Misc

[University Rankings]

 

From observation at the local lake, about half of the birds are coots, 30% are ducks, and 20% are swans.

Most ducks and swans, say 90%, have been seen to waddle. No coot has been seen to waddle (but maybe one could), pr(B waddles|B is a coot) = 0.1, say.

Most ducks, say 90%, have been heard to quack. No coot has been heard quacking, pr(B quacks |B is a coot) = 0.1, say. Similarly for swans.

Someone reports that a certain bird, X, was observed to waddle and to quack. What species, S, is X?

pr(B is a S|B waddles & B quacks) ∝ pr(B is a S) . pr(B waddles|B is a S) . pr(B quacks|B is a S),^†

pr(X is a coot) ∝ 0.5 × 0.1 × 0.1 = 0.005,
pr(X is a duck) ∝ 0.3 × 0.9 × 0.9 = 0.243,
pr(X is a swan) ∝ 0.2 × 0.9 × 0.1 = 0.018,
total  0.005 + 0.243 + 0.018 = 0.266.

pr(X is a duck | X waddles, X quacks) = 0.243 / 0.266 = 0.91 -- if it walks like a duck and talks like a duck it is (probably) a duck, according to naive Bayes. (Bayes because of the use of Bayes's theorem^†, and naive because waddling and quacking are assumed to be independent.)

 

The Federal Court of .au ruled [FCA 65] against 'Cancer Voices [.au],' and for "US-based company Myriad Genetics and Melbourne-based Genetic Technologies, over the patent on a breast and ovarian cancer gene known as BRCA1 ... Justice John Nicholas ruled that the gene could be patented, as it had been isolated completely separately from the human body.", -- [abc][15/2/2013]. Also see FCA65@austlii [www][2/2013].  A pity, I think.

 

The International Table Soccer Federation [ITSF] (i.e., foosball) has [rules] and videos of past championships [www] online.

 

Have finally disentangled the mathematics in the various meandering explanations of the von Mises - Fisher probability distribution on directions in R^D and of MML-ing it.

 

In some cultures sons are valued more than daughters and the male:female sex ratio at birth is much higher than one (ultra-sound, abortion, ...); the ratio is reported to be as high as 1.19:1 in China (WDB). Fisher (1930) showed that natural selection drives the ratio to 1:1 : Every child has one mother and one father. If there is an excess of males, a male has a lower chance of having children than a female. (And v.v. if there is an excess of females.) So, someone having a daughter in such a culture is more likely to have grandchildren than someone having a son. A tendency to have daughters is being selected for. Just give nature time.

(Note, selection drives the ratio at reproductive age to 1:1. The argument does not hold for all species, e.g., where females have multiple young, over time, after a single mating, say. Search for [sex ratio biology] in the [Bib].)

 

The alien computer design in A for Andromeda (1961) still looks more than a match for a human in terms of neuron numbers, but not in synapses; there again, there's the matter of speed.

 

The stable marriage problem featured in the 2012 Nobel prize for Economics.

 

Dilbert is a documentary.

 

The good old Iterated Prisoners' Dilemma (IPD).

 

Enumerating all sequences of n pairs of matched brackets is equivalent to generating rooted, ordered, k-ary trees.

 

The Jacobi algorithm finds Eigen things of a real, symmetric matrix.

 

I really wish I had invented the Burrows Wheeler transform, in which case it would not be known as the BWT.