The values of and of the exponential fit for the six indices and the corresponding simulations.

<p>Student’s <i>t</i>-test is performed to analyze the statistical significance of . A <i>p</i>-value less than 0.05 is considered statistically significant.</p

The return-volatility correlation functions for the S&P 500 and Shanghai indices, and for the corresponding simulations.

<p>The S&P 500 and Shanghai indices are simulated with and , respectively. Dashed lines show an exponential fit with and for the S&P 500 Index and the Shanghai Index.</p

The return-volatility correlation functions for the simulated results of the S&P 500 and Shanghai indices, and for those of the controls.

<p>The S&P 500 and Shanghai indices exhibit the leverage and anti-leverage effects, respectively. For the leverage effect, we consider two cases: is asymmetric; is symmetric. The latter is the control. For the anti-leverage effect, we consider the following cases: both and are asymmetric; only is asymmetric; only is asymmetric; both and are symmetric. The last three cases are controls. For each case, the simulation is performed for 100 times, and the average is displayed.</p

The business sectors of the full time series for the SHSE and TWSE markets are compared with the communities of the medium mode.

<p>Most of the communities of the medium mode could not be associated with the business sectors. The abbreviations are the same as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0139420#pone.0139420.g003" target="_blank">Fig 3</a>.</p

A Microreactor and Imaging Platform for Studying Chemical Oscillators

We present a laser scanning confocal microscopy (LSCM) and continuous flow microreactor (CFMR)-based platform to study the Belousov–Zhabotinsky (BZ) oscillators. We demonstrated that the scanning laser light below a certain power had no detectable influence on the BZ reaction. The CFMR consisted of the poly­(methyl methacrylate) (PMMA) microwell and the polydimethylsiloxane (PDMS) microchannel and maintained the oscillation with a continuous supply of the catalyst-free BZ mixture. The synchronization of the two nonidentical oscillators was studied by the platform. The coupling intensity was controlled by changing the distance between the two oscillators. Results showed that the synchronization occurred as the oscillators were closer than a critical distance. The transition from desynchronization to synchronization was observed when the distance between the oscillators was near a critical value. The results of the numerical simulation by COMSOL agreed qualitatively with the experimental observation

The auto-correlation functions of volatilities for the S&P 500 and Shanghai indices, and for the corresponding simulations.

<p>For clarity, the curves for the S&P 500 Index have been shifted down by a factor of 10.</p

The values of , , , , and for the six indices.

<p>, and are determined from the historical data for each index. We calculate from and , and from . Student’s t-test is performed to analyze the statistical significance of . A p-value less than 0.05 is considered statistically significant. We compute from the linear relation between and for all these indices. As for the Shanghai Index is negative, it is rounded down to the nearest integer, while for other indices are positive, and each of them is rounded up to the nearest integer.</p

The relation of and .

<p>With set to be −4, −3, −2, −1, 0, 1, 2, 3 and 4 respectively, time series is simulated 100 times for . The corresponding is computed and averaged for each . This plot shows a linear relation of and , i.e., , and this result remains robust for between 0.9 and 1.1.</p

The cumulative distributions of absolute returns for the S&P 500 and Shanghai indices, and for the corresponding simulations.

<p>For clarity, the curves for the S&P 500 Index have been shifted left by a factor of 8.5.</p

The probability distribution of the correlation <i>c</i> defined in Eq (9) for the fast mode, medium mode and slow mode.

<p>There are 174 stocks for the SHSE market, and 162 stocks for the TWSE market.</p