Alignment parameter estimation

The maximum search function is designed to locate intensity maxima within a limited area of x apace. Such information is important in order to ensure that the specimen is correctly aligned. The user must supply an initial estimate of the peak location and the boundary of the region of interest. Points surrounding this estimate are sampled in a systematic pattern to form a new estimate of the peak position. Several iterations are performed until the statistical uncertainties in the peak location parameters, as determined by a linearized least squares fit to the intensity data, are within bounds that are consistent with their estimated errors. 

The chapter is divided into three sections the first part is concerned with the derivation of 3D-LogP descriptor and the selection of suitable parameters for the computation of the MLP values. This study was performed on a set of rigid molecules in order, at least initially, to avoid the issue of conformation-dependence. In the second part, both the information content and conformational sensitivity of the 3D-LogP description was established using a set of flexible acetylated amino acids and dipeptides. This initial work was carried out using log P as the property to be estimated/predicted. However, it should be made clear that, while the 3D-LogP descriptor can be used for the prediction of log P, this was not the primary intention behind its the development. Rather, as previously indicated, the rationale for this work was the development of a conformationally sensitive but alignment-free lipophilicity descriptor for use in QSAR model development. The use of log P as the property to be estimated/predicted enables one to establish the extent of information loss, if any, in the process used to transform the results of MLP calculations into a descriptor suitable for use in QSAR analyses. 

The relative lengths of the environmental parameter vectors on the first and second axes (Fig. 7) can be used a measure of importance for the various climate parameters at constraining the directions of the axes. The mean annual temperature has the longest length, followed by enthalpy, specific humidity, and relative humidity. From these scores, we can identify the first axis with mean annual temperature while the second axis aligns with the mean specific or relative humidity. These associations also allow us to infer which character states are most important for estimating the climate parameters as discussed next. 

Another factor to be taken into account is the degree of over determination, or the ratio between the number of observations and the number of variable parameters in the least-squares problem. The number of observations depends on many factors, such as the X-ray wavelength, crystal quality and size, X-ray flux, temperature and experimental details like counting time, crystal alignment and detector characteristics. The number of parameters is likewise not fixed by the size of the asymmetric unit only and can be manipulated in many ways, like adding parameters to describe complicated modes of atomic displacements from their equilibrium positions. Estimated standard deviations on derived bond parameters are obtained from the least-squares covariance matrix as a measure of internal consistency. These quantities do not relate to the absolute values of bond lengths or angles since no physical factors feature in their derivation. 

Field et al.62 developed a general procedure to estimate the Saupe order parameters for spin systems aligned in liquid crystal media by iteratively fitting the experimental and simulated spectral widths of the high-order multiple quantum spectra. 

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