Analog plot

The human eye is extremely good at comparing the size, shape, and color of pictorial symbols [26-30]. Furthermore, it can simultaneously appreciate both the minute detail and the broad pattern. 

The simple way of transforming a table of numbers to a sheet of pictures is by using analog plots. Numbers are converted to symbols according to their magnitude. The greater the number, the larger the symbol. Multiple variables can be portrayed as separate columns or as differently shaped or colored symbols [31]. 

To compare different variables on the same sheet requires some form of standardization to put them on the same scale. Also, a choice must be made between displaying the magnitude of the numbers or their significance [32,33]. Two possibilities are— 

A study using 50 rats of each sex in each of five groups (two controls and three increasing doses) measured body weight and food and liquid consumption every week or month for 2 years. This resulted in 3 variables X 2 sexes x 5 groups x 53 times x 50 animals. Means alone constituted some 1600 four-digit numbers. 

Body weight gains from the period immediately preceding each consumption measurement were used, since these were less correlated. For each variable and at each time, the sums of squares for group differences were divided into four meaningful contrasts  

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Analogous plots for many other reactions of aromatic compounds show a similar linear correlation with the acid dissociation constants of the corresponding benzoic acids. 

The analog plot chart in Figure 4.5 shows relationships for five measures on a time versus dose basis, allowing ready evaluation of interrelationships and patterns. 

There are numerous approaches to the problem of capturing all the information in a set of multi endpoint data. When the data are continuous in nature, approaches such as the analog plot can be used (Chemoff, 1973 Chambers et al., 1983 Schmid, 1983). A form of control chart also can be derived for such uses when detecting effect rather than exploring relationships between variables is the goal. When the data are discontinuous, other forms of analysis must be used. Just as the control chart can be adapted to analyzing attribute data, an analog plot can be adapted. Other methods are also available. 

A graphical method for analyzing enzyme activation (a metal ion for the case shown above). Initial velocities are plotted in Fig. 1 as a function of the total substrate (S) concentration at different, constant concentrations of the activator (A). An analogous plot (Fig. 2) is made... 

Figure 7.12 Effect of analog-to-digital converter sampling rate on resolution (a) analog plot (b) digital representation. (Reprinted from Ref. 10 with permission.)...

In Fig. 7 an analogous plot for the uncatalyzed chlorination of 2-substituted thiophenes in anhydrous acetic acid is reported. The... 

Fig. 1 shows the distribution curves for cis-(NH3)2Ptn at 4 mM chloride-ion concentration representative of that in the cell nucleus. Fig. 2 shows the analogous plot for the trans-isomer. For both isomers the three dominant species at pH 7.4 are the chloro-hydroxo, dihydroxo, and reactive hy-droxo-aqua complexes. 

Control can also be achieved by changing the relative phase 0F between the two light fields, defined by Eq. (12.66). Figures 12.8a and 12.8ft show significant differ- ences in both the position and intensity of the peaks as a function of 0F. By contrast, an analogous plot (not shown) where only V is included shows no variation in peak intensity as a function of 0F. Similarly, Figures 12.8c and 12.8c/ show the strong... 

Figure 26-11b shows an analogous plot of experimental data obtained with a high-quality research-type ultraviolet/visible spectrophotometer. Note that, in contrast to the less expensive instrument, absorbances of 2.0 or greater can be measured here without serious deterioration in the concentration uncertainty. 

Figure 7.4 shows a typical result. The effluent solute concentration is at some minimum level (Cd) for a period of time until the concentration starts to rise as the MTZ arrives at the column exit. When the concentration rises to the maximum allowable effluent solute concentration (Cbt), breakthrough is said to occur. Column loading is defined as the amount of sorbed material in the bed at the breakthrough divided by the total weight of sorbent in the bed. If the bed were continued in operation past time fbt, the effluent solute concentration would continue to rise until the entire bed was completely loaded and the effluent solute concentration equaled the feed solute concentration (Cf). This situation corresponds to column exhaustion. Note that an analogous plot could be made using total fluid volume processed instead of time as a variable. 

When the data in Fig. 5 is plotted according to this relation (i.e. t/(C - C) vs t) a straight line is obtained (see Fig. 6) with only slight curature at low values of t where a first order plot (log C vs t) shows a reasonable straight line. Similar early curvature (56) in analogous plots was attributed to the time required for temperature equilibration. This is opposite to what is expected here since the concentration - time curve indicates a rapid drop in concentration in the early stages rather than a slower decay rate. 

An upland-soil source is also consistent with the metal concentrations found at lower levels in the salt-marsh cores. The iron content is generally proportional to the mass of inorganic sediment and is found in concentrations (almost 4%) considered reasonable for soil (Bowen, 1966). In an analogous plot for Cu, Fig. 16, the concentrations in deep peat and many of the lower clay-band samples are also typical of soil. 

In order to test the validity of equation (7) for the EHB system, we plotted I I as a function of t T, an example of which is shown in Fig. 7. The linear behaviour of the plot indicates good agreement with equation (7). Analogous plots for A-F, B-E and B-F relaxation rates as a function of tj/T also showed good linearity. The linearity of the i versus tj/T plots implies that overall rotation is extremely important in determining intramolecular cross-relaxation rates and that reorientation of each of the relaxation vectors is adequately described by one correlation time. 

Figure 9 Structure correlation plot for the fragment M(CO)M (M = Fe, Co, Ni) each fragment retrieved from the CSD contributes to two (symmetrically related) points in configurationai space. Reproduced from Macchi, P. Garlaschelli, L Sironi, A. J. Am. Chem. Soc. 2002, 124, 14173-14184 with permission of the American Chemicai Society. (An analogous plot was first presented byOrpen. ...

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