Models and Analogues in Biology

By Society for Experimental Biology | Go to book overview
but once we are working with frequency functions we can no longer distinguish cause-and-effect sequence of dependencies in the system loop. In the paper two equivalent sets of parameters are worked out; the system weighting function is determined using correlating functions and the frequency and phase response of the system is calculated using spectral functions. The merits of each determination is discussed but clearly a compromise requires working out in which due account is taken of the two essential requirements; namely, acknowledgment of the closed-loop nature of the system and the need to specify sampling accuracy.
SUMMARY
Systems of interacting quantities are considered where it is required to establish the set of equations expressing the interaction between variables. These equations are first specified as to form and the question arises of estimating values of parameters in the equations. Methods are discussed which from observations of the simultaneous variations of the variables over some period of time give the values of the parameters that best account for the observed behaviour or that will serve best to predict the behaviour of the system at other times.The author has been concerned with certain problems of this kind that arise in engineering and the paper presents some lines of thought about them that may be suggestive of approaches to analogous problems in biology. Most of the systems of interest to biologists involve non-linear relationships. In such cases no general analytical methods are available, but solutions may be sought by the use of physical models or analogues having parameters which may be adjusted until the behaviour of the physical model corresponds with the observed behaviour of the system. The first part of the paper is concerned mainly with such uses of physical models.Analytical methods are available only for linear systems and the second part of the paper reviews some aspects of parameter estimation for such cases. The distinction between fitting with 'minimum square error' and the use of a more general form of statistical estimator is discussed with particular reference to making the best use of short records.
REFERENCES
BARTLETT M. S. ( 1956), Stochastic Processes. C.U.P.
BLACKMAN R. B. & TUKEY J. W. ( 1958). Measurement of Power Spectra. Dover Publications.
EGGLESTON J. M. & MATHEW C. W. ( 1954). Application of several methods for determining transfer functions and frequency response of aircraft from flight data. N.A.C.A. Report, 1204.
FISHER R. A. ( 1956). Statistical Inference and Scientific Method. Oliver and Boyd.
FLORENTIN J. J., HAMSWORTH B. D., RESWICK J. B. & WESTCOTT J. H. ( 1959). Correlation analysis of a heat exchanger. Proc. of Symp. on Instrumentation and Computation in Process Development and Plant Design, Inst. Chem. Eng.
GABOR D. ( 1954). Communication theory and cybernetics. Trans. I.R.E.; P.G.C.T.

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