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The parameters for the studied models were randomly searched through cost optimisation of matching all output profiles (M, E, and P) to a standard sine waveform of 24h-period and unit amplitude to achieve a circadian rhythm with a reasonable size of oscillation.
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The mathematical model (appendix) predicts that the relative size of oscillations in ETCO2 should be directly proportional to the relative size of oscillations in cardiac output (ΔC/C0 ∝ ΔQ̇/Q̇0) (see appendix for definition of terms in equation).
Across the entire study group, the relationship between the relative size of oscillations in ETCO2 and the relative size of oscillations in cardiac output was still significant (r = 0.59, P = 0.01; Fig. 4).
In all five patients who underwent heart rate alternations of different magnitudes, the relative size of oscillations in cardiac output and ETCO2 was strongly correlated (mean of within-patient correlation coefficients was 0.83 ± 0.10, P < 0.0001 in all cases, Fig. 5).
Between different subjects, the same 30 beats/min oscillation in heart rate produced different sizes of oscillations in respiratory parameters (Fig. 4).
The size of the oscillations, the shape of the transients, and even the frequency of the dominant oscillations appearing in Fig. 2 are rather sensitive to the different relative values of the time constants associated with the five key processes listed above (Fig. 2E F).
The size of these oscillations decays exponentially with N, as was seen in Fig. 5.
Earlier astronomers inferred the size of the oscillations indirectly, through the well-known phenomenon of the Doppler shift.
Then, by dividing the angular size of the oscillations into their absolute size (as inferred from redshift measurements), Lane calculated the distance of Zeta Geminorum as 1100 light-years from Earth.
By last Christmas, Lane already had clear evidence of the star's growth and shrinking, and by this spring he had the most accurate estimate ever of the angular size of the oscillations.
X-ray crystallography allows measuring the size of these oscillations.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com