Fig. 3

Gibbs sampling for regulatory functions to show lower CV obtained by numerical simulation. (a) The samples obtained by Gibbs sampling, with only those having CVs not exceeding \(3.0\%\) being shown. The corresponding histogram is displayed on the right. The number of Fourier harmonics for regulatory functions was set to 3. \(\omega =2\pi\), \(\epsilon =0.1\), \(D=3.0\), \(\alpha =3\), \(\beta = 1\), \(k=10\). The dashed line represents the CV of the clock, expressed as \(\epsilon \sqrt{\frac{D}{2\pi \omega }}\)¹⁴. The \(\textrm{CV}\) for the sinusoidal regulation \(f(\theta )=\sin \theta\), represented by the green line, is \(2.6\%\). (b) Distribution of Fourier coefficients for the regulatory function \(f(\theta )\), corresponding to the fluctuations represented by the red and blue dots in (a). Red and blue indicate the top and worst \(5\%\) of all samples from Gibbs sampling. Note that each unit circle, defined by \(A_i^2+B_i^2=1\), is an upper boundary because of the normalization of Fourier coefficients. For further details on Gibbs sampling, see the Methods section.