power law in model organisms

PedroBeltrao — Mon, 07 May 2007 12:35:29 -0400

Why stop there. We can even study the amount of attention paid to different organisms. From the abstract: "The results demonstrate that the distribution of attention paid to different organisms has a smooth distribution that approximates to a scale-free power law" and "The smoothness of the distribution suggests that there is no empirical basis for dividing species under study into model organisms and the rest (...)".

Power law and coding sequence length

Animesh — Sat, 05 May 2007 14:08:49 -0400

Interesting post Jason. I got so engrossed in this power-law thing that when I was looking at length of M.tuberculosis coding sequences [ftp://ftp.ncbi.nih.gov/genbank/genomes/Bacteria/Mycobacterium_tuberculosis_CDC1551/AE000516.ffn] and when I extracted the length of these using script [http://sharma.animesh.googlepages.com/len_no.pl] in two columns [length\tnumber_of_seq in file len.txt] using console [perl len_no.pl AE000516.ffn > len.txt] and did a plot with R [a <- read.table("len.txt");plot(a);] I found something close to power law at first glance [http://sharma.animesh.googlepages.com/len_dis_plot.jpg]. But then when I fired up the matlab and started curve-fitting [http://sharma.animesh.googlepages.com/pow.m], using gaussing [http://sharma.animesh.googlepages.com/gaussian.JPG] and power [http://sharma.animesh.googlepages.com/power.JPG], I saw:

General model Power:
f(x) = a*x^b
Coefficients (with 95% confidence bounds):
a = 60.57 (39.54, 81.6)
b = -0.3576 (-0.4099, -0.3052)

Goodness of fit:
SSE: 9653
R-square: 0.2284
Adjusted R-square: 0.2274
RMSE: 3.474

General model Gauss:
f(x) =
a1*exp(-((x-b1)/c1)^2) + a2*exp(-((x-b2)/c2)^2) +
a3*exp(-((x-b3)/c3)^2)
Coefficients (with 95% confidence bounds):
a1 = 7.408 (5.589, 9.227)
b1 = 364 (343.6, 384.5)
c1 = 137.5 (102.9, 172.1)
a2 = 5.621 (4.583, 6.658)
b2 = 1082 (866.5, 1297)
c2 = 814 (640.4, 987.6)
a3 = 4.863 (2.797, 6.929)
b3 = 744.7 (701.4, 788.1)
c3 = 260 (175.8, 344.2)

Goodness of fit:
SSE: 4542
R-square: 0.637
Adjusted R-square: 0.6333
RMSE: 2.393

Obviously I was wrong about Power-law and clearly 3 mix Gaussian had a better fit. So much for clearing a confused mind :).

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nodalpoint.org - Power Law - Comments

power law in model organisms

Power law and coding sequence length