Monthly Archive for August, 2007

Date on a magazine…what does it mean?

Published on August 31, 2007 in Inspirational & Insightful and Opinion, Commentary & Reviews. 0 Comments Tags: , , , .

Outlook Magazine CoverIf I purchase a magazine that says “August 30, 2007″ on its cover what does it mean? Does it mean that the magazine was issued on August 30, 2007 or does it mean that it expires on August 30, 2007?

After a little thought I came to the conclusion that the dates on the magazine should be designed to make the job simple for the magazine seller. Magazines can be quarterly, monthly, fortnightly or weekly. Also, each shops sells at least 50 different kinds of magazines. So the shop seller will find it tedious to calculate the date at which each magazine should be taken off the shelf. There is a simpler solution: the magazine publisher prints the date at which it expires!

Therefore it seems obvious that the date on the magazine is an expiry date and not an issue date.

MATLAB tip: Avoid loops and use surf command

Published on August 31, 2007 in Computers & Mathematics and Opinion, Commentary & Reviews. 0 Comments Tags: , , , , , .

Frequently we will get a function f(x,y) that we will need to plot. The naive way will be to generate an array for x and y and then iterate through all combinations and then use the plot3 function. Here is a sample:

  1. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  2. % Assume function f(x,y)=-(x^2-2)^2 - (x^2-exp(y))^2
  3. % Crude Method
  4. x = -5:.1:5;
  5. y = 1:.1:4;
  6. points=[];
  7.  
  8. i=1;
  9. for xp = x
  10. for yp= y
  11. f = -(xp^2-2)^2 - (xp^2-exp(yp))^2;
  12. points(i,1) = xp;
  13. points(i,2) = yp;
  14. points(i,3) = f;
  15. i=i+1;
  16. end
  17. end
  18.  
  19. figure;hold on;grid on;
  20. xlabel('x');ylabel('y');zlabel('f');
  21.  
  22. plot3(points(:,1),points(:,2),points(:,3),'.');
  23.  
  24. hold off;
  25. Download this code: plot3d.m

But this code is inefficient. Looping is to be avoided in MATLAB because operations on matrices are faster. Moreover, the plot3 function does not give shading. We get the following as the output:

Graph Using plot3

Avoiding loops, we can implement the above code in a different way. We avoid loops and use the surf command.

  1. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  2. % Assume function f(x,y)=-(x^2-2)^2 - (x^2-exp(y))^2
  3. % Better Method
  4. x = -5:.2:5;
  5. y = 1:.2:4;
  6.  
  7. x_2d = ones(length(y),length(x))*diag(x);
  8. y_2d = diag(y)*ones(length(y),length(x));
  9.  
  10. func = -(x_2d.^2-2).^2 - (x_2d.^2-exp(y_2d)).^2;
  11.  
  12. figure;hold on;grid on;
  13.  
  14. xlabel('x');ylabel('y');zlabel('f');
  15. surf(x,y,func);
  16.  
  17. hold off;
  18. Download this code: surf.m

We get the following output

Graph using surf and no loops

The trick in the above code involves creating the x_2d and y_2d array.

References:
(1) plot3
(2) surf

Zero Rupees Note!

Published on August 30, 2007 in Cute, Funny or Weird. 0 Comments Tags: , , , .

If someone asks you for a bribe you could always hand them a Zero Rupees Note.

Zero Rupees Note

Related article on DNA India.

Quick Introduction to Manifolds

Published on August 28, 2007 in Mathematics and Physics. 0 Comments Tags: , , , , , , , , , , , , , , .

Charts and Atlases

My M.Sc. Project at IIT Madras deal with Manifolds and some numerical computations on them.

The initial part of my M.Sc. project introduced Manifolds in general. I’ve put that up on the web. So if you are interested in a quick and dirty introduction to Manifolds, here it is! There are lots of diagrams and figures to make the concepts easy. Its a fun and fast tutorial that can be completed in a few hours.

Here is the Preface

This HTML document aims to introduce Manifolds. It has been derived (mainly verbatim) from parts of my M.Sc. Physics final project. I used Latex2HTML to convert my latex to the HTML you see here.

Manifolds are fundamental structures in Differential Geometry. The study of Manifolds is useful in various branches of Theoretical Physics, especially High Energy Physics and General Relativity. For instance, Einstein’s theory of General Relativity conjectures that space-time forms a 4 dimensional pseudo-Riemannian Manifold. Superstring Theory explains the compactification of extra dimensions by using Calabi-Yau Manifolds.

Manifolds are abstract mathematical spaces that look locally like \small{\mathbb {R}^n} but may have a more complicated large scale structure. The surface of Earth is a simple example: At small distances it looks like the Euclidean \small{\mathbb {R}^2} but from far away it is \small{\mathbb {S}^2}, the two dimensional surface of a sphere. The behaviour at the small scale and large scale can be totally different. For instance, in \small{\mathbb {R}^2} parallel lines never meet while all lines eventually meet in \small{\mathbb {S}^2}. Because all Manifolds are locally like Euclidean Space we can develop common mathematical techniques to study extremely different kinds of spaces.

We can define increasingly complicated structures on Manifolds so that we may do Calculus on them or define concepts of distance and angles on them. We may also want to study Manifolds in terms of complex variables and perform Complex Calculus on them. In this report we look at the whole hierarchy of Manifolds. We start from Simple Manifolds and progress to Differentiable Manifolds, Riemannian Manifolds and lastly Complex Manifolds. Within Complex Manifolds we study Hermetian Manifolds and Kahler Manifolds. Orbifolds, another special kind of Manifold, are also introduced. All the related mathematics and concepts such as Vector Fields, Tangent Spaces, Metrics, Curvature, Parallel Transport and Connection are explained.

Still interested? Here is the HTML document

Indian wins big math prize

Published on August 26, 2007 in Mathematics and Opinion, Commentary & Reviews. 0 Comments Tags: , , , .

prisvinner_2007_lite.jpg

In March 2007 an Indian won a big award in Mathematics. I had written about it at IIT Madras (for a mailing list). I reproduce the writeup here:

The 2007 Abel Prize has been awarded to S.R. Srinvasa Varadhan (Faculty NYU) (Ph. D. ISI Calcutta 1963) for his contributions to probability theory.

The Abel prize is worth approx USD 997,000 and is presented by the King of Norway. The winner is selected by the Norwegian Academy of Science and Letters. Some people say that the Abel Prize is the Nobel equivalent for Mathematics (Though this can be disputed by those who would give that place to the Fields Medal which has a longer history. Interestingly the fields medal is only awarded to mathematicians under 40. This, I believe makes it
a “flawed” prize. Also, the fields medal would only make you richer by US $13,000).

The Abel prize is named after a Norwegian mathematician Niels Henrik Abel who made many impressive contributions before he died at the age of 26(!).
(When something is commutative i.e. a*b = b*a we also call it Abelian in his honour). What’s interesting to me is that Abel rhymes with Nobel :-) Perhaps that bodes well for the prize in the public’s imagination.

S.R. Srinivas did his Ph. D. in ISI Calcutta (1963) and then went for his postdoc at the Courant Institute of Mathematical Sciences at NYU. Incidently he is from Chennai and did his B.Sc. from Presidency (1959).

I have found Tamil translations on the website of the prize. Go to
here for a tamil translation.

Lets go for the big prizes!! We Indians can do it (perhaps not in
cricket??) !

For those who are really interested

The authoritative source
http://www.abelprisen.no/en/

More Info:
http://en.wikipedia.org/wiki/Abel_Prize

Some news articles:
International Herald Tribune

The Hindu
Minor Quibble: The Hindu incorrectly lists the amount as US $850,000. Its
about US $975,000

The most prestigious journals in science and physics

Published on August 26, 2007 in Opinion, Commentary & Reviews and Science & Technology. 4 Comments Tags: , , , , , , , , .

Nature Magazine CoverScience Magazine CoverCame upon a wonderful paper on arXiv that argues that the ISI Impact factor of a journal is not the correct way to judge how “good” a journal is. The paper argues that there are really two factors to rate a scientific journal on:

  • Popularity
  • Prestige

Summer blockbusters like Godzilla or Independence Day may make a lot of money and become very popular but they will not win any Oscars. Similarly, many Oscar winning movies hardly make an impact at the Box Office. In the movie analogy, a “prestigious” movie is liked by critics, directors and the Oscar committee while a “popular ” movie makes good money at the box office.

The authors argue that the ISI Impact factor of a journal is a flawed metric in the sense it only measures popularity and ignores the prestige element. Also, certain “Review” Journals (Journals that contain articles that summarize past research) get cited more often and thus rise to the top of the list (and therefore distort rankings).

The authors develop a ranking of the prestige of a journal (Pr) and multiply it with the popularity (Po) to get a composite ranking that takes into account both factors. The (Pr x Po) Method is compelling.

Personally, I am attracted to the prestige of a journal rather than its popularity. Some, journals are prestigious and popular. Science and Nature are two such journals.

According to the paper, here are the most prestigious journals in Physics today:

  1. Physics Review Letters
  2. Applied Physics Letters
  3. Journal of Applied Physics
  4. Physics Review D
  5. Physics Review E
  6. Journal of Chemical Physics
  7. Physics Review A
  8. Chemical Physics Letters
  9. Journal of High Energy Physics

Taking the Popularity (Po) and Prestige (Pr) ratings and multiplying them (Po x Pr) one gets a slightly different ranking for Physics:

  1. Physics Review Letters
  2. Applied Physics Letters
  3. Review of Modern Physics
  4. Physics Review D
  5. Journal of Chemical Physics
  6. Journal of High Energy Physics
  7. Physics Letters B
  8. Nuclear Physics B
  9. Journal of Applied Physics

Note that the above two lists only take Physics Journals into account. If Nature and Science were to be considered “Physics” Journals they would be placed at rank 1 and 2 respectively for both lists.

Paper Abstract

Johan Bollen, Marko A. Rodriguez, Herbert Van de Sompel
(Submitted on 9 Jan 2006)
The status of an actor in a social context is commonly defined in terms of two factors: the total number of endorsements the actor receives from other actors and the prestige of the endorsing actors. These two factors indicate the distinction between popularity and expert appreciation of the actor, respectively. We refer to the former as popularity and to the latter as prestige. These notions of popularity and prestige also apply to the domain of scholarly assessment. The ISI Impact Factor (ISI IF) is defined as the mean number of citations a journal receives over a 2 year period. By merely counting the amount of citations and disregarding the prestige of the citing journals, the ISI IF is a metric of popularity, not of prestige. We demonstrate how a weighted version of the popular PageRank algorithm can be used to obtain a metric that reflects prestige. We contrast the rankings of journals according to their ISI IF and their weighted PageRank, and we provide an analysis that reveals both significant overlaps and differences. Furthermore, we introduce the Y-factor which is a simple combination of both the ISI IF and the weighted PageRank, and find that the resulting journal rankings correspond well to a general understanding of journal status.

arXiv:cs/0601030v1

Get the paper here (Click on Download on the top right of Page).

True 3D display

Published on August 26, 2007 in Physics and Science & Technology. 0 Comments Tags: , , , , .

3D Display

The ultimate in display technology has always been to achieve true 3D projection. You may have seen this in countless science fiction movies but its not possible with today’s technology. Researchers in Japan have made some impressive advances. I stumbled upon this blog entry that talks about this development. It is amazing.

AIST develops 3D image projector
AIST improves 3D projector
Burton, Inc