Non-gaussian statistics of anomalous diffusion: The DNA sequences of prokaryotes

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 58, Issue 3, 1998, Pages 3640-3648

  Allegrini, Paolo ^a,b   Buiatti, Marco ^b,c   Grigolini, Paolo ^b,c,d   West, Bruce J ^d  

^a INFM   (Italy)

^b UNIVERSITY OF PISA   (Italy)

^c CNR   (Italy)

^d UNIVERSITY OF NORTH TEXAS   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000003625     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.58.3640     Document Type: Article

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24. Note that there is a subtle difference between this kind of non-Gaussian window and that discussed in Sec. III. In Sec. III we defined the non-Gaussian window as the interval of time between the uncertainty sausage overshooting the condition 〈η(t)〉=0 and the approximate time at which the uncertainty sausage starts steadily including this Gaussian condition. Here the non-Gaussian window is a property of the single trajectory, rather than a property of the average 〈η(t)〉, as enforced by the nature of the DNA sequences. The non-Gaussian window could have been determined in the same way as in Sec. III only in the case of the computer generated DNA sequences of Figs. 33 and 44. However, this would have required an exceedingly long computational time. The computer time necessary to evaluate the uncertainty sausage depends essentially on the position of the maximum of the function 〈η(t)〉. The larger the time at which this function gets its maximum, the larger the corresponding computational time. On the other hand, the time position of this maximum is determined by the value of the parameter A of Eq. (9). As regards the results of cases (a) and (b) of Fig. 22, the time position of the maximum, before t=200 and t=500, respectively, was determined by adopting the value A≈0.025. This choice turned out to be compatible with a reasonably short computational time, thereby making it possible to produce the uncertainty sausage of Fig. 22. The CMM sequences resulting in the non-Gaussian indicator illustrated in Figs. 33 and 44 rest on larger values of T and A. This choice generates maxima between t=1000 and t=100 000, namely, conditions comparable to those of the real DNA sequences of Fig. 44. Thus this choice of A and T made it impossible to evaluate the uncertainty sausage within a reasonably short computational time. In conclusion, to save computational time, we have examined only a single sequence also in the case when this can be computer generated. As a consequence, we do not know whether or not the real DNA sequences examined in Fig. 44 produce a non-Gaussian indicator η(t) lying within the uncertainty sausage. Further computational work should be done to establish this important property.
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