97.

[Cover] [Abbreviated Contents] [Contents] [Index]

Page 192

		2.5.1— Analyzing Data: The Good News

		The data from many biological systems have values that seem to change randomly from one point in time to the next point in time, or among repetitions of the same experiment.

		It had always been assumed that this variability was generated by random mechanisms based on chance events. We now know that deterministic mechanisms can also generate this variability.

		Evaluating the fractal dimension of the phase space set or the bifurcation sequence now makes it possible to analyze data from an experiment to find out if the variability in the data was generated by a random mechanism or by a deterministic mechanism. If the data were generated by a deterministic mechanism, then we can understand and perhaps even control it.

		There has been a lot of excitement in applying these methods to analyze data from many different biological systems to determine if the observed variations were generated by random or deterministic mechanisms.

		We have already seen that the low fractal dimension of the phase space sets of the motion of the surface of hair cells in the ear and the timing of the beats of heart cells in culture has demonstrated that these systems are deterministic. We have also seen that the bifurcation sequence has demonstrated that the variation of the concentration of ATP in time produced by glycolysis is deterministic.

		Evaluating the dimension of the phase space set has been the method that has been used most to determine if data were generated by a random or a deterministic mechanism. If the fractal dimension of the phase space set is very large, then the data were generated by a random mechanism. If the fractal dimension of the phase space set is small, then the data were generated by a deterministic mechanism.

 

[Cover] [Abbreviated Contents] [Contents] [Index]