Using Lomb-Scargle Periodograms to Identify Periodic Genes in ...

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Lomb-Scargle Periodogram Experiment:Multiple FrequenciesSum of 3 Cosines (N=48)Expression-2 0 2 4Expression =3*Cosine(2pt/48) +Cosine(2pt/24) +Cosine(2pt/ 8)N = 480 10 20 30 40Time [hours]Normalized Power Spectral Density0 5 10 20Lomb-Scargle PeriodogramPeriod at Peak = 48 hoursp = 1e-06p = 1e-05p = 1e-04p = 0.001p = 0.01p = 0.050.00 0.05 0.10 0.15 0.20Probability0.0 0.4 0.8Peak Significancep = 2.37e-007 at Peak0.00 0.05 0.10 0.15 0.20Frequency [1/hour]Frequency [1/hour]“Weaker” periodicities cannot always be resolved statistically.14
Lomb-Scargle Periodogram Experiment:Multiple Frequencies: “Duty Cycle”50% 66.6% (e.g., human sleep cycle)duty cycle: 1/2duty cycle: 2/3Expression0.0 0.2 0.4 0.6 0.8 1.0N = 480 10 20 30 40Expression0.0 0.2 0.4 0.6 0.8 1.0N = 480 10 20 30 40Time [hours]Time [hours]Normalized Power Spectral Density0 5 10 15 20 25Lomb-Scargle PeriodogramPeriod at Peak = 24 hoursp = 1e-06p = 1e-05p = 1e-04p = 0.001p = 0.01p = 0.05Probability0.0 0.2 0.4 0.6 0.8 1.0Peak Significancep = 2.54e-007 at PeakNormalized Power Spectral Density0 5 10 15 20 25Lomb-Scargle PeriodogramPeriod at Peak = 24 hoursp = 1e-06p = 1e-05p = 1e-04p = 0.001p = 0.01p = 0.05Probability0.0 0.2 0.4 0.6 0.8 1.0Peak Significancep = 5.06e-006 at Peak0.0 0.1 0.2 0.3 0.4 0.50.0 0.1 0.2 0.3 0.4 0.50.0 0.1 0.2 0.3 0.4 0.50.0 0.1 0.2 0.3 0.4 0.5Frequency [1/hour]Frequency [1/hour]Frequency [1/hour]Frequency [1/hour]One peak with symmetric “duty cycle”.Multiple peaks with asymmetric cycle.15
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Page 48: AcknowledgementsPourquie LabOlivier

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