Graphs Comparison

III. Prediction of Higher Order Function A. Graph Comparison... 

Fig. 4. A schematic illustration of graph comparisons. The purpose of comparing different types of graphs is to identify correlated clusters of nodes.

Although this chapter did not discuss much about the amino acid sequence analysis per se, such as sequence comparison, motif detection, and structure prediction, the sequence analysis is a prerequisite of the network analysis. In fact, the network analysis is an integrated analysis of sequence and other information. For example, in the graph comparison of two pathways, it is not only the overall arrangements of nodes... 

Figure 8. Bar graph comparison of the relative increase in recovery achieved for Pyrene for the following changes in experimental variables 70 vs. 0% dead volume 1 1 vs. 1 20 cell dimensions 90 vs. 70°C and 0.80 vs. 0.65 g/ml. The actual percent recoveries are indicated in the top of each bar.

Figure 2. A bar graph comparison of student math percentiles. Computer-generated graphics offer numerous options in terms of theme of visual aid, chart type, color selections (if color is an option), and other chart attributes, such as use of grid lines and location of caption.

Figure 9.19 Use of Damkholer number (Da, ratio of mixing and process characteristic time) for correlation of data. As the pseudo-first order constant used to model the particle formation rate, is not always known, but is obviously the same for each polymer, (Da/ly) is used to correlate the different sets of data (referring to particles produced using different mixing intensity and different initial polymer concentration in the same mixer) quench volumetric ratio = 0.2. Upper graph PEGylated copolymer in acetone at different inlet concentrations and mixing intensities in Tee mixer (d. = 1 mm). Lower graph comparison of different polymers and solvents (fiUed symbols, acetone open symbols, THF) in CIJ mixer (dj = 1 mm) > PCL = 80,000 , PCL = 14,000 A, PEGylated copolymer O, PHDCA (symbols as in Figure 9.6).

Figure 9.24 Top graph Comparison of the size of the nanoparticles obtained from different suspensions containing sucrose and Cremophor EL (A 5% sucrose + 5% Cremophor EL B 5% sucrose + 2.5% Cremophor EL C 2.5% sucrose + 5% Cremophor EL D 2.5% sucrose + 2.5% Cremophor EL) before freeze-drying ( ) and after freeze-drying carried out at different heating shelf temperatures = -20°C, = -30°C). Acetone, = 5 mg/mL, v. = 1.7 m/s, W/S = 1, quench volumetric ratio = 0.33, = 5...

Data analysis of a water quality study Mathematics Graph interpretation Basic statistics Results assessment Calculation of mean value Collecting data from graph Comparison of mean Hardness of water Reliability of data... 

Figure 8.18 presents an alternative bar graph comparison of relative coordination strength for the entire set of Ni(Lig) complexes in their equilibrium... 

At the outset, we were faced with the difficult decision whether to use the Angstrom unit or the nanometre for the dimensions of molecules. After careful consideration, we have come down firmly in favour of the Angstrom and we believe that this decision will meet with the approval of the majority of our readers. When quoting graphs and tables of data from the literature, we have retained the original units (kcal, Torr, C, tonin, etc.) in the belief that it is more reasonable to state the data in the form used by the original author—except where comparisons are being made between results presented in different units. 

Plot E versus log t for both of these sets of data on the same graph. Now suppose that the units of the 45°C experiment are minutes instead of seconds (this is not the case, but we can pretend that it is). On the basis of this imaginary condition, each of the times at 45°C should be multiplied by the factor 60 sec/min to make the comparison with the 25°C data. Apply this correction to the 45°C data and plot on the original graph. Be sure to select a scale of the original graph so that corrected data can be accommodated also, label various portions clearly. Briefly comment on the results of this manipulation. 

Comparison of Alignment Charts and Cartesian Graphs. There are typically fewer lines on an alignment chart as compared to Cartesian plots. This reduces error introduced by interpolation and inconsistency between scales. For example, to find a point (x,j) on a Cartesian graph one draws two lines, one perpendicular to each axis, and these reference lines intersect at the point x,j). This point (x,j) may correspond to some finite value found by rea ding a contour map represented by a family of curves corresponding to different values of the function. 

Much trade literature is of a high standard, particularly that of suppliers of the so-called engineering polymers . In many cases these manufacturers supply a range of such polymer types and they provide much useful comparative material. This may be in the form of descriptive material and tables of numerical data. Suitable choice of graphs and other diagrams can often give the reader a more immediately absorbed visual comparison. 

Fig. 1.32. (a) Molecular graphs and electron density contours for pentane and hexane. Dots on bond paths represent critical points, (b) Comparison of molecular graphs for bicycloalkanes and corresponding propellanes. (Reproduced from Chem. Rev. 91 893 (1991) with permission of the American Chemical Society.)... 

Figure 52 also shows that the actual recovery curve does not decrease below a certain level. This indicates that a certain amount of material is always recovered to the underflow and bypasses classification. If a comparison is made between the minimum recovery level of solids to the liquid that is recovered, they are found to be equal. Therefore it is assumed that a percent of all size fractions reports directly to the underflow as bypassed solids in equal proportion to the liquid split. Then each size fraction of the actual recovery curve is adjusted by an amount equal to the liquid recovery to produce the "corrected recovery" curve shown in Figure 52. As the Djoc point changes from one application to another, the recovery curves shift, along the horizontal axis. In order to determine a single graph which represents the corrected recovery curve, the particle size of each size fraction is divided by the Dj value and a "reduced recovery" curve can be plotted, as shown in Figure 53. Studies reported by Arterburn have shown that this curve remains constant over a wide range of cyclone diameters and operating conditions when applied to a slurry...

Table 11 Comparison of the Proposed Integrated Approach with Traditional Graph Theory for Selective Polymers...

Comparison of the Sapozhnikov graph for NC with the graph by Hackel and Urbanski shows that in the latter the curve has a minimum which corresponds approx to a mixed acid whose nitric acid-to-sulfuric acid weight ratio is about 6 (mole ratio is about 9) (See article on Nitration in this Vol)... 

The specific surface being a gauge of the fineness of a powder, comparison of the result for M-10 and M-20 in Table 10 shows that the Turbidimeter yielded analyses which were consistent with the burning time data, that is, M-10 is a finer powder than M-20. The Micromero-graph showed a smaller difference between these two lots. The Coulter Counter gave results which were inconsistent with the burning times. It... 

Figure 2.7 Comparison of isothermal work of compression. Graph (b) represents the reversible process for which the work required for the compression is a minimum.

Figure 7.8 Comparison of experimental ln7 for 1 1, 2 1, and 2 2 electrolytes. The symbols indicate the experimental results, with representing HC1 (z+ = 1, z = — 1) representing SrC ( + = 2, r = — 1) and A representing ZnS04 (z+ = 2, z = -2). The lines are the Debye-Huckel predictions, with the solid line giving the prediction for (z+ = 1, z = -1) the dashed line for (z+ = 2, r = -1) and the dashed-dotted line for (z+= 2, z =-2). In (a), In 7- calculated from the limiting law [equation (7.45)] is shown graphed against I 2. In (b). In 7- calculated from the extended form [equation (7.43)] is shown graphed against 7m2.

The operational-factor tests performed with A1 filled compounds in comparison with A2 filled compounds revealed higher predicted wear resistance and wet traction with the same level of rolling resistance. At the same time the graph of tan 8 versus temperature in Figure 17.6 shows that tan 8 is higher than that of the A2 compound at low temperatures (-20°C). 

This results in sensible numbers for the class boundaries and allows for comparisons with other series of observations that have different extrema, for example (.375,. 892) or (.25, 1.11). Strict adherence to the theory-inspired rule would have yielded class boundaries. 327,. 4833,. 6395,. 7958, and. 952, with the extreme values being exactly on the edges of the graph. That this is impractical is obvious, mainly because the class boundaries depend on the stochastic element innate in Xmin resp. x ax- Program HISTO, option (Scale), allows for an independent setting of a subdivided range R with C bins of width R/C, and lower/upper limits on the graph. 

Snarey M, Terrett NK, Willett P, Wilton DJ. Comparison of algorithms for dissimilarity-based compound selection. J Mol Graph Model 1997 15 372-85. 

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