Correction to: Scientific Reports https://doi.org/10.1038/s41598-018-32402-5, published online 21 September 2018

The Article contains an error in Equation 3.

$$\frac{1440}{2\pi }\arctan 2(\mathop{\sum }\limits_{j=1}^{M}\mathop{\sum }\limits_{i=1}^{M}{s}_{i,j}\,\sin \,\frac{2\pi {t}_{i}}{1440}+\mathop{\sum }\limits_{j=1}^{M}\mathop{\sum }\limits_{i=1}^{M}{s}_{i,j}\,\cos \,\frac{2\pi {t}_{i}}{1440})$$

should read:

$$\frac{1440}{2\pi }\arctan 2(\mathop{\sum }\limits_{j=1}^{M}\mathop{\sum }\limits_{i=1}^{M}{s}_{i,j}\,\sin \,\frac{2\pi {t}_{i}}{1440},\mathop{\sum }\limits_{j=1}^{M}\mathop{\sum }\limits_{i=1}^{M}{s}_{i,j}\,\cos \,\frac{2\pi {t}_{i}}{1440})$$

Additionally, the Article contains a typographical error in the Methods section under subheading ‘Calculation of Sleep Regularity Index (SRI) and other sleep indices’ where,

“Sleep midpoint, our index of sleep timing, was calculated as a mean of circular quantities (appropriate for time of day) using the following equation (3), where \({t}_{j}\) denotes time of day in minutes at epoch \({j}\):”

should read:

“Sleep midpoint, our index of sleep timing, was calculated as a mean of circular quantities (appropriate for time of day) using the following equation (3), where \({t}_{j}\) denotes time of day in minutes at epoch \(j\), and \({\rm{\arctan }}2(x,{y})\) denotes the angle between \((x,{y})\) and the positive \(x\)-axis.”