Use of Vertex Index in Structure-Activity Analysis and Design of Molecules

The last few decades have witnessed application of graph theory and topological indices derived from molecular graph in structure-activity analysis. Such applications are based on regression and various multivariate analyses. Most of the topological indices are computed for the whole molecule and used as descriptors for explaining properties/activities of chemical compounds. However, some substructural descriptors in the form of topological distance based vertex indices have been found to be useful in identifying activity related substructures and in predicting pharmacological and toxicological activities of bioactive compounds. Another important aspect of drug discovery e. g. designing novel pharmaceutical candidates could also be done from the distance distribution associated with such vertex indices. In this article, we will review the development and applications of this approach both in activity prediction as well as in designing novel compounds.

Linear Index Coding and Representable Discrete Polymatroids

Discrete polymatroids are the multi-set analogue of matroids. In this paper, we explore the connections between linear index coding and representable discrete polymatroids. The index coding problem involves a sender which generates a set of messages X = {x(1), x(2), ... x(k)} and a set of receivers R which demand messages. A receiver R is an element of R is specified by the tuple (x, H) where x. X is the message demanded by R and H subset of X \textbackslash {x} is the side information possessed by R. It is first shown that a linear solution to an index coding problem exists if and only if there exists a representable discrete polymatroid satisfying certain conditions which are determined by the index coding problem considered. El Rouayheb et. al. showed that the problem of finding a multi-linear representation for a matroid can be reduced to finding a perfect linear index coding solution for an index coding problem obtained from that matroid. Multi-linear representation of a matroid can be viewed as a special case of representation of an appropriate discrete polymatroid. We generalize the result of El Rouayheb et. al. by showing that the problem of finding a representation for a discrete polymatroid can be reduced to finding a perfect linear index coding solution for an index coding problem obtained from that discrete polymatroid.

Separation index of graphs and stacked 2-spheres

In 1987, Kalai proved that stacked spheres of dimension d >= 3 are characterised by the fact that they attain equality in Barnette's celebrated Lower Bound Theorem. This result does not extend to dimension d = 2. In this article, we give a characterisation of stacked 2-spheres using what we call the separation index. Namely, we show that the separation index of a triangulated 2-sphere is maximal if and only if it is stacked. In addition, we prove that, amongst all n-vertex triangulated 2-spheres, the separation index is minimised by some n-vertex flag sphere for n >= 6. Furthermore, we apply this characterisation of stacked 2-spheres to settle the outstanding 3-dimensional case of the Lutz-Sulanke-Swartz conjecture that ``tight-neighbourly triangulated manifolds are tight''. For dimension d >= 4, the conjecture has already been proved by Effenberger following a result of Novik and Swartz. (C) 2015 Elsevier Inc. All rights reserved.

Stability analysis of thick piezoelectric metal based FGM plate using first order and higher order shear deformation theory

This paper presents the stability analysis of functionally graded plate integrated with piezoelectric actuator and sensor at the top and bottom face, subjected to electrical and mechanical loading. The finite element formulation is based on first order and higher order shear deformation theory, degenerated shell element, von-Karman hypothesis and piezoelectric effect. The equation for static analysis is derived by using the minimum energy principle and solutions for critical buckling load is obtained by solving eigenvalue problem. The material properties of the functionally graded plate are assumed to be graded along the thickness direction according to simple power law function. Two types of boundary conditions are used, such as SSSS (simply supported) and CSCS (simply supported along two opposite side perpendicular to the direction of compression and clamped along the other two sides). Sensor voltage is calculated using present analysis for various power law indices and FG (functionally graded) material gradations. The stability analysis of piezoelectric FG plate is carried out to present the effects of power law index, material variations, applied mechanical pressure and piezo effect on buckling and stability characteristics of FG plate.

Index numbers and productivity measurement in multispecies fisheries: an application to the Pacific Coast Trawl Fleet

This study is concerned with the measurement of total factor prodnctivity in the marine fishing industries in general and in the Pacific coast trawl fishery in particular. The study is divided into two parts. Part I contains suitable empirical and introductory theoretical material for the examination of productivity in the Pacific coast trawl Deet. It is self-contained, and contains the basic formulae, empirical results, and discussion. Because the economic theory of index numbers and productivity is constantly evolving and is widely scattered throughout the economics literature, Part D draws together the theoretical literature into one place to allow ready access for readers interested in more details. The major methodological focus of the study is upon the type of economic index number that is most appropriate for use by economists with the National Marine Fisheries Service. This study recommends that the following types of economic index numbers be used: chain rather than fIxed base; bilateral rather than multilateral; one of the class of superlative indices, such as the Tornqvist or Fisher Ideal. (PDF file contains 40 pages.)

DIFFERENTIAL GEOMETRICAL METHODS IN THE STUDY OF OPTICAL-TRANSMISSION (SCALAR THEORY) .1. STATIC TRANSMISSION CASE

Static optical transmission is restudied by postulation of the optical path as the proper element in a three-dimensional Riemannian manifold (no torsion); this postulation can be applied to describe the light-medium interactive system. On the basis of the postulation, the behaviors of light transmitting through the medium with refractive index n are investigated, the investigation covering the realms of both geometrical optics and wave optics. The wave equation of light in static transmission is studied modally, the postulation being employed to derive the exact form of the optical field equation in a medium (in which the light is viewed as a single-component field). Correspondingly, the relationships concerning the conservation of optical fluid and the dynamic properties are given, and some simple applications of the theories mentioned are presented.

DIFFERENTIAL GEOMETRICAL METHODS IN THE STUDY OF OPTICAL-TRANSMISSION (SCALAR THEORY) .2. TIME-DEPENDENT TRANSMISSION THEORY

By generalization of the methods presented in Part I of the study [J. Opt. Soc. Am. A 12, 600 (1994)] to the four-dimensional (4D) Riemannian manifold case, the time-dependent behavior of light transmitting in a medium is investigated theoretically by the geodesic equation and curvature in a 4D manifold. In addition, the field equation is restudied, and the 4D conserved current of the optical fluid and its conservation equation are derived and applied to deduce the time-dependent general refractive index. On this basis the forces acting on the fluid are dynamically analyzed and the self-consistency analysis is given.

High refractive index TiO2 film deposited by electron beam evaporation

The well known 'crystal seed' theory is first applied in this work to prepare TiO2 film: a high refractive index rutile TiO2 film is grown by electron beam evaporation on the rutile seed formed by 1100 degrees C annealing. The average n is larger than 2.4, by far the highest in all the authors' TiO2 films. The films are characterised by optical properties, microstructure and surface morphologies. It is found that the refractive index shows positive relation with the crystal structure, grain size, and packing density and roughness of the film. The film has lower density of granularity and nodule defects on the surface than those of the film deposited by magnetron sputtering. The result shows attractive application in complex filter and laser coatings.

Multi scale shape index for 3D object recognition

We present Multi Scale Shape Index (MSSI), a novel feature for 3D object recognition. Inspired by the scale space filtering theory and Shape Index measure proposed by Koenderink & Van Doorn [6], this feature associates different forms of shape, such as umbilics, saddle regions, parabolic regions to a real valued index. This association is useful for representing an object based on its constituent shape forms. We derive closed form scale space equations which computes a characteristic scale at each 3D point in a point cloud without an explicit mesh structure. This characteristic scale is then used to estimate the Shape Index. We quantitatively evaluate the robustness and repeatability of the MSSI feature for varying object scales and changing point cloud density. We also quantify the performance of MSSI for object category recognition on a publicly available dataset. © 2013 Springer-Verlag.

EFFECTIVE-MASS THEORY FOR GAAS/GA1-XALXAS QUANTUM WIRES AND CORRUGATED SUPERLATTICES GROWN ON (311)-ORIENTED SUBSTRATES

The electronic structures of GaAs/Ga1-xAlxAs quantum wires (corrugated superlattices) grown on (311)-oriented substrates are studied in the framework of the effective-mass envelope-function method. The electron and hole subband structure and optical transition matrix elements are calculated. When x=1, the results are compared with experiments, and it is found that the direct transition becomes an indirect transition as the widths of well and barrier become smaller.

Mode theory and analysis of planar array waveguides

Bloch modes can be excited in planar array due to its periodic lateral refractive index. The power coupled into each eigenmode of the array waveguides is calculated through the overlap integrals of the input field with the eigenmode fields of the coupled infinite array waveguides projected onto the x-axis. Low losses can be obtained if the transition from the array to the free propagation region is adiabatic. Due to the finite resolution of lithographic process the gap between the waveguides will stop abruptly, however, when the waveguides come into too close together. Calculation results show that losses will occur at this discontinuity, which are dependent on the ratio of the gap between the waveguides and grating pitch and on the confinement of field in the array waveguides. Tapered waveguides and low index contrast between the core and cladding layers can lower the transmitted losses.

Study on QSPR of alcohols with a novel edge connectivity index F-m

A novel edge degree f(i) for heteroatom and multiple bonds in molecular graph is derived on the basis of the edge degree delta(e(r)). A novel edge connectivity index F-m is introduced. The multiple linear regression by using the edge connectivity index F-m and alcohol-type parameter delta, alcohol-distance parameter L can provide high-quality QSPR models for the normal boiling points (BPs), molar volumes (MVs), molar refraction (MRs), water solubility(log(1/S)) and octanol/water partition (logP) of alcohols with up to 17 non-hydrogen atoms. The results imply that these physical properties may be expressed as a liner combination of the edge connectivity index and alcohol-type parameter, 6, alcohol-distance parameter, L. For the models of the five properties, the correlation coefficient r and the standard errors are 0.9969,3.022; 0.9993, 1.504; 0.9992, 0.446; 0.9924,0.129 and 0.9973,0.123 for BPs, MVs, MRs, log(1/S) and logP, respectively. The cross-validation by using the leave-one-out method demonstrates the models to be highly reliable from the point of view of statistics.

A new topological index for the Changchun institute of applied chemistry C-13 NMR information system

A method to assign a single number representation for each atom (node) in a molecular graph, Atomic IDentification (AID) number, is proposed based on the counts of weighted paths terminated on that atom. Then, a new topological index, Molecular IDentification (MID) number is developed from AID. The MID is tested systematically, over half a million of structures are examined, and MID shows high discrimination for various structural isomers. Thus it can be used for documentation in the Changchun Institute of Chemistry C-13 NMR information system.

GENERAL ALPHA-N INDEX AND ITS APPLICATION .2. THE CORRELATION BETWEEN THE GENERAL ALPHA-N INDEX AND PHYSICAL-PROPERTIES OF NEUTRAL PHOSPHORUS-COMPOUNDS

The relationship between the alpha-N index and physical properties of neutral phosphorus extractants is studied. Using the general alpha-N index which could describe extractants with minute difference in structure, the good correlation between it and various physical properties of the neutral phosphorus extractants (e.g., densities, refractive index, shift ratio of paper chromatography and IR frequencies of bond P = O) is obtained. The result indicates that general alpha-N index is a good topological index of organic compounds.