Biology Reference
In-Depth Information
Additive noise: SD = 10 y-axis units
2.5
2
1.5
Phase reference point
(maximum at 0 hours)
1
Period
(24 hours)
0.5
0
−
0.5
125
−
1
−
1.5
100
−
2
−
2.5
0
24
48
72
96
120
75
A
Time of max
Time of max
Time
Time of max
Amplitude
(100 units)
20
50
18
16
25
14
12
0
10
8
−
25
6
Mean
expression
intensity
(0 units)
4
−
50
2
0
−
75
0
1
2
3
4
5
6
B
Day
−
100
2.5
2
−
125
1.5
1
0
24
48
72
96
120
144
168
192
216
240
0.5
Time (hours)
0
−
0.5
−
1
FIGURE 11-14.
Mean and variance stationary noisy cosine wave.
−
1.5
−
2
−
2.5
0
24
48
72
96
120
C
Time of max
Time of max
Time
Time of max
value of 0 y-axis units with an 80-hour exponential decay lifetime
[i.e., 80 hours is the time for the mean value to decay to 1/e of its
magnitude 80 hours prior (1/e
20
18
16
¼
1/2.72
¼
0.368)];
14
12
10
2. An oscillatory amplitude that is also time-dependent, such that at
time zero, the oscillatory amplitude is 100 y-axis units, but it too
decays in magnitude in an exponential manner to a final value of
0 y-axis units, again, with an 80-hour exponential decay lifetime;
8
6
4
2
0
0
1
2
3
4
5
6
D
Day
FIGURE 11-13.
An example of period shifting. For the graph in
panel A, the period does not change, and the
acrophase (the point of daily maximum) occurs at
the same time each day (panel B). For the graph in
panel C, the period is larger than 24 hours, and
the daily maximum is delayed by about 2.6 hours
from day to day (panel D).
3. A period of oscillation of 24 hours;
4. A phase reference point (again, the maximum) at 0 hours; and
5. Gaussian-distributed random noise added, such that the standard
deviation of the noise is 25 y-axis units.
We use the simulated data from Figures 11-14 and 11-15 as test data for
several of the analyses discussed below. Subsequently, we apply those
analyses to quantitatively address the questions posed in the Example
presented in Section II.
IV. DATA PREPROCESSING STRATEGIES
If mean and/or variance nonstationarities present formidable
confounds, then data preprocessing strategies may be needed before
