Slouching towards Adelaide

At some point when I was in grad school I became aware of some work on symmetric Venn diagrams. If you google this, you will find this link, which has been maintained but not changed too much since 1997. Other than that, there isn't a lot on the web and there is a particular lack of quantitative direction on how to construct the beautiful rotationally symmetric Venn diagrams such as Adelaide. This was named by Anthony Edwards after the city in which he discovered it. I have always wanted to go to Adelaide, it holds a strange attraction for me, so perhaps that is why that particular 7-set Venn diagram stuck in my head.

When I started working on my coloring book, I immediately thought of the Adelaide diagram but I didn't know how to construct it. After some mistakes today, I think I finally have it down. Here is a colored version:



Code (in Sage) for some version of this will be in the final coloring book.

Mixmead

I've had a mead going for quite a while now - started on September 6th, 2008 - which I just racked for a second time. Its proving to be a troublesome brew, perhaps because I never had a clear vision of what it was supposed to be. I have been calling it the "Mixmead" since its a hodgepodge of all sorts of honey that I was able to get in 2008. Here's the exact recipe:

1. 1.5 lbs Late Summer Wildflower Honey (Talking Oak Farm, WI)


2. 3 lbs Northern Brewer Orange Blossom Honey (CA)


3. 3 lbs Skalko's Honey Bee Farm Honey (Esko, MN)


4. 3 lbs Duluth Whole Foods Coops Honey (God Knows Where, USA)


5. 1 cup Northern Brewer's Gold Malt Extract (for protein, rather than that nasty chemical mead nutrient)


6. 1 handful o'hops from Grant Anderson (thank you Grant!)


7. Lalvin EC-1118 Sabayanus Champagne yeast (Champagne yeast:beer yeast::SWAT team:suburban cop)

I racked this on November 16th, 2008, and added 1/2 cup of Hungarian Adro Forest Honey (fantastic stuff). Tasted too sweet then, despite the commando-like efforts of the champagne yeast.


This second racking, I added a tiny bit (3/16 cup) of brown sugar and 2 heavily steeped tea bags of some rather bitter Ceylon tea. I hope the tea will cut the excessive sweetness a bit (this is a pretty traditional thing to add to meads).


If all goes well, this will be bottled in a month.

Cayley Cubic

To further my polynomial education I've been thinking some lately about the Cayley cubic, which in the affine form I was using is given by x^2 + y^2 + z^2 + z(y^2-x^2) -1 = 0.

I made a little movie of some of the real solution set of the Cayley cubic. Here's one of the stills:

I think the quicktime version works better in browsers, or you can download a slightly higher-quality mp4.

Protein of the Day #19: Fto (Fatso)

Protein names are funny things. Often they are chosen before much of the functionality of the protein is characterized, which means they are usually misleading. I wonder how much progress in biology has been retarded over the years by that simple fact.

The abbreviation Fto comes from "fused toes" mutation, but was also initially called Fatso because it is a relatively large protein (about 500 amino acids, nothing close to the huge ones like titin). Ironically, this name is quite important since it seems that Fto is very important in energy homeostasis in mammals. It is highly expressed in the arcuate nucleus. There is some correlation between Fto mutations and susceptibility to diabetes. Because of all that, the preferred descriptive name now is "fat mass- and obesity-associated gene".

Protein of the Day #18: Cruciferina

Cruciferina: sounds like an all-girl punk group or something. I couldn't find out too much about it, its a cupin-superfamily protein that is a desiccation-tolerant seed storage globulin. "Cupin" comes from the Latin "cupa" for small barrel; cupin proteins have a beta-barrel motif that apparently is useful for all sorts of things. Here's one representation of the barrel (not from Cruciferina in particular) from topsan.org:



Various cupin proteins seem to heavily expressed in the floral nectary tissues studied in my friend Clay Carter's lab.

Books I am reading right now

Fiction:

0a. Anathem, by Neal Stephenson. I finished this one, but I am including it because I liked it so much. Not that Neal needs much advertising.

0b. The Algebraist, by Iain Banks. Fantastic cover, at least the US paperback. I finished this while in South Africa too, but it was one of my favorites this year.

1. The Sacred Book of the Werewolf, by Victor Pelevin. Trippy, odd, hard to describe - but good.

2. Wizard of the Crow, by Ngugi Wa'Thiong'O. Sort of like 100 Years of Solitude in Africa.

3. Victory of Eagles, by Naomi Novik. Good series.

4. Turn Coat, by Jim Butcher. I think I have read everything by him, he doesn't disappoint.

Non-fiction (I am leaving out a lot of math and bio books):

1. Imagining India, by Nandan M. Nilekani. Very good book about modern India, where its going and how it got there.

2. The Manga Guide To Statistics, by Shin Takahashi. Surprisingly good. The Manga Guide to Databases is also pretty good.

Curves of Pursuit

When I visited Stellenbosch University in February, I noticed the math department had some nice posters on various mathematical topics that I thought could be implemented in Sage. The only one I did was "Curves of Pursuit", in which one has n points in a regular n-gon, and each point chases the next. The solutions are prettier when discrete time steps are taken. You can see the code at

http://wiki.sagemath.org/interact/graphics#CurvesofPursuit

Protein of the Day #17: mTOR

mTOR (mammalian target of rapamycin) does a whole lot of things, as the attempted pathway image below shows (from Wikipedia, which I am not ashamed to link to for biochemistry). My interest in it comes from its role in energy balance, particularly in synthesizing information in the hypothalamus. Since I am primarily focused on mammalian hibernation, the fact that mTOR is a serine-threonine kinase is intriguing - its known that transcription and protein translation are shut down during mammalian torpor bouts so the control mechanisms are likely to involve post-translational protein modifications such as phosphorylation. Perhaps mTOR is involved in these mechanisms.

5-body woes

I've been working for the last few weeks with Anders Jensen, Eduardo Leandro, Gareth Roberts, John Little, Manuele Santoprete, and Alain Albouy on some celestial mechanics problems. While I was in Goettingen, Anders and I tried hard to get some results on central configurations in the five-body problem. Unfortunately, we hit one very, very nasty special case in our finiteness proof, which has me musing over a couple of big polynomials that start out looking like this:




Ouch!

Back from CA and Goettingen

Blog's not dead yet...just took a 2 month hiatus. I started feeling guilty about not posting, which doesn't make much sense since its my own blog and it has very few regular readers - even fewer now!

Since my wife now has a much nicer camera for her work, I can bring her small one with me on trips. Its too bad I didn't have it in South Africa, but at least I had it in Goettingen last week where I could take a few pictures of the famous goose girl: