For both simulated data and a circadian metadataset [27] the resulting empirical ITK_CYCLE with asymmetry search eXhibits the greatest sensitivity among the methods that we evaluated.

They test the methods with simulated data and experimental data for the metabolic cycle in yeast, circadian rhythms in the mouse, and the root clock in the flowering plant Arabidopsis thaliana (see [28] for references).

They show that RAIN outperforms the original ITK_CYCLE method as well as a cosine-fitting method [62] for simulated data consisting of sinusoidal and ramp waveforms.

The simulated data allow us to examine how performance varies with sampling density, number of replicates and/ or periods, noise level, and waveform.

Simulated data benchmarks

Examples of simulated data .

shows that the ITK_CYCLE methods have higher-quality classification ability than F24 and ANOVA for these simulated data .

AUROCs for simulated data with 25% noise (standard deviation of Gaussian noise as a percent of amplitude).

Simulated data With rhythmic time series Without asymmetry (A) or With evenly distributed asymmetry (B) was tested With different methods.

Simulated data With rhythmic time series Without asymmetry (left, A and C) or With evenly distributed asymmetry (right, B and D) was tested With different asymmetries.

By directly fitting tuft-constant planes of the simulation data (horizontal planes of Fig.

The sigmoidal functions found by fitting the form of the entire composite equation to the simulation data fit the extracted M and T values well (Fig.

This points to the strength of the composite model, as the same parameters can be found from the simulation data in two different ways.

Comparison of analytical results with simulations data

3 compares the full analytical solution (Equation 7, with H given by Equation 10) against simulation data .

We verified our analytical solution by comparing it to simulation data .