Additional material to manuscript:

Rényi continuous entropy of dna sequences
Susana Vingaa* and Jonas Almeidaa,b

J.Theor.Biol (2004), vol.231(3), pp.377--388

a*Biomathematics Group, ITQB – Univ. Nova Lisboa, R.Qta. Grande - 6, 2780-156 Oeiras, PORTUGAL.
b  Dept Biostatistics, Bioinformatics & Epidemiology, Medical Univ. South Carolina, 135 Cannon Street, Suite 303, P.O. Box 250835, Charleston, SC 29425, USA.


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Convolution of Normal distribution functions

Download full proof referred in Appendix B [convolution_normal.pdf].

DNA Datasets

Download text files (in FASTA format) with all the DNA sequences used in this study [].


Sequence name Brief description


m3 random with inserted motif L=3 'ATC'


random with inserted motif L=4 'ATCG'
m5 random with inserted motif L=5 'ATCGA'
m7e random with inserted motif with error L=7  'ATC*AGC', *denotes any symbol'


repeated motif L=1, 2000 times 'A'
R5 repeated motif L=5, 400 times 'ATCGA'
MC0 markov chain of order 0, pA=0.50, pT=0.30, pC=0.15, pG=0.05
MC1 markov chain of order 1, p(T|A)=p(C|T)=p(G|C)=p(A|G)=0.91; otherwise p(*|*)=0.03
Es experimental promoter regions of B.subtilis - see paper for full description


MATLAB source code

Current version 1.1 (Sep.20, 2004). Next upgrades will be posted here.

See an application example in RenyiManual.pdf and look at functions' help. Run script example.m

Click to download all functions and documents [], which includes the following files:


File name Brief description
readfasta.m Reads sequences from FASTA format files to struct MATLAB variables

Creates CGR/USM coordinates of a sequence


Variances s2 of the Gaussian kernel tested (see example)

renyi2usm_fast.m Calculates Rényi quadratic entropy of CGR/USM coordinates for several s2 and saves results in a file.
simul_renyi_usm2.m Rényi entropies for random sequences - Montecarlo simulation (calls randUSM.m)
randUSM.m Generates USM coordinates of random sequence
usm_entropy.m L-tuple discrete Shannon's entropy. (Calls entropy_renyi.m)


Calculates Rényi discrete entropy of a vector (counts or probabilities)
example.m script with full example of application
RenyiManual.pdf Brief example on how to use the functions described - uses example.m output


[Alfréd Rényi's Biography][Chaos Game Representation (CGR)][MATLAB site]

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Created: 2004 Mar 25 -- Last update: 2004 Oct 27 
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