Moving time window

As pointed out by Liebman et al., given a perfect model, an ideal data reconciliation scheme would use all information (process measurements) from the startup of the process until the current time. Unfortunately, such a scheme would necessarily result in an optimization problem of ever-increasing dimension. For practical implementation we can use a moving time window to reduce the optimization problem to manageable dimensions. A window approach was presented by Jang et al. (1986) and extended later by Liebman et al. (1992). 

Looking at Figure 9.36, it is obvious that the signal could be represented by only one or two frequency components if the transformation was performed within a moving time window. This kind of time-frequency analysis is available in the so-called short-time Fourier transform (STFT). The problem with STFT is that the resolution in time and... 

Augment Data Matrix with the Moving Time Window Approach... 

The moving time window approach uses a length-invariable window and moves it along the time axis with a fixed step. With the approach, local dynamic characteristics of data... 

A dynamic monitoring scheme using moving time window... 

To make the proposed parameters selection algorithms useful in real plants, we propose a dynamic monitoring scheme that addresses the issues of operation steady situations varying with time. With the tolerance limits Qa and t a, a complete procedure for dynamic process monitoring, including moving time window approach and parameters selection criteria, is implemented in real time, as follows ... 

The size of the moving time window, which is used for storing past input-output examples... 

Nevertheless, polarization analysis (the investigation of the different oscillation directions of the various types of seismic waves in space), averaged over moving time-windows, sometimes... 

Additional CWI parameters concern the similarity between the reference and current CFs and temporal averaging. For the application at Okmok, the peak of the time-windowed correlation is required to exceed 0.9 in order for the associated time-lag measurement within the moving time window to be considered when... 

Unfolded state a is characterized by a wide uni-modal and asymmetrical distribution of R, with a slow rise and a sharp drop. The distribution becomes narrower and more symmetrical when the averaging time window is larger than the characteristic time scale of conformational dynamics in this unfolded state. This indicates a correlation between structure and dynamics, where conformations that correspond to shorter R move on faster time scales. 

The distributions of (R)tw obtained for a polypeptide immobilized on the attractive surface are presented in Fig. 11. Surface-immobilization is seen once again not to affect the behavior of the folded state. In this case, surface immobilization is also seen to have a relatively minor effect on the behavior at the midpoint. However, the behavior in unfolded states a and fi is clearly influenced by surface immobilization in this case. More specifically, the (R)tw distributions are hardly affected by the time-window-averaging for values of Tw that were seen to significantly modify the (R)tw distributions in the freely diffusing and repulsive surface-immobilized cases. This can be attributed to the slower dynamics of the unfolded polypeptide on the attractive surface. At the same time, conformations with a small value of R are still seen to move faster than conformations with a large value of R, as for the freely diffusing polypeptide. 

Moving average is the simplest technique for smoothing. The operator determines a time window within which the values are averaged. For the next value the window is lagged one step ahead and the mean is again calculated. The time window will then be... 

Another possibility is to smooth the seasonal fluctuations using the moving average procedure, but this leads to lack of sharpness because a certain number of values in the lagged time window is included. Seasonally adjusted series achieved by seasonal decomposition are also good starting points for trend searching. 

In the strobe or pulse sampling technique, the sample is excited with a pulsed light source. The intensity of the fluorescence emission is measured in a very narrow time window on each pulse and saved on the computer. The time window is moved after each pulse. When data have been sampled over the appropriate range of time, a decay curve of emission intensity vs. time can be constructed. 

When you choose New Window, a second window of the active document is opened. You can then re-size and move the windows so that the desired parts of the worksheet can be seen at the same time. This is useful if you want to Cut or Copy several cell ranges and then Paste them into another area of a worksheet, but the two areas of the worksheet are far apart. 

Now, with the macro taking care of the mechanics of convolution, we can more conveniently explore its properties. First, move the window function y around on the time axis. 

When new measured data are available, move the window in time to include the most recent measurement while maintaining the maximum dyadic window length. The window length is held constant after reaching an upper limit, which will be discussed in Section 5.3. 

This strict adherence to time windows has come under attack in recent years because it neglects patient physiology [18,19], Common sense dismisses the idea that a patient instantly changes from a good treatment candidate to a bad one when the clock moves beyond the window. From clinical experience alone, we know this to be incorrect as there are patients who have large infarcts despite early presentation (Fig. 12.7). Moreover, multiple studies have demonstrated that there can be substantial volumes of viable penumbral tissue between 12 and 24 h from stroke onset [99-101],... 

In the previous section, we utilized local PCA to represent the moving normal modes, which depicted the locally harmonic but globally anharmonic dynamics of proteins. The major difficulty we met within the local PCA was the fact that two principal modes determined in adjacent time-windows, e,variance-covariance matrix C, or the quasidegeneracy in C. From a statistical viewpoint, this difficulty can be attributed to statistical fluctuation in the estimation of the principal modes due to the small sampling size in the determination of local PCA. 

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