Histograms Construction

Fig. 13 Plateau count conductance histograms constructed from the plateaus found in the steplike conductance-distance traces for Au-l,9-nonanedithiol-Au junctions, (a) 1,600 selected out of 4,300 traces employing a 1 nA (max) preamplifier (b) 1,100 selected out of 4,300 traces recorded with the 10 nA (max) preamplifier. All other conditions are identical to those in Fig. 12. The insets in (a) and (b) show that the currents within each series scale approximately linearly with the number of peaks [64]...

Figure 17a shows, as an example, the plateau data-point histograms of T3 at three bias voltages. Each histogram, constructed from more than 1,000 individual traces, reveals a distinct maximum. The peak positions from individual experiments are very reproducible for low bias voltages Vbias < 0-30 V. The broad asymmetric tail region toward higher conductance values is attributed to contributions from... 

Fig. 11.3. Evaluation of stretching uniformity, (a) Histogram constructed from the end-to-end length of seventy T7-DNA-RNAP-QD complexes. A Gaussian fit to the data is centered at 11.75 xm corresponding to 86% of the contour length. The width of the distribution is 1.6 pm corresponding to about 12%. (b) Cropped fluorescence images of fuU length T7-phage genomes flow stretched on a polylysine coated coverslip...

Fig. 11.4. Evaluation of binding specificity. Histogram constructed from 161 distances between a bound QD and the DNA end. To account for both possible orientations of the stretched DNA, only the distance to the closest end was considered. The nonuniform distribution of the binding profile is hkely to do with specific binding to the promoter (and other hot spots )...

I Ikcal/mol. From this initial simulation a histogram is constructed which gives the iber of times a state with an energy in the range E to E + 6E is determined. These histo-a values cire stored in an array H( ). Each of the values in this cirray (H(E)) should initially approximate the energy distribution at the temperature Tq ... 

A radial distribution function can be determined by setting up a histogram for various distances and then looking at all pairs of molecules to construct the diagram. Diffusion coefficients can be obtained by measuring the net distances... 

The distribution curves may be regarded as histograms in which the class intervals (see p. 26) are indefinitely narrow and in which the size distribution follows the normal or log-normal law exactly. The distribution curves constructed from experimental data will deviate more or less widely from the ideal form, partly because the number of particles in the sample is necessarily severely limited, and partly because the postulated distribution... 

The data in Table 4.12 are best displayed as a histogram, in which the frequency of occurrence for equal intervals of data is plotted versus the midpoint of each interval. Table 4.13 and figure 4.8 show a frequency table and histogram for the data in Table 4.12. Note that the histogram was constructed such that the mean value for the data set is centered within its interval. In addition, a normal distribution curve using X and to estimate p, and is superimposed on the histogram. 

To efficiently construct a histogram for grouped data firstly requires the determination of the optimum number of classes the data range is separated into. A suitable... 

Once the mean and standard deviation have been determined, the frequency distribution determined from the PDF can be compared to the original histogram, if one was constructed, by using a scaling factor in the PDF equation. For example, the expected frequency for the Normal distribution is given by ... 

As explained didactically by King and Warshel (1990), a histogram for n/x) can be constructed in which the number of times the condition x = Ae occurs is collected for all x, and the functions P/x) and Pp(x) can be obtained. A technique called umbrella sampling is used for this purpose. Figure 35.3 shows curves for Ag ... 

Figure 4.4 Histogram of the lateral chain dimension for the PMMA-Pe chains in ultra-thin films with thickness 15, 50, and 80 nm.The PMMAchains with a molecularweightof4 x 10 were selected in the SNOM images and analyzed to construct the histogram. Reproduced with permission from The Society of Polymer Science, Japan.

Figure 12.10 Typical time traces of (a) emission intensityand (b) lifetime, measured from a single DMPBI nanocrystal, (c) Photon correlation histogram obtained from the time trace of the emission intensity (a). The lifetimes were obtained by fitting a single exponential function to the decay curves constructed for every 2000...

Histograms tracking the individual and cumulative performances of reactions maybe easily constructed according to reaction yield, atom economy, stoichiometric factor. 

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