1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Hypothesis test for synchronization: Twin surrogates revisited
Rent:
Rent this article for
USD
10.1063/1.3072784
/content/aip/journal/chaos/19/1/10.1063/1.3072784
http://aip.metastore.ingenta.com/content/aip/journal/chaos/19/1/10.1063/1.3072784

Figures

Image of FIG. 1.
FIG. 1.

Recurrence plot of a trajectory from the Lorenz system [Eq. (A2)].

Image of FIG. 2.
FIG. 2.

A: Two neighbors in the one-dimensional space with distance . The nonoverlapping regions (NOR) have the length . B: Two neighbors in the two-dimensional space with distance . The nonoverlapping regions (NOR) depend on and on the radius that defines the neighborhoods.

Image of FIG. 3.
FIG. 3.

Computation of the average number of twins depending on the threshold and the number of points of the time series in the one-dimensional case: A, B [analytical, Eq. (3)], C, D (random uniformly distributed time series), and E, F (chaotic Bernoulli map). The inset in A presents a zoom to show that for the analytical expression for the average number of twins is equal to zero, in accordance with the numerical simulations.

Image of FIG. 4.
FIG. 4.

A: Distribution of distances of the bivariate random uniformly distributed time series (points: numerical simulations; solid: curve fitted). B: Distribution of distances of the Lorenz system [Eq. (A2)] (points: numerical simulations; solid: curve fitted). The curve fitted in both cases has the form .

Image of FIG. 5.
FIG. 5.

Computation of the average number of twins depending on the threshold and the number of points of the time series in the two-dimensional case: A, B [analytical estimation, Eq. (4)], C, D (bivariate random uniformly distributed time series), and E, F [chaotic Lorenz system, Eq. (A2)]. The length of the time series used for the left panels was (A, C, E) and the values for the thresholds were (B), (D) and (F).

Image of FIG. 6.
FIG. 6.

Comparison between the twin surrogates and the “real” trajectories for several statistics for the logistic map [Eq. (A1)] depending on the threshold of the recurrence matrix. A: Mean value of the ACF. B: Standard deviation of the ACF. C: Mean value of the MI. D: Standard deviation of the MI. E: MDL, and F: MVL.

Image of FIG. 7.
FIG. 7.

Comparison between the twin surrogates and the “real” trajectories for several statistics for the Lorenz system [Eq. (A2)] depending on the threshold of the recurrence matrix. A: Mean value of the ACF. B: Standard deviation of the ACF. C: Mean value of the MI. D: Standard deviation of the MI. E: MDL, and F: MVL.

Image of FIG. 8.
FIG. 8.

Comparison between the twin surrogates and the “real” trajectories for several statistics for the AR-model [Eq. (A3)] depending on the threshold of the recurrence matrix. A: Mean value of the ACF. B: Standard deviation of the ACF. C: Mean value of the MI. D: Standard deviation of the MI. E: MDL, and F: MVL.

Image of FIG. 9.
FIG. 9.

Errors of the twin surrogates depending on the embedding delay for the Lorenz system. A: Mean value of the ACF. B: Standard deviation of the ACF. C: Mean value of the MI. D: Standard deviation of the MI. E: MDL, and F: MVL. The curves have been computed for the following values of the embedding dimension: (+ solid), (× long-dashed), (∗ short-dashed), and (◻ dotted).

Image of FIG. 10.
FIG. 10.

Errors of the twin surrogates depending on the length of the time series for the logistic map. A: Mean value of the ACF. B: Standard deviation of the ACF. C: Mean value of the MI. D: Standard deviation of the MI. E: MDL, and F: MVL.

Image of FIG. 11.
FIG. 11.

Errors of the twin surrogates depending on the length of the time series for the Lorenz system. A: Mean value of the ACF. B: Standard deviation of the ACF. C: Mean value of the MI. D: Standard deviation of the MI. E: MDL, and F: MVL.

Image of FIG. 12.
FIG. 12.

Errors of the twin surrogates depending on the length of the time series for the AR-model. A: Mean value of the ACF. B: Standard deviation of the ACF. C: Mean value of the MI. D: Standard deviation of the MI. E: MDL, and F: MVL.

Image of FIG. 13.
FIG. 13.

Simultaneous recording of left and right fixational eye movements. A) Horizontal component of the left (red, solid line) and right (blue, dashed line) eye. B) Detrended data.

Image of FIG. 14.
FIG. 14.

Comparison between the twin surrogates and the “real” trajectories for several statistics for the fixational eye movements from one subject depending on the threshold of the recurrence matrix. A: Mean value of the ACF. B: Standard deviation of the ACF. C: Mean value of the MI. D: Standard deviation of the MI. E: MDL, and F: MVL.

Image of FIG. 15.
FIG. 15.

A) Twin surrogate of the left (red, solid line) and right (blue, dashed line) filtered fixational eye movements, horizontal component. B) Segment of another filtered trial of the same subject. The twin surrogates reproduce the structure of the measured time series very well.

Image of FIG. 16.
FIG. 16.

Histogram of the values obtained for with (bars). The dashed vertical line indicates the value obtained for for the original data. Hence, in this case the null hypothesis is rejected, which indicates that there is PS between the left and right fixational eye movements. This test was performed with the data from subject 2, trial 10.

Tables

Generic image for table
Table I.

Results for the test for PS between the trajectories of the left and right fixational eye movements performed for 30 trials for 21 subjects. Trials in which the participants blinked, were discarded. 100 twin surrogates were used for the test.

Loading

Article metrics loading...

/content/aip/journal/chaos/19/1/10.1063/1.3072784
2009-03-31
2014-04-24
Loading

Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Hypothesis test for synchronization: Twin surrogates revisited
http://aip.metastore.ingenta.com/content/aip/journal/chaos/19/1/10.1063/1.3072784
10.1063/1.3072784
SEARCH_EXPAND_ITEM