Local similarity measure

Considering a collection of functional groups of the same chemical formula but located in a series of different molecules, local similarity measures among these functional groups can be based on their fuzzy membership functions (for a discussion of local similarity measures see sections 5 and 6). These similarity measures provide clues for the similarities and differences in their reactivities, caused by the similarities and differences in their molecular environments. 

Local Shape Codes and Local Similarity Measures... 

When searching for local similarities of two molecules, the decoded local shape matrices Ib(a,b,Mi) of molecule M) are compared to various diagonal blocks of the global shape matrix s(a,b,M2) of molecule M2. In the most general case, the local shape matrix Ib(a,b,Mi) is used as a template, and it is compared to k-dimensional blocks of s(a,b,M2) obtained by all possible simultaneous row and column permutations. If the size ordering is considered important then only those permutations are taken which preserve the monotonicity of size ordering in the permuted diagonal block that is compared to the template. A local similarity measure... 

Each member in an ensemble uses a local aggregation function (such as average) to generate a schema matching similarity measure from the similarity measures of the attribute correspondences. Local similarity measures can then be aggregated using a global similarity measure (e.g., max) to become the ensemble similarity... 

The mapping of properties to surface features in SPERM can be regarded as a limiting case of the last class of local similarity measures to be discussed here, these being measures that are based upon electrostatic, steric, and hydrophobic fields analogous to those that underlie current approaches to 3D QSAR (see Comparative Molecular Field Analysis (CoMFA) and Quantitative Structure-Activity Relationships in Drug Design). 

Asymmetric simhaiity measures allow fuzzy super- and substructure searching. A substructure search is defined as looking for structures containing the given query and a superstructure search is defined as looking for structures embedded in the given query. In both cases asymmetric local similarity is estimated. 

It is up to the researcher to decide whether to use a Cartesian similarity measure or a dihedral measure and what elements to include in the summation [29]. It should be stressed that while the RMS distances perfonn well and are often used, there are no restrictions against other similarity measures. Eor example, similarity measures that emphasize chemical interactions, hydrophobicity, or the relative orientation of large molecular domains rather than local geometry may serve well if appropriately used. 

Dickinson et al. also used microelectrodes to measure dissolved oxygen (DO), H2O2, and local within biofouling deposits on stainless steel surfaces exposed to river water to further resolve the interfacial chemistry that resulted in ennoblement. Data were then compared with those from similar measurements as close as possible to the environment of a non-fouled substratum. 

EMSA assays can also be exploited to measure STAT nuclear localization, which is, similar to NFkB localization, a measure of STAT activity. Determination of JAK phosphorylation is carried out by immunoprecipitation of the JAK proteins from cell lysates, followed by SDS-PAGE electrophoresis, immunoblotting with antiphosphotyrosine antibody and JAK-specific antibody re-probing [99]. 

Having resolved the molecular perception problem and achieved a unique representation of all atoms, bonds, and rings in the molecule, the second major step is the definition of the most useful measure for local similarity of atoms and atomic environment. For the purpose of COSMO/rag, we need to achieve the state that atoms are considered as most similar, if their partial molecular surfaces and surface polarities, i.e., polarization charge densities, are most similar. But since the latter is not known, at least for the new molecule under consideration, we have to ensure that the local geometries and the electronic effects of the surrounding atoms are most similar. Obviously, two similar atoms should at legist be identical with respect to their element and their hybridization. Turning this information into a unique real number, a similarity index of the lowest order (zeroth order) can be defined for each atom from the atom element numbers and... 

Shape Similarity Measures of Functional Groups Based on Local Shapes... 

Let us finally say that maximizing a distance measure becomes something analogous to minimize the similarity measure r(i,j) defined in section 6.4.5. Thus localization in this context becomes the same as to obtain within a shell the least similar set of functions. 

The most popular tool currently in use is BLAST (Basic Local Alignment Search Tool) (3 7) from the NCBI. BLAST is an example of a heuristic that attempts to optimize a specific similarity measure. The most recent revisions to the algorithm are gapped BLAST and PSI-BLAST (38), with improved accuracy for PSI-BLAST using composition-based statistics... 

FT-RAIRS measurements of CO have also been used to identity facets of oxide supported Cu particles [78, 82]. The low sensitivity of RAIRS on single crystal ZnO(OOOl) prevented the observation of adsorbed CO or CO2, despite their observation in NEXAFS [78], although the local metallic dielectric allowed CO to be observed on the Cu particles. There appear to be no examples of HREELS being used to carry out vibrational spectroscopy of adsorbates on oxide supported metal particles. A HREELS study of Ag on MgO(lOO) films [95] was used only to characterise the Ag induced attenuation in the substrate Fuchs-Kliewer phonons, and the appearance of the metal/oxide interfacial plasmon at higher energies. HREELS has also been used to characterise the oxide/oxide interface between NiO and thin film MgO(lOO) [96]. Similar measurements of substrate phonon attenuation were made in HREELS studies on Pt films grown on ZnO(OOOl) [97]. 

For the simpler case of molecule pair interactions, such as the interactions between two reactants, local shape complementarity is of importance. The basic principle of local shape similarity measures is also applicable for the construction of local shape complementarity measures. 

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