Ridge optimization

The ridge optimization method starts off analogous to the LST by locating the highest-energy point along a line between the reactant and product. Two intermediate points are then... 

There are generally three types of peaks pure 2D absorption peaks, pure negative 2D dispersion peaks, and phase-twisted absorption-dispersion peaks. Since the prime purpose of apodization is to enhance resolution and optimize sensitivity, it is necessary to know the peak shape on which apodization is planned. For example, absorption-mode lines, which display protruding ridges from top to bottom, can be dealt with by applying Lorentz-Gauss window functions, while phase-twisted absorption-dispersion peaks will need some special apodization operations, such as muliplication by sine-bell or phase-shifted sine-bell functions. 

Figure 35B, the IMPACT-HMBC spectrum combines optimal a/cH suppression, absence of F1 ridges, and very good signal to noise ratio using a minimum experimental time. It should be also stated that the attribution of the resonances can be correctly performed only in the case of the IMPACT-HMBC spectrum (Figure 35B). 

FIGURE4.38 Ridge regression for the PAC data set. The optimal ridge parameter AK —4.3 is evaluated using repeated 10-fold CV. The resulting (average) predictions (in black) versus the measured y-values are shown with two different scales because of severe prediction errors for two objects. 

Experimentally measured ph for the system (17) for two qualitatively different situations are shown in Figs. 7 and 8. It is immediately evident (1) that the prehistory distributions are sharp and have well-defined ridges (2) that the ridges follow very closely the theoretical trajectories obtained by solving numerically the equations of motion for the optimal paths, shown by the full curves on the top planes. It is important to compare the fluctuational path bringing the system to (qf, relaxational path back towards the stable state in thermal equilibrium, Fig. 7, and away from it, Fig. 8. Figure 7 plots the distribution for the system (17) in thermal equilibrium, namely A = 0. The... 

Figure 8. Fluctuational behavior measured and calculated for an electronic model of the nonequilibrium system (17) with A = 0.264, D — 0.012. The man figure plots the prehistory probability density (pk x,t]Xf,0) and posthistory distribution to/from the remote state Xf — —0.63, t — 0.83, which lies on the switching line. In the top plane, the fluctuational (squares) and relaxational (circles) optimal paths to/from this remote state were determined by tracing the ridges of the distribution [62],...

Delmau, L.H., Birdwell, J.F. Jr., Bonnesen, P.V. et al. 2002. Caustic-side solvent extraction Chemical and physical properties of the optimized solvent. Oak Ridge National Laboratory. ORNL/TM-2002/190. 

Forrester, J.B. and Kalivas, J.H., Ridge regression optimization using a harmonious approach, J. Chemom., 18, 372-384, 2004. 

Response surface models are local Taylor expansion models which are valid only in the explored domain. It is often found that the stationary point on the response surface is remote from the explored domain and in the model may not describe any real phenomenon around the stationary point. Mathematically, a stationary point can be a maximum, a minimum, or a saddle point but it sometimes corresponds to unrealistic reponses (e.g. yield > 100%) or unattainable experimental conditions (e.g. negative concentrations of reactants). When the stationary point is outside the explored domain, the response surface is monotonous in the explored experimental domain and zx directions which correspond to small coefficients will describe rising or falling ridges. Exploring such ridges offers a means for optimizing the response even if the response surface should be oddly shaped. 

Figure 50. (a) The Oak Ridge thermal ellipsoid plot (ORTEP) drawing of Fc—Q. b) Optimized... 

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