USA yesterday, France today, India tomorrow

When I board the plane for India next week, and hopefully before I grow web feet, it will be the third country and continent I will have visited in less than a month. This itinerant researcher travels easily in time and space and culture only because I take my internet bubble with me everywhere. I am so completely entertained and enthralled by Kishore's hijinks, I could be anywhere and want for nothing.

USA yesterday, France today

The interlude is now over and I am back to overcast Rennes. A world away in the Florida bible belt, Anuj Srivastava is doing very interesting work with Riemannian shape spaces and one of its applications is to DTI white matter fibers. In working with anatomical brain data sets, I have found that for successful classification, we need to use a combination of physical features. So although Dr Srivastava's primary interest is in shape spaces, some of our work in the last year has been to define joint manifolds which can be used for a variety of classification tasks--clustering, labeling, atlas building and quantitative analysis for differential diagnosis. These manifolds may be extended to enable joint analysis that uses not just physical features but also scalar functions.

World Mosquito Day

It is true, there is such a day. Ross spent months, years even bent over a microscope, with only buzzing mosquitoes and whimpering natives--feverish volunteers for his grand experiment--for company. In this narrow blinkered world, you start believing the myths you tell yourself to egg you on. One dapple-wing on the microscope and then another and another and another, four in all from his set of ten now offered up clues to the mode of transmission. To mark this moment and in keeping with the tradition of hubris that is the hallmark of European discovery, he declared Mosquito day.

By coincidence I've just finished reading The Calcutta Chromosome. Central to the story, which might be described as historical science-fiction, a medical mystery with traces of Sherlock Holmes, is Ross, and this discovery on August 20th. Coincidences weave through the plot and I'm not entirely sure, if having read the book, I might not now be part of this bizzare tale. There are many reviews on the web, I think the general consensus is that the author was in a hurry to finish the book. I give seven out of nine dapple-wings to this highly entertaining story.

Differential geometry

Many of us across diverse application domains--data mining, handwriting recognition, computer vision, medical image analysis--are finding that we need at least a passing familiarity with differential geometry. Differential geometry supplies tools to do computations and analysis in nonlinear spaces or manifolds.

In medical imaging, the nonlinear manifolds might be the shape spaces of continuous curves or surfaces, or it might be the space of positive definite matrices used in diffusion tensor imaging (DTI). In computational geometry, it might be the space of 3D rotations SO(3) and in data mining, the working assumption is that the ubiquitous high dimensional data actually reside in tractable lower dimensional spaces--in nonlinear manifolds.

Some of these useful tools from differential geometry are tangent spaces, geodesics, exponential maps and inverse exponential or log maps.

Afternoon tea in London

Lazy afternoons and tea--my two favorite things. And the English have combined these and made it an institution. So naturally when I was in London last week, I stopped by for tea. Sketch is an ultra trendy place in Mayfair--but how does this compare with an English afternoon in Dubai or Paris? Dubai--I was there in April--was most English. I don't know, it might have been the unhappy brown skinned waitstaff in full livery that reminded me of that very English place, the Viceroy's lodge in Fort William!

Florida in August ...

or France? Well, all of France has shut down whereas Florida is just hot, humid and worse than Singapore. I think I'll take Florida.

Now this is a perfect scene.

It's Pléneuf Val-André, Brittany at its best. It's France in the run-up to August. (Our group went there for a retreat in June. Well, I retreated, some others were paying tribute to Machiavelli.)

So why do I prefer Florida? I'll be working with Anuj Srivastava at FSU, This will be my first opportunity to work closely with a professor. And there will be 4 months of this. I'm excited.

I should mention I have a grant from UEB, and if that is not enough, my regular INRIA CORDIS grant is there. One should be grateful even if it is August and Thanksgiving is many months away.

Language Pathways

I'm looking at the arcuate fasciculus, a white matter fiber tract that serves as a relay between the Broca and Wernicke region of the brain. As background, I'm reading some papers by Marco Catani who has done some interesting work on the language networks in the brain.

Language models have their roots in the 19th century and in the first part of this paper, Catani et al. survey these early models. Then as now, the understanding progressed in small increments, and indeed the picture is still evolving. One physician, Reil, identified the arcuate fasciculus, perhaps in the dead of night in a cold disection room full of cadavers. A second (Burdach) named these fibers. A third, Wernicke, proposed a model linking the Broca and Wernicke regions and a fourth, Constantin von Monakow, suggested that this link was in fact the arcuate fasciculus.

(To be updated)

Linear Algebra like you've never seen before

Of course, in Mathematics there are rockstar performers too. Take this lecture by Gilbert Strang. The audience is involved, the delivery is brilliantly timed, you see things you never saw before and you leave wanting more. Luckily, there is a whole series of these lectures.

And there are even more of his lectures on the MIT OCW website.

Oh, and since the topic was positive definite matrices, there are 3 ways to tell if you have one (t=47:17 on the video):
1. all the pivots are > 0
2. all the eigenvalues are > 0

3. \quad x^TKx > 0 \quad \forall x \neq 0 

Latex on Blogger

To set-up latex, I modified the Blogger Layout using these simple instructions.

And now I can happily type in equations such as this:

\int_{0}^{1}\frac{x^{4}\left(1-x\right)^{4}}{1+x^{2}}dx
=\frac{22}{7}-\pi.

Updated February 2012
The above does not work any longer on my version of the blogger software. Please Make A Note lists another source with which I get:

for the equation above.

Remembering MJ

The year was 1983. MTV was new. Everything actually--I had just come to America. And this video had me mesmerized.

These days I prefer Manish Vij to Michael Jackson. Read his tribute--and you'll see why.

Topographical classification of the corpus callosum

The corpus callosum(CC) has no obvious landmarks. This is more true for the large central corpus than the more distinct genu and splenium. Methodologies for partitioning the CC are summarized here.

The Witelson scheme, the oldest, dating back to 1989, is used as a reference in this paper, to initialize bundles for clustering by Expectation Maximization (EM).

Creating DTI fiber bundles with spectral clustering

Recent work (2004-2007) at the Harvard LMI lab has shown that spectral clustering can be successfully used to create bundles from DTI fiber tracts. These clusters do not always correspond to anatomical bundles but they do to a large extent.
The picture on the right shows DTI fiber tracts extracted from the corpus callosum.
Some of my results of spectral clustering, applied to this data set, are presented below.





The clusters are consistent across 12 same-sex subjects--we get bundles from the rostrum, genu, corpus and splenium, the 4 sections of the corpus callosum, in each case. The distance measure is the mean closest point described in this paper by O'Donnell and Westin. Interestingly, a median closest point distance failed to produce more than one cluster--i.e. the distances between individual fibers were all the same in this case.

VOST--Version Originale Sous-Titrée

Danny Boyle on filming in Bombay:

There's lots of things that can be solved with cash. And there's occasional things that can't be solved with cash, which become a bureaucratic nightmare for some reason, and there's no distinction between the two. There's no way of reading a situation and saying, "Yes, that'll be a bureaucratic nightmare, but that one we'll be able to buy off." It just depends on the day, apparently. The most extraordinary thing, you'd be given permission for, and then the weirdest, simplest things, you just wouldn't be able to obtain permissions. And it would go on and on and on forever and ever, and there was no way to know. You have to kind of approach it with an open, quite optimistic mind, no matter what's thrown at you, because it will only ever result in damaging the film if you let any kind of despondency get to you. You have to remain optimistic, and that's clearly how people live their lives there. Against all the odds, they retain kind of a spirit which allows them to get through against insufferable odds. The poverty, the traffic, the lack of infrastructure, the flooding during the monsoons—there's just so many things that are coming at you at the whole time that your spirit has to remain, and that's certainly true. It enters the minutia of filming.

A timely and very handy piece of advice. I'm off to the movies now because I think there will be more research tips where that came from.