Degree of similarity

The obvious way to form a similarity between the Wigner rotation matrix and the adiabatic-to-diabatic transformation mabix defined in Eqs. (28) is to consider the (unbreakable) multidegeneracy case that is based, just like Wigner rotation matrix, on a single axis of rotation. For this sake, we consider the particular set of T matrices as defined in Eq. (51) and derive the relevant adiabatic-to-diabatic transfonnation matrices. In what follows, the degree of similarity between the two types of matrices will be presented for three special cases, namely, the two-state case which in Wigner s notation is the case, j =, the tri-state case (i.e.,7 = 1) and the tetra-state case (i.e.,7 = ). 

Fig. 1), these are adjudged to be bioequivalent. The FDA sets the degree of similarity needed to be so termed. This concept is of obvious importance for the acceptance of generic dmg products for marketing. 

Compatibility with Personnel Expectations Compatibility refers to the degree of similarity between the direction of physical movement of a control or an instrument indicator and the worker s expectations. Many errors are due to the fact that the operation of the controls or the layout of the displays is incompatible with population stereotypes. For instance, on a control panel it is customary to increase the value of a parameter by turning the appropriate switch clockwise and reduce its value by turning it coimterclockwise. (Note that this stereotype is the opposite for controls which control flow directly, e.g., valves.) If such a stereotype is violated, errors may occur. Although such errors may be recoverable in the short run, under the stress of a process transient they may lead to serious consequences. 

If a phylogenetic comparison is made of the 16S-Iike rRNAs from an archae-bacterium Halobacterium volcanii), a eubacterium E. coli), and a eukaryote (the yeast Saccharomyces cerevisiae), a striking similarity in secondary structure emerges (Figure 12.40). Remarkably, these secondary structures are similar despite the fact that the nucleotide sequences of these rRNAs themselves exhibit a low degree of similarity. Apparently, evolution is acting at the level of rRNA secondary structure, not rRNA nucleotide sequence. Similar conserved folding patterns are seen for the 23S-Iike and 5S-Iike rRNAs that reside in the... 

Molecular similarity searching provides the possibility of finding unrelated but functionally analogous molecules. This is a very nice feature because many distinct structures in contact with a CSP often share the same active sites. The compounds which have a structure similar to the structure of the sample query can be displayed automatically in order of their similarity. The degree of similarity is measured by a numerical value on a scale of 0 to 100 that may be included in the output form. An example of a similarity search is shown in Fig. 4-3. In this example, a search is being performed for the AZT with a similarity value >65 %. 

The same type of vibration spectra is obtained for other heptafluorotantalates and heptafluoroniobates of alkali metals as well, with the degree of similarity depending to a certain degree on the nature of the second cation. The bands usually shift to the red when going from Li to Cs. This shift is related to a slight increase in the share of Ta-F bond covalence. 

The ability to compare semiochemical patterns and to assess degrees of similarity is a likely mechanism underlying the establishment, and eventually the maintenance of genetic divergence. Amongst Tamarins (Saguinus spp.) and Marmosets, both for within- and between- (related) species distinctions, the complexity of their scent marks provides a discriminatory mechanism (Epple et ai, 1987 Smith et al., 1997). Mixed species groups of these monkeys are enabled to co-exist, to... 

Conventional XRF analysis uses calibration by regression, which is quite feasible for known matrices. Both single and multi-element standards are in use, prepared for example by vacuum evaporation of elements or compounds on a thin Mylar film. Comparing the X-ray intensities of the sample with those of a standard, allows quantitative analysis. Depending on the degree of similarity between sample and standard, a small or large correction for matrix effects is required. Calibration standards and samples must be carefully prepared standards must be checked frequently because of polymer degradation from continued exposure to X-rays. For trace-element determination, a standard very close in composition to the sample is required. This may be a certified reference material or a sample analysed by a primary technique (e.g. NAA). Standard reference material for rubber samples is not commercially available. Use can also be made of an internal standard,... 

A map that organizes some living creatures by their degree of similarity. 

There are a number of uncertainties associated with estimating air permeabilities in this way. The soil associations described by the SCS on the county maps generally consist of one or more major soil series and may also include one or more minor soil series. The fraction of the mapped area occupied by these minor soil series, and the degree of similarity of physical... 

The 10,11-epoxide of chlorovulone I (107) was also obtained in low yield (0.05%) from the hexane extract of C. viridis [124], Its structure was assembled from spectroscopic data which showed a high degree of similarity to that obtained for chlorovulone I (100) except for UV and 1H NMR features due to the Cl0,11-olefin. Confirmation of structure came from synthesis of 107 by epoxidation of chlorovulone I. Epoxy-chlorovulone I (107) was found to possess the same 12R hydroxyl stereochemistry. The cis relationship of the epoxide and hydroxyl group was indicated by an intramolecular hydrogen bond as revealed by characteristic IR absorptions at high dilution. This 10,11-epoxide derivative... 

Use of correlation coefficients between amino acid profile data in order to efficiently quantify the degree of similarity between unknown samples and reference proteinaceous materials [7]. The method processes quantitative amino acid concentrations either as per cent relative content (pg g 1 %) or per cent molar content (mol %). A match of more than 0.9 is necessary to ensure a reliable identification of the proteinaceous binder. Table 9.3 reports results obtained on samples coming from the Tintori Collection analysed with two different analytical procedures showing a good correlation with the egg-based binder [96]. 

Ryanodine receptors have a high-degree of similarity to IP3 receptors and they are responsible for Ca2+ influx from sarcoplasmic reticulum of skeletal and cardiac muscles. The ryanodine receptor also forms a very large homotetramer,... 

The amino acid sequences of the glutamate transporters show a high degree of similarity with between 40-60% of amino acid residues identical between subtypes. At present, the three-dimensional (3D) structure of the transporters is unknown and indirect methods based on amino acid sequence hydropathy plots and amino acid accessibility methods have been employed to predict the transmembrane topology of the transporters. Two similar models developed by the groups of Amara (12,13) and Kanner... 

Initially the substance at Rt 19.95 was identified as 2-nonen-l-ol based on mass spectrum library search. The comparison with a commercial 2-nonen-l-ol standard indeed revealed a high degree of similarity between the mass spectra, but a distinct deviation regarding the retention time suggesting a similar molecule with a chain length greater than 2-nonen-l-ol. The substance Rt 20.95 was tentatively identified as 6,10-dimethyl-5,9-undecadien-2-one which corresponds with the authentic standard regarding mass spectra and retention time. 

It is therefore highly desirable to establish an algorithm that allows to consistently perform molecular alignment before concluding any degree of similarity between molecules. Generally speaking, two approaches are used routinely. 

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