A new algorithm for computing distance matrix and Wiener index of zig-zag polyhex nanotubes

The Wiener index of a graph G is defined as the sum of all distances between distinct vertices of G. In this paper an algorithm for constructing distance matrix of a zig-zag polyhex nanotube is introduced. As a consequence, the Wiener index of this nanotube is computed

Elastic Theory of Defects in Toroidal Crystals

We report a comprehensive analysis of the ground state properties of axisymmetric toroidal crystals based on the elastic theory of defects on curved substrates. The ground state is analyzed as a function of the aspect ratio of the torus, which provides a non-local measure of the underlying Gaussian curvature, and the ratio of the defect core-energy to the Young modulus. Several structural features are discussed,including a spectacular example of curvature-driven amorphization in the limit of the aspect ratio approaching one. The outcome of the elastic theory is then compared with the results of a numerical study of a system of point-like particles constrained on the surface of a torus and interacting via a short range potential.Comment: 24 pages, 24 figure

1-Periodic Nanostructures

Triply periodic structures are the usual subjects of crystallographic studies while the objects of these are the crystals or reticulations. There are amorphous materials with no ordered atomic arrays and some ordered structures with no translational periodicity, eventually called quasicrystals. This study presents a variety of five-fold symmetry molecular networks with 1-periodicity. The construction and topology (the genus calculation included) of these structures is described in terms of the net parameters, in a crystallographic manner

Mathematical structural descriptors and mutagenicity assessment: a study with congeneric and diverse datasets^$

<p>Quantitative bioactivity and toxicity assessment of chemical compounds plays a central role in drug discovery as it saves a substantial amount of resources. To this end, high-performance computing has enabled researchers and practitioners to leverage hundreds, or even thousands, of computed molecular descriptors for the activity prediction of candidate compounds. In this paper, we evaluate the utility of two large groups of chemical descriptors by such predictive modelling, as well as chemical structure discovery, through empirical analysis. We use a suite of commercially available and in-house software to calculate molecular descriptors for two sets of chemical mutagens – a homogeneous set of 95 amines, and a diverse set of 508 chemicals. Using calculated descriptors, we model the mutagenic activity of these compounds using a number of methods from the statistics and machine-learning literature, and use robust principal component analysis to investigate the low-dimensional subspaces that characterize these chemicals. Our results suggest that combining different sets of descriptors is likely to result in a better predictive model – but that depends on the compounds being modelled and the modelling technique being used.</p