Thursday, December 30, 2010

CS: A comment on USPS as a continent sized sensor/ Diatoms and Flower Constellations / Concave regularizations and MAP priors for sparse topic models

I usually illustrate blog entries with the most recent raw images taken by the Cassini spacecraft as I want to be reminded that we are currently discovering new worlds as we speak. Two days ago, you may have noticed that Saturn had a feature that looked like a feature that could be found on Jupiter. The Bad Astronomy blog has a piece on this new feature. It looks like a storm ... a large one.

In a comment to yesterday's concept of using the USPS as a continent-sized sensor, Meena Mani said:
"It is simply amazing to have such a forward looking concept being articulated. " And now that it has been articulated it seems amazing that it hadn't been before. I think, it has to do with privacy concerns.
The privacy issue is being addressed in the report and I agree that it may indeed be a big deal. However, there are a lot of non-imaging capabilities that could be instantiated (electromagnetic, aerosol,...). Even some imaging capabilities could be implemented without much risk to privacy. For instance, what about using hyperspectral imaging in support to either pollution assessment or precision agriculture.Concepts based on the use of cheap CASSI Imagers would be ideal for that purpose. Well it looks like others are also thinking about giant sensors like the people behind the Living Earth Simulator. For one thing, I'd rather we use already existing infrastructure such as either the USPS or the electric grid.

On a totally different note, I came across the mention of diatoms (Dick Gordon is working on these things). According to wikipedia,

Diatoms[1] are a major group of algae, and are one of the most common types of phytoplankton. Most diatoms are unicellular, although they can exist as colonies in the shape of filaments or ribbons (e.g. Fragillaria), fans (e.g. Meridion), zigzags (e.g. Tabellaria), or stellate colonies (e.g. Asterionella). Diatoms are producers within the food chain. A characteristic feature of diatom cells is that they are encased within a unique cell wall made of silica (hydrated silicon dioxide) called a frustule. These frustules show a wide diversity in form, but usually consist of two asymmetrical sides with a split between them, hence the group name. Fossil evidence suggests that they originated during, or before, the early Jurassic Period. Diatom communities are a popular tool for monitoring environmental conditions, past and present, and are commonly used in studies of water quality.

I was stunned by the shape of these diatoms as they all resemble some instances of much larger objects.

For instance, the five stars shape diatoms occur only inside circles (l_2 norm = cste). This is probably a coincidence but when Daniele Mortari designs his Flower Constellation orbital trajectories for spacecratfs orbiting earth, the five star shape also appears in a circle envelope. Let us remember that his trajectories appear in a 1/(l_2 norm)^2 well. Matt Wilkins' thesis on the subject of flower constellations can be found here. There are many configurations for these orbital trajectories that seem to be dependent on six parameters and I clearly remember that you could produce those straight/convex/concave triangles and sqaure shown above.. Flower constellations around Earth have a size of about 50,000,000 meters while diatoms have size of the order of 2-200 micrometers, that's about 13 orders of magnitude!

 I just found this final report for a course at Cornell: Concave regularizations and MAP priors for sparse topic models by Johan Ugander


Kevembuangga said...

For instance, the five stars shape diatoms occur only inside circles (l_2 norm = cste). This is probably a coincidence ...

Or not, the shapes look so similar that they could very well be made by entirely identical or at least isomorphic iterated function systems (functionally, not in their embodiments).
Then the funny question would be, what is the "thing" which crawls around the Diatoms shapes the same way as a craft in orbit?
May be we are oblivious of a few extra dimensions in the process of form creations, not extra physical dimensions above space-time but dimensions in the state space of the growth process.

Igor said...

You are right, maybe not. What I am really thinking about is that the shaping of that bio process make be the equivalent of the discrete process shown in the spacecraft constellation. More specifically, the diatom shape would probably be a cue that the membrane making up the diatom follow a 1/r^2 law which would be a different potential than the 1/r^6 of the Van der Walls potential. In short, there is something in how these molecules makings up the membrane are put together that makes it that the short and long rang potential behave as 1/r^2 (as opposed to the usual expected 1/r^6). It is obviously speculation at this point but I think it needed to pointed out in some fashion.