Molecular Topology 22.1 Novel Connectivity Descriptors Based on Walk Degrees

An algorithm for generating novel connectivity topological descriptors, denoted SP (subgraph property), is proposed and exemplified for P being the number of vertices N, walk degree wt\u27e), Randić index X, and Wiener index W. SP indices based on wt\u27e) and x wt\u27e) (Razinger\u27s extension of x index) are tested for correlation with some physico-chemical properties of octane isomers

QSAR Study on Caffeine Derivatives Docked on Poly(A)RNA Polymerase Protein Cid1

Caffeine is the most commonly ingested alkylxantine and is recognized as a psycho-stimulant. It improves some aspects of cognitive performance, however it reduces the cerebral blood flow both in animals and humans. In this paper a QSAR study on caffeine derivatives, docked on the Poly(A)RNA polymerase protein cid1, is reported. A set of forty caffeine derivatives, downloaded from PubChem, was modeled, within the hypermolecule strategy; the predicted activity was LD50 and prediction was done on similarity clusters with the leaders chosen as the best docked ligands on the Poly(A)RNA polymerase protein cid1. It was concluded that LD50 of the studied caffeines is not influenced by their binding to the target protein. This work is licensed under a Creative Commons Attribution 4.0 International License

Szeged Fragmental Indices

Novel Szeged indices, defined on unsymmetric matrices, which collect various fragmental topological properties, are proposed. They are illustrated on selected graphs possessing heteroatoms, multiple bonds and stereoisomers. Correlations on organic structures with herbicidal activity and explosive properties support the usefulness of these newly proposed indices

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

Exploring Statistical and Population Aspects of Network Complexity

The characterization and the definition of the complexity of objects is an important but very difficult problem that attracted much interest in many different fields. In this paper we introduce a new measure, called network diversity score (NDS), which allows us to quantify structural properties of networks. We demonstrate numerically that our diversity score is capable of distinguishing ordered, random and complex networks from each other and, hence, allowing us to categorize networks with respect to their structural complexity. We study 16 additional network complexity measures and find that none of these measures has similar good categorization capabilities. In contrast to many other measures suggested so far aiming for a characterization of the structural complexity of networks, our score is different for a variety of reasons. First, our score is multiplicatively composed of four individual scores, each assessing different structural properties of a network. That means our composite score reflects the structural diversity of a network. Second, our score is defined for a population of networks instead of individual networks. We will show that this removes an unwanted ambiguity, inherently present in measures that are based on single networks. In order to apply our measure practically, we provide a statistical estimator for the diversity score, which is based on a finite number of samples

Modeling complex metabolic reactions, ecological systems, and financial and legal networks with MIANN models based on Markov-Wiener node descriptors

[Abstract] The use of numerical parameters in Complex Network analysis is expanding to new fields of application. At a molecular level, we can use them to describe the molecular structure of chemical entities, protein interactions, or metabolic networks. However, the applications are not restricted to the world of molecules and can be extended to the study of macroscopic nonliving systems, organisms, or even legal or social networks. On the other hand, the development of the field of Artificial Intelligence has led to the formulation of computational algorithms whose design is based on the structure and functioning of networks of biological neurons. These algorithms, called Artificial Neural Networks (ANNs), can be useful for the study of complex networks, since the numerical parameters that encode information of the network (for example centralities/node descriptors) can be used as inputs for the ANNs. The Wiener index (W) is a graph invariant widely used in chemoinformatics to quantify the molecular structure of drugs and to study complex networks. In this work, we explore for the first time the possibility of using Markov chains to calculate analogues of node distance numbers/W to describe complex networks from the point of view of their nodes. These parameters are called Markov-Wiener node descriptors of order kth (Wk). Please, note that these descriptors are not related to Markov-Wiener stochastic processes. Here, we calculated the Wk(i) values for a very high number of nodes (>100,000) in more than 100 different complex networks using the software MI-NODES. These networks were grouped according to the field of application. Molecular networks include the Metabolic Reaction Networks (MRNs) of 40 different organisms. In addition, we analyzed other biological and legal and social networks. These include the Interaction Web Database Biological Networks (IWDBNs), with 75 food webs or ecological systems and the Spanish Financial Law Network (SFLN). The calculated Wk(i) values were used as inputs for different ANNs in order to discriminate correct node connectivity patterns from incorrect random patterns. The MIANN models obtained present good values of Sensitivity/Specificity (%): MRNs (78/78), IWDBNs (90/88), and SFLN (86/84). These preliminary results are very promising from the point of view of a first exploratory study and suggest that the use of these models could be extended to the high-throughput re-evaluation of connectivity in known complex networks (collation)