc Picard. Also an all digital Arnold Schwarzenegger appears in Terminator Salvation.