Hibernating Squirrels, SVD, and Fire Ant Genetics

Today I Learned:
1) When squirrels hibernate, they lose a significant amount of neurons and synapses. When they awake from hibernation, they very quickly -- within two hours -- start growing a whole lot of new neurons and make a ton of connections, then start pruning them back down, just like a young mammal. Neurologically, then, squirrels go through teenagehood every time they hibernate.

2) ...a nice trick for reducing the dimensionality of very large data sets called Singular Value Decomposition (SVD). The idea is rather similar to PCA, if you know that. The basic idea is to change the basis in which you are looking at your data so that your data fall "more cleanly" on the axes (and no, I'm not going to define what "more cleanly" is here because I don't really understand it yet). The idea is that often there are bases with smaller dimension than your full data on which you can project your data without losing much information. If you can find them, then you can represent your data in that basis and drop some of the dimensions, making them (computationally) easier to work with.

You start by putting all of your data in a matrix M, where the rows are vectors of single datums (say, points in a time series, or positions of a particle in a box) and the columns are dimensions (say, specific times in the time series, or spatial axes in the box). Then you use some fancy math to factor M into some more matrices U, S, and V with M = USV*, where V* is the complex conjugate of V (basically its inverse) and S is a diagonal matrix (that is, all of its elements are 0 except the ones on the diagonal). There's a theorem that says that you can always do this.

Now, the cool thing about U, S, and V is that U and V describe the bases I was talking about earlier, while the elements of S (remember, there are only elements on the diagonal) describe the "scales" of each of those basis elements. Those elements are called the "singular values" of M, and they tell you which bases can be dropped without losing much information.

3) Red fire ants, the invasive and painful species found in the Southern US, China, Hong Kong, and South America, have multi-queen colonies with mixed non-sister worker populations, at least in the US. This condition is called polygeny.

This didn't used to be the case. It used to be that fire ants had distinct colonies, with well-demarcated, fiercely-defended borders (monogeny, the usual situation for ants of most species). Then, one day, there arose a mutation in the Gp-9 gene in one of the colonies. Gp-9 (I don't know what it stands for but I'm guessing "gene product 9") is involved in recognition of self-colony vs non-self-colony. The new polygenious variant a) causes affected workers to not care about defending territories, and b) causes affected workers to hunt down and kill monogenious queens in the nest. Don't ask me how. In any case, because the polygenious variant is so self-selective, it quickly spread through the fire ant population.