Biology Reference
In-Depth Information
2
2
Variance
ð½
0
Þ ¼ ð
MDC
=
2
Þ
¼ð
SD
Þ
;
as expected. When the hormone concentration is not zero, the second
term of the sum in Eq. (9-1) accounts for the additional variation at
any given concentration that depends on the choice of the CV from
Figure 9-7.
To summarize, in determining hormone pulsatility properties from
experimental data, it is important to use analysis methods that can
accommodate small numbers of data points with variable uncertainties
and allow for missing values. We now discuss some of the
computational procedures specifically developed for the analysis of
hormone concentration time-series data. Although the topic of hormone
pulsatility may seem rather specialized, many of the mathematical and
statistical challenges are representative of a much broader class of
quantitative problems.
We begin with some standard time-series analyses for detecting periodic
behavior.
III. CLASSICAL METHODS FOR ANALYZING HORMONE
CONCENTRATION TIME SERIES
A. Fourier and Power Spectrum Methods
Visual inspection of Figure 9-5 indicates the LH secretory events to be
approximately equally spaced in time and of equal height. That is to say,
the LH secretory profile in Figure 9-5 may appear to be periodic.To
review the terminology, a function G(t) is called periodic with period T,
if for any value of t:
G
ð
t
Þ¼
G
ð
t
þ
T
Þ;
and T is the smallest positive constant for which the condition is
satisfied.
¼
¼
The most common periodic functions are G(t)
sin(t) and G(t)
cos(t),
and their period is T
¼
2
p
; that is, sin(t
þ
2
p
)
¼
sin(t) and
cos(t
cos(t). Also, the variable t usually represents the time
elapsed since a fixed moment in time.
þ
2
p
)
¼
E
XERCISE
9-1
Show that each of the functions h(t)
¼
sin(2
p
t) and r(t)
¼
cos(2
p
t) has a
period of T
¼
1.
