Author details

We will now discuss the ultradian rhythm fragmentation. The Fourier scree diagram, the CWT power spectrum and the SSA scree diagram suggest a trade-off effect. If subject A is taken as a reference, then subject C would seem to exhibit a very strong circadian rhythm associated with an important reduction of rhythm fragmentation at a wide range of ultradian scales, and, as a consequence, there is a flattening of the 1=f power law over the same frequency range, resulting in an overall rigid rhythm; subject B, on the other hand, is characterized by a reduced circadian contribution and an increased rhythm fragmentation over a wide range of ultradian scales, which leads to an increased power law slope over the same frequency range, resulting

Of course, the three time series studied in the present contribution are not sufficient to draw any definite conclusions on the average values of the circadian parameters and their variability or on rhythm fragmentation at ultradian scales; therefore, a much larger statistical study is needed, but we have shown that circadian and ultradian scales can be studied within the same approach, and we hypothesize that partial variances are related over wide circadian and

In recent years, there is a shift in interests in chronobiology where a larger emphasis is now put on an accurate quantification of irregularities of circadian rhythms and ultradian rhythm fragmentation to follow underlying pathologies. Wavelet analysis has probably been the method of choice to describe irregular rhythms at different time scales, but wavelet analysis has the drawback to depend on the choice of a mother wavelet which is arbitrary and user dependent. Data-adaptive time-series decomposition, where the basis functions are generated by the data itself, such as singular spectrum analysis (SSA) may offer an alternative. In the present contribution, we have shown that SSA is at least as versatile and accurate as wavelet analysis in the description and quantification of irregular rhythms at the circadian and ultradian time scales and may be a useful method to be adopted in the field of chronobiology.

Financial funding for this work was supplied by the Dirección General de Asuntos del Personal Académico (DGAPA) from the Universidad Nacional Autónoma de México (UNAM), grants PAPIIT IN106215 and IV100116 and in particular grant IA105017 in the context of which the Fourier filter was discussed into detail with Wady A. Rios-Herrera, Francisco F. de Miguel, Martha Yoko Takane Imay, David Serrano, Octavio B. Lecona and Silvia Diaz Gómez. We also gratefully acknowledge grants 2015-02-1093, 2016-01-2277 and CB-2011-01-167441 from the Consejo Nacional de Ciencia y Tecnologia (CONACyT). We are thankful for the

in an overall more random rhythm.

54 Circadian Rhythm - Cellular and Molecular Mechanisms

ultradian scales.

7. Conclusions

Acknowledgements

Ruben Fossion1,2\*, Ana Leonor Rivera1,2, Juan C. Toledo-Roy1 and Maia Angelova3

\*Address all correspondence to: ruben.fossion@nucleares.unam.mx

1 Complexity Science Centre, National Autonomous University of Mexico, Mexico City, Mexico

2 Nuclear Science Institute, National Autonomous University of Mexico, Mexico City, Mexico

3 School of Information Technology, Melbourne Burwood Campus, Deakin University, Burwood VIC, Australia
