Landscape-plot

The manual investigation and interpretation of such complicated chromatograms is a very time-consuming enterprise. To facilitate the evaluation of HPLC-chromatograms there are several software-aided methods available, the two main methods being the extract-ion -function and the landscape -plot. 

A major disadvantage of the extracted ion traces is the possibility of overseeing unknown by-products since only the expected masses are monitored. An excellent overview of all masses is given by the 2-dimensional landscape-plot with the retention times on the x-axis, and the molecular masses on the y-axis. Figure 17.21(a) and (b) show the TIC and the related landscape-plot respectively of apart of Figure 17.19(b). The common problem... 

The need for housing certain functions of plant operation has been pointed out. The design engineer will usually have the assistance of architects to provide an over-all plan for buildings, open structures, and landscaping. Plot plans and models of process equipment areas are developed and then architectural designs are submitted for the final... 

Figure B3.3.10. Contour plots of the free energy landscape associated with crystal niicleation for spherical particles with short-range attractions. The axes represent the number of atoms identifiable as belonging to a high-density cluster, and as being in a crystalline environment, respectively, (a) State point significantly below the metastable critical temperature. The niicleation pathway involves simple growth of a crystalline nucleus, (b) State point at the metastable critical temperature. The niicleation pathway is significantly curved, and the initial nucleus is liqiiidlike rather than crystalline. Thanks are due to D Frenkel and P R ten Wolde for this figure. For fiirther details see [189].

Fig. 5. The left hand side figure shows a contour plot of the potential energy landscape due to V4 with equipotential lines of the energies E = 1.5, 2, 3 (solid lines) and E = 7,8,12 (dashed lines). There are minima at the four points ( 1, 1) (named A to D), a local maximum at (0, 0), and saddle-points in between the minima. The right hand figure illustrates a solution of the corresponding Hamiltonian system with total energy E = 4.5 (positions qi and qs versus time t).

HS Chan, KA Dill. Protein folding m the landscape perspective Chevron plots and non-AiT-henius kinetics. Proteins 30 2-33, 1998. 

Chan, H. S., and Dill, K. A. (1998). Protein folding in the landscape perspective Chevron plots and non-Arrhenius kinetics. Proteins Struct. Fund. Genet. 30, 2-33. 

Comparing Figure 4-5 with the corresponding plot from the straight line fit in Figure 4-3, an important difference is that the landscape is no longer parabolic. There is a flat region and a very steep increase at the back comer. Nevertheless, the contour lines clearly indicate that there is a minimum near the correct position. 

More careful examination of this shape reveals two important facts, (a) Plots of ssq as a function of k at fixed Io are not parabolas, while plots of ssq vs. Io at fixed k are parabolas. This indicates that Io is a linear parameter and k is not. (b) Close to the minimum, the landscape becomes almost parabolic, see Figure 4-6. We will see later in Chapter 4.3, Non-Linear Regression, that the fitting of non-linear parameters involves linearisation. The almost parabolic landscape close to the minimum indicates that the linearisation is a good approximation. 

Fig. 2. Example of rough activity landscape. This figure shows the activity landscape for a series of related antibacterial compounds plotted in using the 2D BCUT descriptors to arrange the compounds. (A) Shows how the compounds are arrayed in a 2D representation of the chemistry space with the height of the marker being proportional to the minimum inhibitor concentration of the compounds [the smaller the minimum inhibitory concentration (MIC) the more potent the compound]. (B) This second panel presents the upper figure as a 2D figure to enhance the sharp cutoff between active and inactive compounds, emphasizing the point that activity landscapes are rarely smooth continuous functions.

Fig. 2. Dihedral energy exploration of pentane. (A) Pentane (C5H12) molecule with two dihedral bonds (rotatable bonds). (B) 2D contour plot of the energy landscape for pentane. (C) 3D contour plot of the energy landscape of pentane. The large circle and peak in the center of the plots (B) and (C), respectively, are the result of carbons 1 and 5 in close proximity ( = 57, -57, / = -57, 57).

Figures 3.4 and 3.5 show two possible in-licensing opportunities and how the method can reveal the fit7 of each to the internal landscape or the relative merits with regard to the marketplace and be plotted against each other and a quadrant chart produced to visualize the result.

Figure 8.50 A comparison of the performance of atom-atom potentials using the UNI method80 and PIXEL potentials in the description of the energy landscape for 133 naphthalene crystal structures. The experimental crystal structure is represented by a cluster of 5 points representing very similar structures with different unit cell settings. Energies are given on the abscissa in kj mol 1. The plot shows the usual way of representing the results of crystal structure calculations with the expectation that the most stable structure should be at the lowest energy and exhibit the highest density. (Reproduced with permission from The Royal Society of Chemistry).

Structure-activity similarity (SAS) maps, first described by Shanmugasundaram and Maggiora (35), are pairwise plots of the structure similarity against the activity similarity. The resultant plot can be divided into four quadrants, allowing one to identify molecules characteristic of one of four possible behaviors smooth regions of the SAR space (rough), activity cliffs, nondescript (i.e., low structural similarity and low activity similarity), and scaffold hops (low structural similarity but high activity similarity). Recently, SAS maps have been extended to take into account multiple descriptor representations (two and three dimensions) (36, 37). In addition to SAS maps, other pairwise metrics to characterize and visualize SAR landscapes have been developed such as the structure-activity landscape index (SALI) (38) and the structure-activity index (SARI) (39). 

The fitness function is simply the mapping between points in sequence space and their fitnesses. The fitness landscape is the combination of the fitness function and the neighbor relationship. With neighbors defined by point mutation, for an N-site molecule, the landscape is the N-dimensional surface that results from plotting the fitness function over an N-dimensional Cartesian coordinate sequence space (Fig. 13). 

Fig. 3. Semi-log plot of the correlation function for random walks on the TVK-landscape for TV = 96 and (from top to bottom) K = 2,8, and 48. In calculating the correlation function, neighbors of each residue are chosen randomly with equal probability. Reprinted from Weinberger (1990) with permission, 1990 by Springer-Verlag.

Fig. 12. The average number of mutations tried at a suboptimal fitness plotted versus the fitness for the case D = AN = 1500, where A is the alphabet size and AT is the sequence length. Note the rapid increase in the number of required trials when the sequence reaches the inner boundary region. The line is generated analytically under the assumption of the random energy landscape. Reprinted with permission from Macken, C. A., Hagen, P. S., and Perelson, A. S., Evolutionary Walks on Rugged Landscapes, SIAM J. Appl. Math., 51 (1991), p. 821. Copyright 1991 by the Society for Industrial and Applied Mathematics. All rights reserved.

Fig. 21. The diffusion constant on a neutral network D0 is plotted versus the mutation rate pm. The simulations ( ) are for RNA sequence length N = 76 and population size M = 1000 and are allowed to equilibirate before the statistics are taken. The solid line is the theoretical D0 and ( ) are flow-reactor simulations for a flat landscape. The dotted line is calculated for D0X, where A = 0.3 is the estimated fraction of neutral mutants. Reprinted from Huynen etal. (1996) with permission. Copyright (1996) National Academy of Sciences, USA.

Average the temperatures at which crystal formation occurs for solutions that contain the same volume of water. Plot these data on graph paper. Set up your graph sideways on the graph paper (landscape orientation). Plot solubility on the vertical axis. (The units are grams of solute per 100 mL of water.) Plot temperature on the horizontal axis. 

Moreover, this fitting shows that in the considered temperature-frequency landscape, only the temperature dependence of As = As(T) and r = x(T) is observed, while the other parameters B, (3, A, and q are not temperature-dependent. Thus, the proposed phenomenological model (114) as a modification of the CD function (21) with a conductivity term could be successfully applied for simultaneous fitting of dc-conductivity, the main process, and the EW presented in the master plots (see Fig. 27). 

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