Uniform sampling

In the systematic approach, the contaminated signal was processed using transients with parameters selected from a uniformly sampled grid in the parameter space. For each parameter value, the quality of the processed signal was computed. An example result is presented in Figure 2 which shows the performance as a function of the two parameters and / p. The parameter values /, and which yielded the lowest entropy were selected for processing. 

Reports of sterilisation (qv) against bacteria by nonthermal effects have appeared, but it is generally beheved that the effect is only that of heating (164). Because microwave heating often is not uniform, studies in this area can be seriously flawed by simplistic assumptions of uniform sample temperature. 

In this chapter, we are not concerned with establishing the thickness of a uniform sample that is, we shall not deal with thickness gaging, which has already been discussed (3.2), but with determining the thickness of a film that rests upon a substrate of different composition for example, tin plate upon steel. 

Figure 4.40. Content uniformity samples (10 each) taken from the beginning, middle, and end of a production run and each assayed for the compounds A and B. The results were sorted according to size both the slopes and the averages are very similar and well within the allowed range.

An alternative approach to the discretion of the translation parameter i( involves uniform sampling of the measured signal at all scales, i.e., u = kr, with k e Z. The resulting decomposition algorithm is of complexity OiN log N), and the associated reconstruction requires the computation of N log N coefficients, i.e., it contains redundant information. 

Fig, 10. Methodology for multiscale (a) decomposition and (b) reconstruction, using wavelets, with uniform sampling (m, n) e Z. ... 

Fig. 11. Wavelet decomposition (a) dyadic sampling using Daubechies-6 wavelet (b) uniform sampling using cubic spline wavelet.

The gas flow direction was from the top to bottom of the figure. No divergence is observed in the dispersion curve of the capillary, indicating that under the given conditions the dispersion of flow is small, and that this scheme is thus adequate to study the dispersion within a device of interest. This may appear unexpected, as microfluidic devices are usually assumed to exhibit laminar flow, however it can be explained by the fast lateral diffusion of individual gas molecules, which uniformly sample the whole cross section of the tube in a very short time compared with the travel time. Below each image, its projection is shown together with an independ-... 

An approach that does not suffer from such problems is the ABF method. This method is based on computing the mean force on and then removing this force in order to improve sampling. This leads to uniform sampling along . The dynamics of corresponds to a random walk with zero mean force. Only the fluctuating part of the instantaneous force on remains. This method is quite simple to implement and leads to a very small statistical error and excellent convergence. 

In the Metropolis algorithm the components of the displacement vector 8y are obtained by uniformly sampling from the domain D, centered in the coordinates of the molecule y in the i configuration, and defined by the maximum allowed displacement max an(j maximum allowed rotation 8(>MAX parameters (convergence celerity greatly depends on the values used for these two parameters). That is, all the positions inside domain D have the same probability to be chosen as new trial configurations. Thus ... 

Two methods are commonly used in order to select the rotation axis t,. In the method of Barker and Watts [27,28] , is chosen by uniformly sampling between the axis x,y and z in a fixed frame of reference. The second method makes use of the Euler angles [29],... 

Homogenization Reducing sample particle size and creating a uniform sample Sonication, grinding... 

These descriptors were calculated for all compounds in the set of interest. Finally, cell-based subset selection was performed using uniform sampling of one compound per cell, with the choice of compound within the cell weighted by activity in the primary assay. The number of bins per axis was varied to achieve the closest possible match to the desired selection size. 

One cannot overemphasise the importance of accurate abundance measurements and estimates of the errors involved in them. If suitable data are unavailable, or if their quality cannot be properly assessed, it is quite impossible to draw astrophysical conclusions. In this respect, systematic observation campaigns are preferable, collecting large and uniform samples of good quality. One might seek to achieve the aims on the following hst ... 

Normalized signal produced, as a function of elution volume, at the outlet of a size-exclusion chromatography set-up, by an instantaneous injection of a uniform sample. 

Figure 3 The collapse of the peptide Ace-Nle30-Nme under deeply quenched poor solvent conditions monitored by both radius of gyration (Panel A) and energy relaxation (Panel B). MC simulations were performed in dihedral space 81% of moves attempted to change angles, 9% sampled the w angles, and 10% the side chains. For the randomized case (solid line), all angles were uniformly sampled from the interval —180° to 180° each time. For the stepwise case (dashed line), dihedral angles were perturbed uniformly by a maximum of 10° for 4>/ / moves, 2° for w moves, and 30° for side-chain moves. In the mixed case (dash-dotted line), the stepwise protocol was modified to include nonlocal moves with fractions of 20% for 4>/ J/ moves, 10% for to moves, and 30% for side-chain moves. For each of the three cases, data from 20 independent runs were combined to yield the traces shown. CPU times are approximate, since stochastic variations in runtime were observed for the independent runs. Each run comprised of 3 x 107 steps. Error estimates are not shown in the interest of clarity, but indicated the results to be robust.

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