The complexity measures sorted by the average error drop-off rate <i>α</i> mostly follow the standard one over square root relationship (<i>α</i> = 0.5).

<p>The error drop-off rate was computed for “brown noise” time series of ten lengths ranging from 100 to 10000 points over 100 instances. The dotted vertical lines indicate which pairs of neighboring measures are significantly different at <i>p</i><0.001 (uncorrected).</p

Number of spikes (as a percentage of points in a time series, x-axis) and their magnitude (in units of standard deviation of original time series, y-axis) affect Hurst estimates differently.

<p>The z-axis represents normalized to [0, 1] range one-sample t-test differences from the <i>H</i>-estimates of time series without spikes (each point on the surface is the t-value difference in <i>H</i> resulting from the introduction of spikes to the time series; the set of all t-scores for all measures was linearly transformed to [0, 1] range to show relative change due to presence of spikes). Volume is calculated as the difference between the surface and the plane defined by <i>H</i>-values of unaltered time series (spike magnitude of zero).</p

Inter-subject correlation across eleven participants for GRST-LOST task shows that most activation is restricted to areas involved in audiovisual processing.

<p>The glass brain (left) shows distribution of ISCs throughout the brain, while the heat map (right) outlines the areas deemed active at <i>r</i>>0.15. Though the activation appears symmetric, the maximally activated voxel is located on the left (MNI = −64, −20, 2).</p

Comparison of combinations of signal processing.

<p>Results of an ANOVA of processing by measure (20) by subject (22 for FACES, 11 for GRST-LOST) show significant improvements in sensitivity and grey-white matter contrast of Hurst estimates (<i>df</i> = 1 for each comparison). The AUC-T values were derived from ROC curves constructed using top 1% of t-values of task vs. rest contrast. The AUC-ISC values were derived from ROC curves constructed using top 1% of z-transformed inter-subject correlations (ISC). The GM>WM values were derived from differences in Hurst estimates for grey and white matter voxels. Positive results significant at p<0.05 are highlighted.</p

Mean (and standard error across 11 subjects) (A) GM>WM contrast (T-values on y-axis) and (B) overlap with activation for top 10% of the values (AUC on y-axis) increase for most of the Hurst estimates as the length of the time series (x-axis, minutes) increases.

<p>The two lines represent windows that start at the beginning (red) and the end (blue) of the task. Vertical lines between pairs of window sizes indicate that the subsequently larger window size significantly improves GM>WM contrast (A) or AUC (B) as compared to the smaller one for both forward and backward counting windows (p<0.025 each). The highlighted plots in (B) indicate measures that attained an AUC of 0.85 or more.</p

Summary of performance of Hurst estimates.

<p>Summary of measure comparisons highlights <i>H_FFT</i>, <i>H_pWelch</i>, and <i>H_HFD*</i> as the most reliable methods overall.</p

Variation in Hurst exponent estimates (black) correlates with arousal (red), valence (blue), and ISC-derived activation (green) throughout the GRST-LOST task.

<p>All estimates were computed over fifteen 10-minute windows evenly distributed throughout the task with 77% overlap, with the window centers plotted on the x-axis and z-scores of normalized variables on the y-axis. Error bars represent standard errors across the 11 participants. For arousal and valence, the positive values represent segments of the show rated as more calm and pleasant, while negative ones represent excited and unpleasant. The self-report measures were highly correlated (<i>r</i> = 0.92, <i>p</i><<0.001). Highlighted plots represent complexity measures that correlated with either valence, arousal, or activation at <i>p</i><0.01 level.</p

Estimates of the Hurst exponent are consistent and monotone for simulated wavelet-based fractional Brownian motion time series with Hurst exponent ranging from zero to one.

<p>Along with estimates for the simulated time series (blue), estimates for the time series integral (black) and derivative (green) are also shown. The red dotted line represents the theoretical value. Mean error is calculated as the average of the errors at each point; starred errors were computed for the derivative.</p

Comparison of Hurst estimates of simulated data.

<p>Volume under the surface of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0063448#pone-0063448-g002" target="_blank"><b>Figure 2</b></a>, error drop-off rate alpha of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0063448#pone-0063448-g005" target="_blank"><b>Figure 5</b></a>, and computation time (in seconds) for 1000 time series of length 256, 1024, 4096, and 16384 points. The computations, optimized using MATLAB Parallel Computing Toolbox, were performed on a quad-core Intel i7-960 @ 3.6 GHz.</p

Correlations between Hurst estimates of simulated time series.

<p>Correlations between Hurst parameter estimates show that they are consistent but not precise. <i>Below Diagonal</i>: correlations between the measures computed over the same 1000 time series with <i>H</i> = 0.5 show that for most measures, errors on estimating the same exponent are not strongly correlated (light green to white to blue) with the exception of a few positively correlated (dark green) measures. <i>Above Diagonal</i>: correlations between Hurst estimates of the same 1000 time series with <i>H</i> values distributed uniformly between 0 and 1 show that measure estimates are consistent across a range of exponents, with some measures showing stronger correlation (green) than others (yellow).</p