Power laws are everywhere. Examples have been found in the number of nodes and connections to them on the Web (pretty eh?) and wealth (the rich keep getting richer). In biology power laws have at least been described in protein interaction graphs and gene family sizes.
Apparently, citations in biomedical literature and research funding (a product of biological researchers) was also found to have a power law relationship as described in a recent paper in Genome Biology. I wonder if this relationship is necessarily the structure of scientific progress?
Now does a power law fit the number of papers being published and referencing power laws? Still too early to tell...
Comments
power law in model organisms
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
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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