Resolution-based similarity measures

The chirality quantification technique proposed by Harary and Mezey [54,55] is motivated by the Resolution Based Similarity Measure (RBSM) approach used in more general molecular similarity analysis [243]. This method does not rely on a single reference object. Instead, it characterizes shape on any desired finite level of resolution by considering various A(J,n) parts of square lattices, called lattice animals or P(G,n) parts of cubic lattices called polycubes which can be inscribed within the two- or three-dimensional objects J or G, respectively. In the above... 

The Fundamentals of Resolution Based Similarity Measures (RBSM)... 

The first example of similarity measure we shall consider is a resolution based similarity measure (RBSM). This particular realization of a RBSM is conceptually simple, but it is not recommended for highly detailed shape comparisons since its practical applications are computationally feasible only for relatively low levels of resolution [240,243],... 

Consider a given molecular contour surface G(a). If the size s of the cubes is chosen small enough, then any finite polycube P can fit within G(a). As in the two-dimensional case, we do not consider orientation constraints and we assume that the contour surface G(a) and polycube P may be translated and rotated with respect to one another the relative orientation of G(a) and the cubic grid is not fixed. In this model, the identity of a polycube is independent of its orientation. Two polycubes P and F are regarded identical if and only if they can be superimposed on one another by translation and rotation in 3D space. Note, however, that the polycube method of shape analysis and determination of resolution based similarity measures can be augmented with orientation constraints, suitable for the study of molecular recognition and shape problems in external fields or within enzyme cavities [240,243]. 

Resolution Based Similarity Measures (RBSM). These methods are based on evaluating the level of resolution required to distinguish molecules the higher the required level of resolution, the more similar are the molecules... 

ADMA = adjustable density matrix assembler AFDF = additive fiizzy density fragmentation GSTE = geometrical similarity as topological equivalence MEDLA = molecular electron density loge assembler MEP = molecular electrostatic potential RBSM = resolution-based similarity measures SGM = shape group methods VDWS = van der Waals surface ID, 2D, 3D = one, two, and three dimensions. 

Resolution-based similarity measures Similarity expressed by the geometrical or topological resolution required to distinguish objects. 

Resolution-based Similarity Measures, T-hulls, and Scaling-Nesting Similarity Measures... 

Another approach of great importance for studies of excited state dynamics is sub-picosecond time resolved spectroscopy. A number of authors have reported femtosecond pump-probe measurements of excited state lifetimes in A, C, T, and G [13-16] and base pair mimics [17]. Schultz et al. have reported time resolved photoelectron spectroscopy and electron-ion coincidence of base pair mimics [18]. these studies can also be compared with similar measurements in solution [19-24], While time resolved measurements provide direct lifetime data, they do have the limitation that the inherent bandwidth reduces the spectral resolution, required for selecting specific electronic states and for selecting single isomers, such as cluster structure and tautomeric form. 

In some of the preceding representations, a natural interrelationship between fuzziness and resolution is used, leading to resolution-based chirality, symmetry and similarity measures. ... 

Molecular Similarity Measures and Chirality Measures Based on Resolution and Fuzzy Set Theory... 

Pictures of high resolution appear crisp, whereas pictures of low resolution appear fuzzy. A decrease of resolution is accompanied by an increase of fuzziness. Consequently, similarity measures based on the minimum level of resolution required to distinguish objects can be formulated in terms of the maximum level of fuzziness at which the objects are distinguishable. Similarity can be regarded as fuzzy equivalence. This principle provides an alternative mathematical basis for using the methods of topological resolution [262] in similarity analysis the theory of fuzzy sets [382-385]. 

The results show that at 2 torr, ku = 2.5 X 10 8 and at 760 torr ku = 1.0 X 10 8 cm.3 molecule-1 sec.-1 This is reasonably good agreement in view of the possible errors. Furthermore, the values of ku obtained are consistent with earlier estimates based on comparisons with similar reactions (10, 19). Our purpose in presenting it here is to illustrate the potential use of flames in estimating more accurate rate constants for reactions like Reaction 14. Of course, the influence of diffusion must always be accounted for in such estimations diffusion is particularly important at low pressures and for small ion concentrations. (It is often advantageous to work at low pressures because the spatial resolution is much better than at 1 atm. At low pressures most measurements are made in or close to the reaction zone itself. At high pressures, where the reaction zone is thinner, measurements are made both in the reaction zone and in the burned gases.)... 

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