Editing and Preparation of Data Vector

3.1.1. Creation of Data Sets to Be Analyzed

The program SIGGEN was employed to create data sets similar to biological data. A simple sinusoid was chosen, but other waveforms can be produced by this program. A circadian period of 24.75 h was chosen for all data sets. This noninteger value provides a realistic test of the capabilities of the analysis programs. In all examples, the amplitude was set at unity and was positive everywhere except as noted. Both the MESA and autocorrelation routines in the suite always fit a straight line to the data by regression and subtract it to eliminate any linear trend. This has the added benefit of adjusting the mean of the series to zero. Eliminating this so-called "DC offset" emphasizes the periodic portion of the signal in the subsequent analysis. In general, amplitude will affect spectral power, but not RI. All data sets consisted of 10 d of readings with a sampling rate at twice per hour with one exception, as noted (SET III). A more rapid sampling rate has been shown to be unnecessary for periodicities in the circadian range and very high rates may actually be undesirable if behavioral data are being summed into "bins" (15).

In SET I, the data were produced with amounts of white noise added in the following percentages: 10, 20, 30, 40, 50, 60, 70, and 80. The raw data set generated with 80% noise is shown in Fig. 1 (see Note 7).

In SET II, data were produced identically to SET I, except that a long-range sinusoidal trend was added with a period of 40 d, with the phase angle adjusted so that the data have an approximately monotonically increasing envelope from t = 0 to 10 d. The amplitude of this sinusoid was set at 10-fold that of the circadian periodicity. Figure 2 depicts data containing 80% noise with the long-period trend added.

In SET III, data were produced as in SET I and additionally had a 1-h circhoral ultradian component added. The peak-to-peak amplitude of the circadian rhythm was 10-fold that of the ultradian, which was unity. Sampling rate was set to 12/h (i.e., at 5-min intervals) to characterize more adequately this relatively high-frequency component (7). Such circhoral rhythms have been uncovered in human deep-core body temperature using the sensitive methods outlined here (14). Figure 3 shows the data containing the standard circadian periodicity along with an ultradian periodicity of 1 h. In this example 80% noise was added.

For SET IV, a series of files created with data sampled twice per hour and with a 24.75-h periodicity was generated. In these examples, phase was delayed by 0, 2, 4, 6, 8, and 22 h, respectively, to show the output of CROSSCO.

Fig. 1. An artificial data set consisting of a unit amplitude sinusoid and periodicity of 24.75 h with an added 80% white noise. Data were sampled at half-hour intervals over the equivalent of 10 d.
Fig. 2. The data set depicted in Fig. 1, but in this case with a monotonic trend added with amplitude functionally five times that of the sinusoid. Period and amplitude of the signal remain in Fig. 1.

Fig. 3. (A) Data as Fig. 2, containing a periodicity of 24.75 h and 80% noise, but with a unit amplitude ultradian rhythm having a period of 1 h added. This cannot be seen in the unfiltered data. (B) The same data set after removal of the circadian range periodicity using FILCON.

Fig. 3. (A) Data as Fig. 2, containing a periodicity of 24.75 h and 80% noise, but with a unit amplitude ultradian rhythm having a period of 1 h added. This cannot be seen in the unfiltered data. (B) The same data set after removal of the circadian range periodicity using FILCON.

— 1 1.1 1.2 1.3 1.4 1.5 1.6 17 1.» 1.9 2 v Time {days)

— 1 1.1 1.2 1.3 1.4 1.5 1.6 17 1.» 1.9 2 v Time {days)

Fig. 3. (continued) (C) Here, a 1-d interval of the data is shown at a magnified scale to illustrate the noisy hourly rhythm.

3.1.2. Format of Data

The analysis software is configured to allow batch processing of concatenated files. Input data are placed in a single column. Each separate file is given a descriptive, reasonably short title (here, fewer than 15 characters) at the start of the vector. The end of each individual file is signaled by appending -5000. Batch processing is terminated with the word "END." Output of both spectra and autocorrelations is written file by file in two columns, with either spectral power or autocorrelation values in the first column and either period or lag in the second. In autocorrelation output, the 95% confidence value indicating "significant rhythmicity" is given below the title (see Note 8). For actual rhythmicity data, the columns of input are concatenated and formatted as above using an editor. Output for individual spectra and correlograms excised from the concatenated file were plotted using MATLAB (see Note 9). An example of the raw data format follows: I80

1.173287

5.549589E-01

8.012864E-01

4.805624E-01

1.060405

3.837983E-02 2.867427E-01 4.349197E-01 6.987450E-01 8.844982E-01 1.210237E-01 4.635225E-01 -5000.000000 END

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