Mircea V. Diudea

Electrically conductive gold-coated collagen nanofibers for placental-derived mesenchymal stem cells enhanced differentiation and proliferation.

Gold-coated collagen nanofibers (GCNFs) were produced by a single-step reduction process and used for the growth and differentiation of human adult stem cells. The nanomaterials were characterized by a number of analytical techniques including electron microscopy and spectroscopy. They were found to be biocompatible and to improve the myocardial and neuronal differentiation process of the mesenchymal stem cells isolated from the placental chorionic component. The expression of specific differentiation markers (atrium, natriuretic peptide, actin F and actin monomer, glial fibrilary acidic protein, and neurofilaments) was investigated by immunocytochemistry.

Nanoporous carbon allotropes by septupling map operations

Spongy carbon nanostructures, also called schwarzites, have been synthesized. They consist of highly connected covalent networks, periodic in the three dimensions of Euclidean space. The intimate structure of schwarzites has a topology of triply periodic minimal surfaces. They can be tessellated by some geometric operations on maps, including the newly proposed septupling operations. Formulas for calculating the lattice parameters of iteratively transformed maps are presented. Examples are given for both finite/closed cages and infinite/open all-sp2 carbon structures. Strain energy calculations for structures, consisting of thousands of atoms, show that such carbon allotropes are very relaxed and approach to the non-strained graphite sheet.

Indices of Reciprocal Properties or Harary Indices

Reciprocal topological properties are used for building up novel indices referred to as Harary indices. They are defined by the aid of matrix algebra and examplified on appropriate sets of graphs. Analytical relations for calculating the indices, defined both on the basic and the reciprocal property, in particular classes of graphs are derived. The correlating and discriminating ability as well as the limitations of these indices are discussed.

WIENER AND HYPER-WIENER NUMBERS IN A SINGLE MATRIX

A novel unsymmetric square matrix, CJu, is proposed for calculating both Wiener,1 W, and hyper-Wiener,2 WW, numbers. This matrix is constructed by using the principle of single endpoint characterization of paths.3 Its relation with Wiener-type numbers is discussed.

Cluj Matrix Invariants

The newly proposed matrix, ℂ𝕁u (unsymmetric Cluj matrix), is examplified for cycle-containing structures. Its relation with the matrix 𝕊ℤu (unsymmetric Szeged matrix) is discussed both as definition and related indices. The derived “Cluj” numbers are compared to the Wiener matrix- and Szeged matrix-derived numbers and tested for discriminating and correlating ability on selected sets of graphs.

The energetic stability of tori and single-wall tubes

Tessellated tori, generated here from square-like tiled lattices, are closely related to cylinders and capped tubes. This way of building them enables the orientation of their bonds, and so the geometric proportions of the torus, to be specified for molecular mechanics calculations and, along with their transformation into capped tubes this is illustrated and discussed in the light of their energetic stability.

Szeged index - Applications for drug modeling

In this review we describe various applications of Szeged (Sz) index for modeling physicochemical properties as well as physiological activities of organic compounds acting as drugs or possess pharmacological activity.

Molecular Graph Matrices and Derived Structural Descriptors

Abstract A number of recently graph matrices encoding in various ways the topological information is presented. Four graph operators are used to compute 19 topological indices for a set of 306 alkanes. The intercorrelation coefficients of the 19 topological indices are computed and used to identify highly intercorrelated indices.

Network analysis using a novel highly discriminating topological index

When characterizing networks structurally, the discriminating ability of a topological measure (or also called index) is crucial. This relates to investigate its discrimination power (or also called uniqueness or degeneracy) that indicates how meaningful the given measure can distinguish nonisomorphic networks. In terms of biological and chemical graph analysis, a highly discriminative measure is desirable because it then has the ability to detect minor structural changes within the given network. In this article, the discriminating ability of a new super index based on Shell-matrices and polynomials is tested using (real) atomic and synthetic structures. As a result, the new descriptor can distinguish all graphs uniquely. We emphasize that some molecular descriptors which are embedded in the super index have already shown excellent correlating ability with alkanes properties. In view of the fact that most of the existing topological graph measures are degenerated, the new super index seems to be a good starting point for performing further studies in the context of network analysis. In the future, we also intent to use other sets of networks, for instance molecular graphs, to further examine the index and its meaning. In particular, we emphasize that only those indices which possess low computational complexity do have the potential to be applied for analyzing complex systems properly.

DETOUR-CLUJ MATRIX AND DERIVED INVARIANTS

Detour-variant, CJΔu, of the recently proposed Cluj matrix, CJDu, is defined and exemplified. Cluj indices built up on the two variants of the Cluj matrix are evaluated and compared, for selected sets of graphs. A new graph-theoretical local property is defined, namely, the “internal ending of all longest paths joining a vertex i, with degi > 1, with all the remaining vertices in the graph”, as the property of the vertex i (called an internal endpoint) to have all its entries in CJΔu equal to 1. Classes of graphs possessing a minimal CJΔp value (i.e., in which all vertices are internal endpoints) have been identified. Correlating tests of the invariants calculated on the two variants of Cluj matrices are also performed.