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Physical Review E

Volumn 47, Issue 5, 1993, Pages 3730-3733

Finite-size effects on long-range correlations: Implications for analyzing DNA sequences

(6) Peng, C K a Buldyrev, S V a Goldberger, A L b Havlin, S a Simons, M b,c Stanley, H E a

a BOSTON UNIVERSITY (United States)

b BETH ISRAEL DEACONESS MEDICAL CENTER (United States)

c MASSACHUSETTS INSTITUTE OF TECHNOLOGY (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANIMAL; ARTICLE; CHROMOSOME WALKING; DNA SEQUENCE; FOURIER ANALYSIS; METHODOLOGY; NASA DISCIPLINE CARDIOPULMONARY; NASA DISCIPLINE NUMBER 14-10; NON-NASA CENTER; NUCLEOTIDE SEQUENCE; PHYSIOLOGY; RAT; THEORETICAL MODEL;

NASA DISCIPLINE CARDIOPULMONARY; NASA DISCIPLINE NUMBER 14-10; NON-NASA CENTER;

ANIMAL; BASE SEQUENCE; CHROMOSOME WALKING; FOURIER ANALYSIS; MODELS, THEORETICAL; RATS; SEQUENCE ANALYSIS, DNA; SUPPORT, NON-U.S. GOV'T; SUPPORT, U.S. GOV'T, NON-P.H.S.; SUPPORT, U.S. GOV'T, P.H.S.;

EID: 0027605271 PISSN: 1063651X EISSN: None Source Type: Journal
DOI: 10.1103/PhysRevE.47.3730 Document Type: Article

Times cited : (243)

References (14)

1
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- (1992) Nature , vol.356 , pp. 168
- Peng, C.K.¹ Buldyrev, S.V.² Goldberger, A.L.³ Havlin, S.⁴ Sciortino, F.⁵ Simons, M.⁶ Stanley, H.E.⁷

2
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- Long-Range Correlation and Partial 1/fα Spectrum in a Noncoding DNA Sequence
- Long range correlation in a noncoding DNA sequence was reported independently by
- (1992) Europhysics Letters (EPL) , vol.17 , pp. 655
- Li, W.¹ Kaneko, K.²

3
- 0000204878
- and later was confirmed by
- (1992) Phys. Rev. Lett. , vol.68 , pp. 3805
- Voss, R.F.¹

4
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- The long range correlations were found to extend over the entire yeast chromosome III region (315,000 nucleotides) by
- (1992) Nature , vol.360 , pp. 636
- Munson, P.J.¹ Taylor, R.C.² Michaels, G.S.³

5
- 0000142714
- LONG RANGE CORRELATION IN HUMAN WRITINGS
- Very recently, the DNA walk approach has been extended to quantify the nature of long range correlations in human writings (up to 106 characters) [, ] and in heart rate intervals (up to 104 beats) , 70, 1343, C. K. Peng, J. Mietus, J. Hausdorff, S. Havlin, H. E. Stanley, A. L. Goldberger, Phys. Rev. Lett.
- (1993) Fractals , vol.1 , pp. 47
- Schenkel, A.¹ Zhang, J.² Zhang, Y.C.³

6
- 84927468968
- This simple rule is based on the binary classification of four DNA nucleotides; adenine and guanine are purines and cytosine and thymine are pyrimidines.

7
- 0000555231
- (1988) Phys. Rev. Lett. , vol.61 , pp. 1438
- Havlin, S.¹ Selinger, R.B.² Schwartz, M.³ Stanley, H.E.⁴ Bunde, A.⁵

8
- 0000927585
- (1991) Phys. Rev. A , vol.44 , pp. R2239
- Peng, C.K.¹ Havlin, S.² Schwartz, M.³ Stanley, H.E.⁴

9
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- (1992) Phys. Rev. A , vol.46 , pp. R1724
- Prakash, S.¹ Havlin, S.² Schwartz, M.³ Stanley, H.E.⁴

10
- 84927503249
- The property of η*(q)=η(-q) is needed to guarantee that the inverse Fourier transform gives a sequence of real numbers. Equation ( refdelta) can be derived from this criterion.

11
- 84927466745
- This is not the only way to generate correlated variables, but the algorithm of Eq. ( refuq) has two advantages: (i) For β=0, we obtain Gaussian white noise. (ii) For β=2, we obtain Brown noise (a representation of Brownian motion).

12
- 84927496696
- The definition of αlocal will affect its fluctuations. In this study, we measure the slopes of successive pairs of data points that are uniformly distributed on a logarithmic scale of ell. To be more precise, we define αlocal( elli,N) =[ log10 F( elli+1) - log10 F( elli)]/ ( log10 elli+1 - log10 elli), where elli is the integer part of 2i/2) and i=0,1,2,3, ldots. This same definition of αlocal has been used by many authors in the context of calculating critical point exponents; the analog of Fig. 2 was constructed for a range of genes first by A. A. Tsonis, J. B. Elsner, and P. A. Tsonis (unpublished), and by S. V. Buldyrev, A. L. Goldberger, S. Havlin, C. K. Peng, M. Simons, and H. E. Stanley, Phys. Rev. E (to be published).

13
- 84927464548
- We have also checked 34 different sequences (including sequences of length ranging from 3000 to 300,000 nucleotides) and found that the fluctuations in the successive slopes αlocal are comparable to the fluctuations in the artificial sequence.

14
- 84927492954
- For the analogous problem of studying fluctuations in exponent α in d dimensional systems due to finite size effects, we expect that Δαlocal( ell,N) sim ( ell/N)d/2. For a fractal system, d should be replaced by df, the fractal dimension of the system.

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