304

X-squared = 33.0009, df = 10, p-value = 0.0002723

Warning message:

In chisq.test(table) : Chi-square approximation may be incorrect

The warning message in this case is due to the insufficient number of samples, can be

neglected here (exercise example). The p-value is 0.0,002,723, so we can reject the null

hypothesis, i.e. the number of airbags depends on the type of car.

We want to draw the graph in R and look at it more closely (e.g. attractors, stable state

of the system [local minimum], tolerated disturbances that the system can still compensate

for [local maximum]).

The R script would look like this:

> x<-seq(-5, 5, by=0.1)

> plot(x, -cos(x)-0.1*x^2, type="l")

19.27

Example 19.4

The state of biological systems can be described with mathematical formulas. The

formula f(x) = − cos(x) − 0.1x² describes (in a very simplified way) the equilibrium

of the erythrocyte production in the body. Here, the x-axis shows the amount of red

cells in the body, and the y-axis represents the energy the body invests to get back

into balance. Small disturbances are easily compensated by the system, large distur­

bances affect the vital functions and can no longer be compensated.

Example 19.5

A cyclist is injected with a dose of erythropoietin (Epo). At the start time of the

measurement t0, n0 molecules of Epo dock onto each hematopoietic cell. As Epo

detaches from the receptors over time and is broken down by the body, only n0*e-t

molecules are still docking at time t. Each molecule of Epo docked to the cell acti­

vates alpha-STAT transcription factors via a signaling cascade per unit time t by

phosphorylating them. Phosphatases are permanently active in the cell, which

remove the phosphate residue from the STAT transcription factors and thus deacti­

vate them. The phosphatases deactivate beta-% of the active transcription factors per

time unit t – and this already from time t0.

19  Tutorial: An Overview of Important Databases and Programs