Fluid model.

<p>Fluid model.</p

Plot of the force on the edge loaded by different speeds (<i>v</i>) versus time:a) v = 0.1m/s b)v = 0.2m/s c)v = 0.4m/s d)v = 0.8m/s.

<p>Plot of the force on the edge loaded by different speeds (<i>v</i>) versus time:a) v = 0.1m/s b)v = 0.2m/s c)v = 0.4m/s d)v = 0.8m/s.</p

Simulation results for the fluid structure interactions: a) Viscous force versus speed, b) Effective spring constant versus speed.

<p>Simulation results for the fluid structure interactions: a) Viscous force versus speed, b) Effective spring constant versus speed.</p

Root-mean-square amplitude curves as a function of frequency for a one-dimensional oscillator with damping.

<p>Root-mean-square amplitude curves as a function of frequency for a one-dimensional oscillator with damping.</p

Effective one-dimensional model for cantilever vibration in air.

<p>Effective one-dimensional model for cantilever vibration in air.</p

Pictures and diagrams of the AFM cantilevers: a) NP-A b) NP-C c) NSC14 d) SCM.

<p>Pictures and diagrams of the AFM cantilevers: a) NP-A b) NP-C c) NSC14 d) SCM.</p

The cross correlation between average realized volatility and average absolute return volatility is much higher than cross correlation between any separate realized volatility and absolute return volatility of each stock.

<p>(a) shows an example time series, realized volatility and absolute return volatility of the stock Nintendo, and the average correlation coefficients of all TOPIX Core30 components ; (b) shows the average and time series of all TOPIX Core30 components with the correlation coefficient between them is 0.65.</p

The probability density function of absolute return volatility and realized volatility of TOPIX Core30 Index members drawn on a log-log plot.

<p>Both of them follow power-law distribution. The slope of realized volatility is a bit larger than that of absolute return volatility , which indicates that realized volatility has slightly larger fat tails than absolute return volatility. For realized volatility about 1996 of the 2500 power law fitness KS tests fail to reject the null while for absolute return volatility about 1482 of the 2500 power law fitness KS tests failed to reject the null. The results suggest that the power law distribution may fit both of them but realized volatility has better fit with power law compared to absolute return volatility. The power law fitness KS test details may refer <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0102940#pone.0102940-Gallos1" target="_blank">[30]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0102940#pone.0102940-Clauset1" target="_blank">[31]</a>.</p

The conditional probability density for the largest and smallest 1/6th portion of the absolute return volatility (black line) and realized volatility (blue dots).

<p>The cross-over area (gray area) of absolute return volatility is much larger than the cross-over area (dark gray area) of realized volatility. Noted that we had normalized the variance of both values to 1, the results may mostly reflect that the neighboring days' memory of and are significantly different.</p

Long term memory effect in volatility subset clusters.

<p>Shown is the mean conditional volatility of the absolute return volatility (black triangles) and the realized volatility (red squares) given consecutive values that are above (+) or below (−) the median of the entire volatility data set. The upper part of the curves is for + clusters while the lower part is for – clusters. For the + clusters, the mean conditional volatilities for both methods increase with the size of the cluster, behavior opposite to that for the – clusters, indicating the presence of long-term memory in both volatility methods.</p