Histogram Representation

Using this method makes comparisons difficult. If we divide each mass fraction by the screen interval, we obtain the relative frequency for each class  

TABLE 15.5 A Representative Sieve Analysis for a Sample Size of 900 g 

Sieve No. Mesh Size (mm) Average Particle Size Mass (kg) Mass Fraction Cumulative Mass Fraction Oversize Cumulative Mass Fraction Undersize 

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Figure lb. Histogram representation of a particle size distribution. Reproduced with permission from Ref. 8. Copyright 1985 Oxford IBH Publishing. 

Recently, an entropy-based approach has been introduced to compare the intrinsic and extrinsic variability of different descriptors, independent of their units and value ranges. The method was originally introduced in communication theory and is based on Shannon entropy, which calculates descriptor-entropy values using histogram representations. Shannon entropy is defined as ... 

Figure 4.1 Ligand-based virtual screening methods. The figure shows different computational methods for screening compound databases that take either a local or a global view on molecular structure. Molecular similarity methods that operate on molecular descriptors, histogram representations, superposition or (reduced) molecular graphs evaluate molecular structure globally. By contrast, local structural features are explored by substructure and pharmacophore searching or QSAR modeling.

Equation (6.37) describes a continuous function, whereas the spectrum is a histogram. Therefore, the algorithm in Eq. (6.10) must be applied to convert Eq. (6.37) to a histogram representation. 

FIGURE 3.2 SE and DSE calculations. Histogram representations of values of a molecular descriptor with relatively high information content in two compound databases (A and B) and either distinct (top) or similar (bottom) value distributions. SE values are an entropic measure of information content. For the distributions, calculated scaled SE and DSE values are reported. DSE calculations add value range dependence as a parameter to information content analysis. 

The principal feature of MONK 6 is tire incorporation of a new point form nuclear data base. The FOND system of collision processing in MONK S has been replaced by the DICE mc ular coding package, which achieves enhanced accuracy via a histogram representation of all primary reaction cross sections using a fixed mesh. DICE is linked, via the program MOULD, with the UKNDF library, which contains up-to-date evaluations of differential cross sections. 

Fig. 6. Histogram representation of americium/europium separation factors (as representative of lanthan-ide/actinide group separation factors) for a representative collection of separation methods ...

HARDWARE The physical electronics equipment. HISTOGRAM Representation of a variable by means of vertical bars here, the actual shape of a peak in a spectrum due to it being composed of discrete channels. 

FIGURE 10.5 Histogram representation of the mass spectral peaks that would be observed for the (a) carboxypeptidase and (b) aminopeptidase digestion of the peptide DAEFR forming a perfect ladder mixture. 

FIGURE 10.17 Histogram representation of the mass spectral peaks that would be observed for the a. 

For statistical purposes, a histogram representation may be preferred, where the x-axis shows the concentration predicted values and the y-axis shows the pixel counts [21]. This histogram may provide information on the characteristics of the sample and on the quality of the calibration model. As for sample characteristics, the homogeneity of compound distribution is represented by the width of... 

Figure 9.20 Histogram representation of the position-dependent tunneling current...

We will describe below the SE formalism in detail and explain how it can be used to estimate chemical information content based on histogram representations of feature value distributions. Examples from our work and studies by others will be used to illustrate key aspects of chemical information content analysis. Although we focus on the Shannon entropy concept, other measures of information content will also be discussed, albeit briefly. We will also explain why it has been useful to extend the Shannon entropy concept by introducing differential Shannon entropy (DSE) to facilitate large-scale analysis and comparison of chemical features. The DSE formalism has ultimately led to the introduction of the SE-DSE metric. 

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