Average Cycle Length

Suppose the initial state is Sq, and consider the sequence of iterates 

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Figures 3,20, 3,21 and 3,22 show how the number of cyclic states (Nc), the average cycle length Crmave) and total fraction of states on cycles fc) changes as...

Table 8.9 shows that while the number of attractors increases exponentially, the average cycle length increases rather slowly as a function of N. Random Boolean nets with connectivity one are also generally only moderately stable with respect to minimal perturbations. 

Fig. 34. KINPTR commercial cycle length prediction. Average cycle conditions 2.3 LHSV, 5.8 H2 recycle ratio, 3685 kPa pressure, C6- 455 K Mid-Continent.

The description of a network structure is based on such parameters as chemical crosslink density and functionality, average chain length between crosslinks and length distribution of these chains, concentration of elastically active chains and structural defects like unreacted ends and elastically inactive cycles. However, many properties of a network depend not only on the above-mentioned characteristics but also on the order of the chemical crosslink connection — the network topology. So, the complete description of a network structure should include all these parameters. It is difficult to measure many of these characteristics experimentally and we must have an appropriate theory which could describe all these structural parameters on the basis of a physical model of network formation. At present, there are only two types of theoretical approaches which can describe the growth of network structures up to late post-gel stages of cure. One is based on tree-like models as developed by Dusek7 I0-26,1 The other uses computer-simulation of network structure on a lattice this model was developed by Topolkaraev, Berlin, Oshmyan 9,3l) (a review of the theoretical models may be found in Ref.7) and in this volume by Dusek). Both approaches are statistical and correlate well with experiments 6,7 9 10 13,26,31). They differ mainly mathematically. However, each of them emphasizes some different details of a network structure. 

In a normal ovulatory menstrual cycle, menstruation occurs every 28 days on average. Normal women display considerable variation in cycle length that varies from 25 to 30 days." Amenorrhea, the absence of menstrual bleeding, is traditionally categorized as either primary (women who have never menstruated) or secondary (women in whom menstruation is present for a variable time and then ceases). Amenorrhea is a relatively common disorder, with an estimated prevalence of 5% in the general population and as high as 8.5% in an unselected adolescent postpubescent population. ... 

HRT describes the change in sinus cycle length that follows a premature ventricular complex (PVC). After a PVC, there is an increase in blood pressure due to prolonged filling during the compensatory pause. Reflex parasympathetic activation occurs and the heart rate slows. HRT is measured by averaging approximately 15 to 20 beats after a PVC. Impaired HRT predicts both total mortality and SCD in post-MI patients (72,73). In an ATRAMI substudy, low HRT was associated with an approximately four-fold increase in relative risk of fatal and nonfatal cardiac arrest (73). HRT is an appealing... 

The optimal length of period leading to maximal average productivity is influenced by the space time With increasing space time, the optimal cycle length becomes longer (Fig. 5A). This is due to the time needed to wipe out the inhibiting species after the switch isopropanol/inert. 

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