Histograms interactions

One therefore needs a smooth density estimation techniques that is more reliable than the histogram estimates. The automatic estimation poses additional problems in that the traditional statistical techniques for estimating densities usually require the interactive selection of some smoothing parameter (such as the bin size). Some publicly available density estimators are available, but these tended to oversmooth the densities. So we tried a number of ideas based on numerical differentiation of the empirical cdf to devise a better density estimator. 

Figure 1 Schematic of an EDS system on an electron column. The incident electron interacts with the specimen with the emission of X rays. These X rays pass through the window protecting the Si (Li) and are absorbed by the detector crystal. The X-ray energy is transferred to the Si (Li) and processed into a dig-itai signal that is displayed as a histogram of number of photons versus energy.

The exponential tail in the conductance histograms in regions adhesive interactions between Au atoms, and prevents the occurrence of a jump-out-of-contact characteristics. Similar observations were also reported under UHV conditions [195] and in air [216]. 

Line chart Pictogram Pie chart Contour plot Stereogram Color map Histogram Means plot Sliding reference distribution Notched box plot Factor space/response Interaction plot Contour plot Predicted response plot Confidence region plot Confidence limits Graph paper Power curves Nomographs Sample-size curves Trilinear coordinates... 

Fig. 2 0---0 intermolecular/interionic interactions between COOH and COOH/COO( 1 groups in protonated or partially deprotonated polycarboxylic acids. Top histogram the distribution of 0---0 interactions obtained without neutral/charge discrimination (mean value 2.632 A). When the presence of an ionic charge is taken into account the distributions of 0---0 distances are those in the middle [(n)0(H)-"OCOOH(n) and (")0(H)-"Ocoon( mean value 2.650 A] and in the bottom [( )0(H) Ocoo( ), mean value 2.5333 A] histograms... 

Table 2 summarizes the numerical results on average intermolecular/interi-onic 0---0 and intramolecular/intra-ionic C-0 structural parameters for the [COOH]n---[COOH]n, [COOH]a---[COOH]a and [COOH]A---[COO]A inter-molecular interactions, together with those obtained for the [COOH] A- [COO ]A sample in the case of the hydrogen oxalate anion. Data were retrieved from the CSD with a cut-off distance on 0-"0 separations of 3.0 A. A visual prospect of the data listed in column III is provided in Fig. 6, where histograms of intramolecular C-0 distances within the protonated and deprotonated COOH/COO groups are presented. 

Fig. 3. Histogram of the pair-wise interaction energy between the F molecules.

Cluster analysis is far from an automatic technique each stage of the process requires many decisions and therefore close supervision by the analyst. It is imperative that the procedure be as interactive as possible. Therefore, for this study, a menu-driven interactive statistical package was written for PDP-11 and VAX (VMS and UNIX) series computers, which includes adequate computer graphics capabilities. The graphical output includes a variety of histograms and scatter plots based on the raw data or on the results of principal-components analysis or canonical-variates analysis (14). Hierarchical cluster trees are also available. All of the methods mentioned in this study were included as an integral part of the package. 

Figure 8.36 Histograms (a) for C—H N hydrogen bonding interactions as in (b). (Reproduced by permission of The Royal Society of Chemistry).

Figure 8.61 Histogram of intermolecular C-0 terminal and bridging distances for C-H- C=0 bonded complexes in the CSD. Interactions to the more basic bridging CO ligands are significantly shorter. (Reprinted with permission from [91] 1995 American Chemical Society).

Fig. 11. Binding of calmodulin to an array of a diverse set of 144 human proteins enables novel, calcium-dependent interactions to be identified. (A) Binding of Cy3-labeled anti-His tag antibody to the array allows the relative amount of protein in each spot to be determined. (B) Binding of Cy3-labeled calmodulin allows potential interacting partners to be identified. (C) Histogram showing the relative amount of calmodulin bound per unit protein in the presence of calcium ions. (D) Histogram showing the relative amount of calmodulin bound per unit protein in the presence of calcium ions and a high concentration of a divalent metal ion chelator, ethylenediamine tetra-acetic acid.

The two ion gradients that develop in the dialysis experiment are conveniently quantitated in terms of interaction coefficients. A histogram (Fig. 21. IB) diagrams the ion concentrations in a similar experiment as cartooned in Fig. 21.1 A. The total number of KC1 ion pairs that migrates across the membrane as equilibrium is established, when normalized by the number of RNA molecules present, becomes the interaction coefficient rkci- Another way to find the same number is to count the total number of KC1 ion pairs on each side of the membrane at equilibrium... 

LeadScope s data visualization technology makes the interpretation of complex data a routine task. Two-dimensional histograms and scatter plots provide pictorial representations of data sets that can be manipulated using interactive controls. Adjustable sliders, that dynamically reshape data sets, allow users to focus on interesting property ranges. Histograms can also be color-coded to emphasize how compound data correlates to biological activity. 

Results of a hydrochemical study in basaltic aquifers of Hawaii (Hufen et al., 1974) are given in Table 11.2 and in a histogram in Fig. 11.4.This case study is of special importance because it deals with basaltic aquifers, in contrast to carbonate aquifers, to be discussed in the following section. The tritium values in the Hawaii study were 0.3-2.9 TU in 1974, indicating that most or all of the water had a pre-1952 age. The corresponding 14C concentrations were 85-97 pmc. The pre-1952 14C in the atmosphere was about 100 pmc. Hence, part of the waters reported in Table 11.2 maintained all their initial 14C, whereas others lost up to 15% of their initial value. This loss could occur for two reasons (1) interaction with 14C-devoid carbonate rocks (secondary in the basaltic terrain) and (2) aging of the water, reflected... 

Figure 9.12. Histograms of the distribution of interaction strengths for ammonia (left) and carbon dioxide (right) adsorption of y-Al203, MgO and mixed MgAl-oxides obtained from LDHs. After Shen el al. [183].

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