For components containing segments with stronger positive correlations
() and fixed
, we find that at small scales (
), the
slope of
does not depend on the fraction
and is close to that
expected for a stationary signal
with identical correlations
(Fig. 10). Surprisingly we find
that in order to collapse the
curves obtained for different values
of the fraction
, we need to rescale
by
instead
of
, which is the rescaling factor at small scales for components
containing segments with correlations
. Thus
is a threshold indicating when the rescaling factor
changes. Our simulations show that this threshold increases when the
segment size
increases.
For components containing a sufficiently small fraction of correlated
segments (
), we find that in the intermediate scale regime there is a
crossover to random behavior with slope
. The
curves obtained
for different values of
collapse in the intermediate scale regime if we
rescale
by
(Fig. 10). We note that this
random behavior regime at intermediate scales shrinks with increasing the
fraction
of correlated segments and, as expected, for
close to
this regime disappears (see the
curve in Fig. 10).
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