Difficult part: It took me a fair amount of time to understand why N2 in figure 6.3 is an equilibrium point, though I think I realize why now (it should be because qEN is being subtracted from the other plot, and thus the result will be 0 at N2, indicating an equilibrium point). Other than that, I generally understood the reading, though "unit effort" struck me as an odd concept.
Reflective part: It's interesting that despite the depensation model seeming to account for damaged fish populations, Myers et al. found this generally not to be the case (assuming the validity of the study). Also, as I implied earlier, I'd be interested to see how exactly E translates into the real world.
Monday, October 22, 2007
Sunday, October 14, 2007
October 16
Difficult part: for the most part, the reading seemed fairly straightforward, especially since I've already had differential equations. That said, I'm not sure where the constants in equations (1), (2), and (3) in Cayrel et al. come from.
Reflective part:
This seems somewhat different from what we've done thus far, in that the underlying math is not terribly complicated, but the scientific principles from which the math is derived are fairly involved and, in the case of Cayrel et al., comprise the bulk of the paper (contrast to the phyllotaxis paper, which focused almost exclusively on the math, while hand-waving the science). Cayrel et al. seems fairly obtuse, but much of the difficulty comes from astrophysics, rather than the math.
Reflective part:
This seems somewhat different from what we've done thus far, in that the underlying math is not terribly complicated, but the scientific principles from which the math is derived are fairly involved and, in the case of Cayrel et al., comprise the bulk of the paper (contrast to the phyllotaxis paper, which focused almost exclusively on the math, while hand-waving the science). Cayrel et al. seems fairly obtuse, but much of the difficulty comes from astrophysics, rather than the math.
Wednesday, October 3, 2007
October 4th, 2007
Difficult part: the most difficult part was easily the derivation of the generalized Zipf's law. In particular, I'm not entirely sure what the normalization condition mentioned in 3 is (though I have some idea).
Reflective part: the two papers seem to demonstrate, quite effectively, the perils of neglecting to thoroughly examine one's model to make sure it really supports what one wants to say. Zipf assumed that the correlation seen between word rank and frequency was due to some "law of economy", when in fact it derived inherently from the nature of his model.
Reflective part: the two papers seem to demonstrate, quite effectively, the perils of neglecting to thoroughly examine one's model to make sure it really supports what one wants to say. Zipf assumed that the correlation seen between word rank and frequency was due to some "law of economy", when in fact it derived inherently from the nature of his model.
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