Biology Reference
In-Depth Information
To assess statistically the probability that a significant rhythm is
present in y
lr
(t) (in relation to, or as modeled by, a cosine functional form
of the corresponding period and optimal phase), COSOPT employs
empirical resampling methods applied directly in terms of the parameter
b
at each test period and corresponding optimal phase. One thousand
Monte Carlo cycles are carried out in which surrogate realizations of
y
lr
(t) are generated by both (1) randomly shuffling the temporal
sequence of the original data; and (2) adding pseudo-Gaussian-
distributed noise to each surrogate point in proportion to the
corresponding value of point uncertainty (e.g., replicate SEM). In this
way, both the influence of temporal patterning and the magnitude of
pointwise experimental uncertainty are specifically accounted for in the
surrogate realizations. Then, as with the original y
lr
(t) sequence, optimal
values of
2
, and
retained in memory for each surrogate at each test period/optimal
phase.
a
and
b
are determined, along with a corresponding
w
For each test period/optimal phase, the mean and standard deviation of
the surrogate
b
values are then calculated. These values, in relation to
the
value obtained for the original y
lr
(t) series, are then used to
calculate a one-sided significance probability p based on a normality
assumption (which is, in fact, satisfied by the distribution of
b
values
obtained from the 1000 randomized surrogates). This probability is then
multiple measures corrected (MMC) for the number of original data
points comprising the time series to obtain the probability p(MMC)
b
¼
p)
N
, N
¼
1
13, which provides a more conservative assessment of
significance. A summary of the analytical session is then produced for
each time series, composed of entries for only those test periods that
correspond to
(1
2
minima.
w
In order to assess the performance of COSOPT, simulated data sets were
prepared to approximate previously encountered gene chip profiles
from experimental examinations of expression time series (Harmer
et al. [2000]; Panda et al. [2002]; Ceriani et al. [2002]). One thousand
surrogate data sets were prepared at each condition considered (see
below), in which time series possessed 13 data points, representing 48
hours of observation obtained at 4-hour sampling intervals. All time
series were surrogate realizations of a 24-hour-period cosine wave
ranging in representational time from
24 hours, at which
acrophase (the time of maximum) occurred at time zero. All data sets
were composed of N(0,1) noise, to which 24-hour cosine profiles were
added to produce data with signal-to-noise ratios of either 0, 1, or 2. This
was achieved by adding nothing, or a unit-amplitude cosine wave, or an
amplitude-2 cosine wave, respectively.
24 hours to
þ
At each signal-to-noise ratio, replicate sampling also was varied, ranging
from 1, 2, 3, 4, or 5 replicate observations being averaged per data
point. A final variable considered in the analyses was whether or not
