Smoothing and Resolution

Whereas the complete RDE vector describes a probability distribution, the individual vector components are related to the relative frequencies of atom distances in the molecule. Thus, the individual g(r) values are plotted in a frequency dimension whereas r lies in the distance dimension (Eigure 5.1). The smoothing parameter B can be interpreted as a temperatnre factor that is, is the root mean square 

RDF descriptors are calcnlated for a certain distance range. This range depends primarily on the size of the largest molecnle to be calculated. It is not mandatory to cover the entire molecnle size to describe a certain feature of a compound. Since 

FIGURE 5.1 RDF descriptor calculated for a polycyclic system. The complete RDF function represents a probability distribution the individual peaks are related to the relative frequencies of atom distances in the molecule. 

Choosing a distance range that covers the size of the majority of molecules in a data set is acceptable for most applications of RDF descriptors. The RDF descriptor length may be limited if only short distance information is important. For instance, a maximum distance of 4 A is usually sufficient to describe a reaction center. 

The parameter B determines the line width of the peaks in an RDF. B depends on the resolution of distances, that is, the step size used for calculating the RDF descriptor components. With decreasing B and increasing number of atoms, an RDF descriptor usually exhibits increasing overlap of peaks. Overlaps in RDF descriptors are not necessarily a disadvantage it can be a desired property for the processing of RDF descriptors with methods that rely on interpolation, such as artificial neural networks (ANNs). The relationship between B and the resolution Ar is 

---

Bromba, M. U. A., and Ziegler, H., Variable Filter for Digital Smoothing and Resolution Enhancement of Noisy Spectra, Ana/. Chem. 56,1984, 2052-2058. 

Bromba, M.U.A. and Ziegler, H., Variable filter for digital smoothing and resolution enhancement of noisy spectra, Anal. Chem., 56, 2052, 1984. 

Some people are confused by the difference between Fourier filters and linear smoothing and resolution functions. In fact, both methods are equivalent and are related... 

The E. coli M41 mutant CPS (46) has a complex chemical sequence. Its repeating unit is an anionic hexamer a tetrasaccharide -A-B-C-D- in the main chain and a disaccharide -F-E- side chain, E attached to C (Table II). Polycrystalline and oriented fibers of the sodium salt of 46 have produced good diffraction data, with reflections up to 3 A resolution. Careful X-ray analysis60 has shown that the polymer forms a left-handed, smooth and sinuous, 2-fold helix of pitch 30.4 A. As shown in Fig. 39a, the main chain is fairly close to the helix axis. A notable observation is that side chain E-F, turned up toward the non-re-... 

Note As the signals become noisy, mass accuracy may even suffer from too high settings of resolution. Often centroids are determined more accurate from smooth and symmetrically shaped peaks at moderate HR conditions. One should also be aware of the fact that the position of a peak of 0.1 u width needs to be determined to V50 of its width to obtain 2 mmu accuracy. 

When X is 2-dimensional, Xt is smooth and there is a morphism tt X S" X which is a resolution of singularities by a result of Fogarty [17]. This present a contrast to Hilbert schemes for dimX > 2. 

In the realm of hydrolytic reactions, Jacobsen has applied his work with chiral salen complexes to advantage for the kinetic resolution of racemic epoxides. For example, the cobalt salen catalyst 59 gave the chiral bromohydrin 61 in excellent ee (>99%) and good yield (74%) from the racemic bromo-epoxide 60. The higher than 50% yield, unusual for a kinetic resolution, is attributed to a bromide-induced dynamic equilibrium with the dibromo alcohol 62, which allows for conversion of unused substrate into the active enantiomer <99JA6086>. Even the recalcitrant 2,2-disubstituted epoxides e.g., 64) succumbed to smooth kinetic resolution upon treatment with... 

The demand that the solution 6 be consistent with the data i results in the improved resolution that we expect from a deconvolution method. As we have explained, however, it also results in the amplification of high-frequency noise. The smoothing of this noise to some extent defeats the purpose of deconvolution. The tradeoff between smoothness and consistency is explicit in the formulation of a method first described by Phillips (1962) and further developed by Twomey (1965). In this method, we minimize the quantity... 

Fig. 22 Q branch of the RQ4 subband of v4 of CD3F recorded on a grating spectrometer. Trace (a) is the raw data after smoothing and base-line subtraction. The resolution based on the widths of single lines is 0.010 cm-1. Trace (b) is the result of deconvolving this data set with a gaussian of FWHM = 0.010 cm-1. The resolution is 0.0045 cm-1. Trace (c) is a calculated spectrum based on the analysis of an earlier spectrum with a resolution of 0.028 cm-1. The resolution in trace (b) is 0.0045 cm -1 and in trace (e) is 0.0040 cm"1.

Figure 7. High resolution carbon, Cls, spectra from Tokai glassy carbon samples following smoothing and baseline subtraction for various treatments. The treatments include a, O (Linde, 99.6%) RFP b, O (liquid carbonic, USP grade) RFP ...

It is important to determine the optimum filter for any particular application. Too much smoothing and the signal itself is reduced in intensity and resolution. Too little smoothing, and noise remains. The optimum smoothing function depends on peak-widths (in datapoints) as well as noise characteristics. 

The most frequently applied ligands are 2,2 -binaphthol (BINOL la) and 2,2 -bis(diphenyl-phosphino)binaphthyl (BINAP lb). Both antipodes of these compounds are commercially available in enantiopure form, though not at little cost [3]. It is rewarding, therefore, to become acquainted with the syntheses of these compounds, which have been described in detail [4J and have been simplified substantially on the basis of recent publications [5J. The iron(lIl)-catalyzed dimerization of 2-naphthol (2) to give racemic BINOL (rac)-la succeeds smoothly and on a large scale (Scheme 1). Its resolution can be achieved easily with N-benzylcinchoidinium chloride (3) and yields both (/ )- and (5 )-la in high enantiomeric excesses. After conversion into the ditri-flate 4, enantiopure la can be coupled with diphe-nylphosphine (or, in lower yield, with cheaper chlorodiphenylphosphine) in a nickel-catalyzed... 

When a CRO has been chosen, the contract should include a detailed definition of the scope of work required along with a clear understanding of when the data is considered clean and ready for analysis. A test run of data transfer from the CRO to the sponsor should be done early in the study to identify any problems in data formatting and transmission. The milestones and deliverables must be tracked closely during study conduct in order to ensure that appropriate progress payments are made. The importance of regular communication cannot be overemphasized. The early identification and resolution of technical or process problems is necessary for a smooth database closure and transfer of data. Transfer of data often contains more issues and surprises than anticipated. 

---