By Theodosios Pavlidis
Organic Oscillators: Their Mathematical Analysis
summary: organic Oscillators: Their Mathematical research
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Extra info for Biological Oscillators: their Mathematical Analysis
T h e study of circadian (or other) rhythms in microorganisms is more likely to help us understand the nature of the clock than studies in higher-order organisms. Indeed the simpler the organism the lesser the probability that the output of the circadian regulator will not be obscured by intermediate systems as much as it would in a higher-order organism. Also it is easier to study the effect of chemical agents on the clock. In a higher organism such agents may never reach the basic regulator because of the complex metabolic systems involved.
It should also be pointed out that the circadian clock is genetically determined [Bru-5, Fel-3, Kon-1, Pit-8, Ric-1]. 3 35 Chan-1]. Under natural conditions insects emerge from pupae just before dawn when the humidity of the environment is usually highest. T h e importance of a "clock" for such an organism need not be overemphasized. Since the transition is a "one-shot" phenomenon, the rhythm can be observed only in a population of pupae of different ages. It is possible to record the number of flies emerging every hour and thus form a histogram of this number for various of the day.
Let y be the intersection of / and L. 4) Since the first and last terms are fixed, the plot of P ( x ' , y) vs P ( x , z) will be a parallel shift of the plot of P ( x , z) vs P ( x , z). 3 illustrates this case. 5. I f no point χ of L is mapped by S on an isochrone corresponding to a point ν of the limit cycle which is such that the time required to reach χ from ν is greater than Tj2 for a phase delay or less than T\2 for a phase advance, then the P R C will have no discontinuities. Proof. T h e hypothesis implies that during the computation of the phase difference no use of the modulo Τ operation will be made.
Biological Oscillators: their Mathematical Analysis by Theodosios Pavlidis