Maximum similarity

The zero prevents negative similarity. The pair of segments with the maximum similarity i< found by first locating the matrix element with the maximum value of Hj j and then tracing... 

The align/pharmacophore experiment orients the molecules to obtain maximum similarity in chemical features. This application can then generate a pharmacophore model consistent with all the molecules. 

Figure 14 shows the computed responses for 0fj, 0q, and oh These coverages increase slowly during NO adsorption but rise rapidly and pass through a maximum when H2 is added to the flow. The responses for 0jjh and 0 u are similar in shape to the response for 0qjj but are significantly smaller in magnitue and, hence, have not been shown in Fig. 14. It is significant to note that the maxima in 0q and 0jj occur at times which coincide with the time at which the rates of N2 and N2O reach a maximum. Similarly, the maxima in 0qh and 0 appear at times nearly identical to the times at which the rates of H2O and NH3 formation reach a maximum.

Due to the spin polarization effect, the magnetic orbitals can be difficult to identify from a spin-unrestricted calculation. Since the total energy of a Kohn—Sham determinant is invariant under unitary transformations between the spin-up orbitals among each other and spin-down orbitals among each other, one can arrange each spin-up orbital to overlap at most with each spin-down orbital on the basis of the corresponding orbital transformation (COT) (88—90). Then, the molecular orbitals (MOs) are ordered into pairs of maximum similarity between spin-up and spin-down orbitals and can be separated into three groups (i) the MOs with spatial overlap close to one (doubly occupied MOs),... 

The USR (Ultrafast Shape Recognition) Method. This method was reported by Ballester and Richards (53) for compound database search on the basis of molecular shape similarity. It was reportedly capable of screening billions of compounds for similar shapes on a single computer. The method is based on the notion that the relative position of the atoms in a molecule is completely determined by inter-atomic distances. Instead of using all inter-atomic distances, USR uses a subset of distances, reducing the computational costs. Specifically, the distances between all atoms of a molecule to each of four strategic points are calculated. Each set of distances forms a distribution, and the three moments (mean, variance, and skewness) of the four distributions are calculated. Thus, for each molecule, 12 USR descriptors are calculated. The inverse of the translated and scaled Manhattan distance between two shape descriptors is used to measure the similarity between the two molecules. A value of 1 corresponds to maximum similarity and a value of 0 corresponds to minimum similarity. 

FLUORESCENCE Spectra. Fluorescence data are presented in Table V. All samples derived from drinking water gave an emission maximum between 417 and 430 nm, whereas the excitation maximum ranged between 346 and 365 nm. Miami IB showed an excitation maximum similar to the CFH samples, but the maximum was quite different from the one exhibited by the aquatic humic substances from the Satilla River. The emission maximum of these samples (Table V), however, was very similar. 

Temperature dependency of the rate of destruction is determined by the effect of temperature upon the cavitation process there is an optimum temperature at which the intensity of cavitation is maximum similarly, the rate and depth of destruction depend upon the frequency of acoustic vibrations. 

Owing to the individual fragmentation based on the described concept of maximum similar substructure the accuracy loss of COSMO/rag is only about 0.05-0.1 log-units compared to direct DFT/COSMO calculations (Fig. 11.9) for typical life science data sets. Water solubility appears to be especially insensitive to the approximations of COSMO/rag. As shown in Fig. 11.10, the rms error only increased from 0.66 to 0.71 log-units for the dataset used in the development of the drug solubility method. 

The lineshape function 5 (t) of solid Neon (Figure 14.8) shows a maximum similar to PIB (Figure 14.6). The slowing-down times rth according to the two state model analysis are in the range of 20 ps to 40 ps [3, 4, 11] and thus are similar to Ah in materials with optical phonons. The process responsible for the shorter slowing-down times in Ne is not yet fully understood and requires further study. 

We first obtain the mean flow by solving the coupled DDEs (6.3.11) and (6.3.13) by standard four-stage Runge-Kutta method. These equations have been solved by taking maximum similarity co-ordinate, r max = 12 equally divided into 4000 sub-intervals. For different Re and K, mean flow has been obtained here. Fixing K, instead of Gr, is motivated by our discussion in the introduction where we have noted that for instability of mixed-convection boundary layers, K is more relevant than Gr. As we have investigated the mixed convection problem in air, we have fixed the value of Pr = 0.7 for all cases. Obtained mean-field results for the non-dimensional velocity and temperature are shown in Fig. 6.1. 

Automatic Search of Maximum Similarity Between Molecular Electrostatic Potential Distributions. ... 

Using the - similarity score based on the weighted combination of steric, electrostatic and hydrophobic properties, molecule alignment is performed starting from a random orientation of two molecules relative to each other the best alignment is achieved with the maximum similarity score. 

By different mathematical transformations. Molecular Quantum Similarity Indices (MQSI) are derived from molecular quantum similarity measures. They are divided into two main classes C-class indices, referred to as correlation-like indices ranging from 0 (maximum dissimilarity) to 1 (maximum similarity), and D-class indices, referred to as distance-like indices ranging from 0 (maximum similarity) to infinity (maximum dissimilarity). C-class indices can be transformed into D-class indices d, by the following ... 

To exemplify a molecular similarity method, we employed here a 3D shape-based molecular similarity approach using OpenEye scientific software (OpenEye). A set of 27 molecules (Amoore, 1971) were compared to benzaldehyde (query molecule). The representation used here is based on the volume of each molecule. A conformational ensemble is built for the molecules in the database, whereas the conformation of the query remains fixed (the chemical nature of benzaldehyde does not entail different conformers, though in many cases the conformation of the query molecules might be complex and crucial). After the conformers of each molecule in the data set are built, each one of them is compared with the query and a similarity value is computed. For the particular program employed here (ROCS), the similarity is quantified as a score formed by two terms, one takes into account the chemical nature of the molecules while the other relies on molecular shape, such score is referred to as combo score. The maximum similarity value is 2 which can only be obtained from the comparison of a molecule with itself in the exact same conformation (perfect match). The normalized values (from 0 to 1) for the odor and combo score similarities are compared in the graph shown in Fig. 2.4. As can be observed, as the combo score increases, the odor similarity to benzaldehyde also increases. This correlation shows that part of the odor similarity was captured by the molecular... 

Manaut, F., Sanz, F., Jose, J, and Milesi, M, (1991) Automatic search for maximum similarity between molecular electrostatic potential distributions,... 

Overlaps between dean reads are computed as follows. An overlap between two reads is defined as a global alignment of the reads with the maximum similarity score. Match and difference scores are weighted by base quality values. For efficiency, the computation of an overlap between two reads is restricted to a band of diagonals centered at the start position of the optimal local alignment computed previously. The width of the band is the number of diagonals required to cover the optimal local alignment plus the band expansion size specified by the user. 

FIGURE 9 Tyrosine phosphorylation of rasGAP occurs before the transient increase in [Ca +Jj and declines before Ca + declines during activation of a,-adrenergic receptors with phenylephrine. All experiments were performed with canine femoral VSMC. Each hatched bar represents the mean values for Ca + determination in 64 cells, whereas the open bar represents mean values for tyrosine phosphorylation of rasGAP in four experiments. Maximal phosphorylation as determined by densitometric analysis was taken to be 100% and all other points were expressed as percentage of maximum. Similar results were obtained during the transient increase in [Ca +li evoked by stimulation of serotonin receptors (not shown). 

Recently Rubinstein et al. 190) observed a maximum similar to that... 

The descriptors of a molecule can be considered a vector of attributes. These attributes may be real numbers or they may be binary in nature in the case of the latter a value of 1 often indicates the presence of some feature and a value of 0 its absence. Having defined the descriptors, the next step is to compute a quantitative measure of the similarity [Willett et al. 1998]. Many similarity coefficients are in the range 0 to 1, with 1 indicating maximum similarity (note that this does not necessarily mean that the molecules are identical). Similarity is often considered to be complementary to distance, such that subtraction of the similarity coefficient from one gives the distance between two molecules. Such distances may then be used in methods such as cluster analysis (see Section 9.13). 

The validity of the Lemieux-Chii interpretation was entirely supported, and the picturesque rabbit-ear idea shown untenable, by a theoretical study that used an ab initio (Hartree-Fock) calculation, with fluoromethanol as the model compound. The calculations showed that the stable conformation has the C-F bond trans to one electron pair and gauche to another, whereas the conformation in which the C-F bond bisects the electron pairs is the energy maximum. Similar interpretations were established for hydrazine, hydroxylamine, and hydrogen peroxide. The concept can be stated in general terms as a destabilization of a conformation that places a polar (C-X) bond eclipsed between two electron pairs. 

In contrast to what is needed in Eq. [38], functions f r) and g(r) are normally represented in separate local coordinate frameworks, with origins at the corresponding molecular centers of mass, Therefore, the coefficient C will change along with a rigid translation vector R and a rigid rotation vector 0, which transform one local system of coordinates into the other. That is, C can be regarded as a six-dimensional correlation coefficient, C = C(R, 0). The maximum similarity between the two molecular properties f r) and g(t) will correspond to the relative orientation that maximizes C(R, 0). 

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