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Archive for the 'Computers & Mathematics' Category
If you are a scientist you will frequently want to write an equation in your blog. The methods that are commonly used are quite inelegant. In this article I talk about a wonderful new way to write equations in Wordpress through the use of LaTeXMathML. Actually this method will work for any webpage, not only Wordpress blogs.
Typically, you will use a plugin that allows you to write LaTeX in your blog. The plugin will translate LaTeX to images of the equation when your blog is viewed in a browser. That can be a problem when you have many equations (pages with a gif for every equation is definitely not cool).
Philosophically you might also ask: Why should math be treated on a different footing? Text for everything else but images for equations? You may also be worried about the loss of semantic meaning. Text can be understood by search engines but images (of equations) cannot. If equations could be understood by search engines it would allow all kinds of applications like searching for particular equations and so on in the future. Enter MathML. MathML is a markup language like HTML used to display mathematical expressions. Currently MathML is understood only by Firefox. Internet Explorer understands it but you need to install the MathType plugin.
So how do you go about using LaTeX in your Wordpress Blog? The simplest way is to install a link to Javascript code that dynamically converts all your LaTeX code between two successive dollar signs into MathML. Sample:
\$\omega = \omega_0 + \sum_{i=0}^{30} n^2\$
gets converted to:
$\omega = \omega_0 + \sum_{i=0}^{30} n^2 + \int_{0}^{\infty} \frac{\sin x}{x} dx$
Note that this will only work on Firefox. Whats cool that the above math snippet is not an image…you can select parts of it with your cursor. Go ahead and try it out!
To get this working on your blog enter the following HTML code in your Wordpress header. Go to Presentation->Themes. Edit the header code. Insert the following:
<script type="text/javascript"
src="http://www.maths.nottingham.ac.uk/personal/drw/LaTeXMathML.js">
</script>
You enter LaTeX as and when you require it in your blog post by putting it between two dollar signs. The Javascript dynamically converts LaTeX to MathML when page is accessed using the Firefox browser. It doesn’t seem to work in Internet Explorer yet…though in theory it should work with the MathPlayer plugin installed.
To learn more, check out LaTeXMathML. Happy LaTeXing!
This is a story of how the impossible became possible. How, for centuries, scientists were absolutely sure that solids (as well as decorative patterns like tiling and quilts) could only have certain symmetries – such as square, hexagonal and triangular – and that most symmetries, including five-fold symmetry in the plane and icosahedral symmetry in three dimensions (the symmetry of a soccer ball), were strictly forbidden. Then, about twenty years ago, a new kind of pattern, known as a “quasicrystal,” was envisaged that shatters the symmetry restrictions and allows for an infinite number of new patterns and structures that had never been seen before, suggesting a whole new class of materials. By chance, solids with five-fold symmetry were discovered in the laboratory at about the same time. Even so, for nearly twenty years, many scientists continued to believe true quasicrystals were impossible because, they argued, such a pattern could only be formed with complex and physically unrealistic inter-atomic forces.
Impossible Crystals is an abstract but ultimately satisfying video lecture by Paul Steinhardt, Albert Einstein Professor of Physics at Princeton University. The presentation is targeted at the layman but realistically, some background in solid state physics/symmetry is necessary to appreciate what Steinhardt is saying. You don’t need a high speed internet connection: you can simply download the PDF and listen to the MP3 of the presentation. There are many other public lectures available for download at Perimeter (see link that follows).
Link to the presentation (look for Impossible Crystals)
Wikipedia entry for Quasicrystal
Wikipedia entry for Aperiodic Tiling
Another teaser image
You may know about del.ici.ous the social bookmarking site that allows you bookmark, tag and share your favorite sites.
Along the same lines there is CiteULike. Conceptually its like del.ici.ous but its much more than that. CiteUlike is targeted at the research community. Citeulike allows you to:
- Simply specify the URL of a research paper (on Science, Nature, PRL etc.). CiteULike will automatically pick up the details like abstract, authors, DOI link etc.
- Tag your papers so you can search for them later
- Upload your papers so you can build a online repository of your favorite scientific papers
- Become members of user groups with similar research interests as yours and share papers with them. This way you will never miss out on any important papers
- Other cool features like rating a paper on how important it is to you. You can prioritize your reading time by using this feature.
CiteULike is an amazing tool and I use it to organize all the research papers I’m interested in.
Interested? Here is the FAQ for CiteULike.
I’m very excited to talk about an open source mathematics system: SAGE.
SAGE aims to be an open source replacement for MATLAB/Mathematica/Maple. Whats amazing about Sage is the great functionality it gets by working nicely with already available open source math software (Maxima, Numpy etc). Its cute slogan “Building the car instead of reinventing the wheel” summarizes its software reuse philosophy. Because SAGE incorporates many different software projects, its quite complete (though it may never be as consistent or clean like a Mathematica or MATLAB). SAGE uses Python which possibly makes it the only computer algebra system that uses a mainstream computer programming language. The use of Python gives SAGE tremendous flexibility and power.
One of SAGE’s most amazing features…which is actually the main point of the blog…is that you can use it online!! This is really cool because you can do this from a browser anywhere on the Internet. In the future, if you are stuck on a computer which does not have MATLAB/Mathematica, despair not for you can use SAGE.
The SAGE online interpreter is available here. The style of SAGE is a bit like Mathematica. You enter an expression into Notebooks and type Shift+Enter to evaluate it. You can do all kinds of nifty things like collaborate with others and publish your notebook on the web.
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Nice introductory video on SAGE. Guaranteed to get you all excited…
Another screenshot
SAGE Logo
Technologies in SAGE
This is BIG NEWS. India has arrived on the supercomputing scene with a bang! As of November 2007, India has the 4th fastest computer in the world!! This supercomputer is located in Pune and cost about \$30 million to build.
Twice a year, top500.org compiles the most respected supercomputer performance rankings. A computer by Computational Research Laboratories(CRL), Pune placed 4th on the November 2007 top500.org rankings. CRL is funded by Tata Sons, India’s largest business group.
My first reaction was disbelief because Indian computers typically do not figure prominently on top500.org. Then I did some hunting on the Internet and reassured myself that it was really all true. Ratan Tata (Industry leader and Chairman, Tata Sons) and Ramadorai (Chairman, CRL and CEO Tata Consultancy Services) were talking about their achievement. Major newspapers were carrying the story.
Then I got worried that perhaps the benchmark numbers were flawed or inflated. We Indians are so used to bad news that good news is hard to believe 
. But those fears were laid to rest when I noticed that the 5th rank was taken by a Swedish government computer that has almost the same processors, architecture, interconnect etc. to EKA*. If the Swedish guys with a similar configuration are 5th, our 4th rank made sense!
Then another thing started worrying me: Supercomputers of this power typically cost \$100 to \$200 million plus. How did our guys manage to build one at \$30 million only? (After all, all the hardware has to be imported…so there would be very little cost savings compared to, say, an American facility). The answer is not clear but a blurb from CRL’s homepage reassuringly says the following:
CRL’s vision is to be a global leader in the field of HPC by developing its own intellectual property and by achieving spectacular disruptions in the prevailing price-performance levels (emphasis mine)
I think what has happened is that we are seeing the emergence of the next generation of supercomputers built with cheaper and newer technologies. CRL is simply the first off the block. In the coming few months we should see more computers based on similar architectures (and low price) causing upheaval in the rankings.
This news item has just made my day. I have a big Math exam today (its 4 am now) and here I am blogging about EKA! Good Night!
November 2007 supercomputer rankings
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*The 4th rank Indian and 5th rank Swedish computers are quite similar in configuration
Indian: Cluster Platform 3000 BL460c, Xeon 53xx 3GHz, Infiniband
Hewlett-Packard (14240 processors)
Swedish: Cluster Platform 3000 BL460c, Xeon 53xx 2.66GHz, Infiniband
Hewlett-Packard (13728 processors)
Some academics cringe when students turn to Wikipedia as a reference for term papers, but this teacher made it an assignment to write a Wikipedia article. Students found themselves having to write differently when works were submitted to wikipedia, vs in the classroom; they were now written for more than one reader.
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