Guanidinium and hydrogen carbonate rosette layers: Distance and degree topological indices, Szeged-type indices, entropies, and NMR spectral patterns.

Supramolecular chemistry explores non-covalent interactions between molecules, and it has facilitated the design of functional materials and understanding of molecular self-assembly processes. We investigate a captivating class of supramolecular structures, the guanidinium and hydrogen carbonate rosette layers. These rosette layers are composed of guanidinium cations and carbonate anions, exhibiting intricate hydrogen-bonding networks that lead to their unique structural properties.

Collapse of an early adolescent girl. Syncope? Simple or sinister?

An early adolescent girl presented to the emergency department (ED) of her local hospital following a syncopal episode after a warm bath on a background of increasing breathlessness for 1-year duration. On examination, she was fully alert, no pain or injuries from her syncope, she was warm and well perfused, her respiratory rate at rest was normal and she showed no signs of respiratory distress, there were no signs of seizure activity such as incontinence or tongue biting, she had a raised Jugular Venous Pressure (JVP), a loud pansystolic murmur, there was no cyanosis and no oedema. She was referred for a chest radiograph due to her history of breathlessness and for an ECG based on the examination findings of a murmur.

Atypical Kawasaki Disease Presentation in a Previously Healthy Infant: A Diagnostic Challenge.

Kawasaki disease (KD) is an acute systemic vasculitis primarily affecting children, characterized by fever and multisystem involvement. We present a compelling case of KD in a previously healthy 13-week-old infant who presented with fever, irritability, reduced feeding, and the subsequent development of classical mucocutaneous manifestations, including bilateral non-purulent conjunctivitis, cracked lips, and an erythematous rash. Laboratory findings revealed elevated inflammatory markers, thrombocytosis, and neutrophilic leukocytosis, consistent with the diagnosis.

Characteristic polynomials, spectral-based Riemann-Zeta functions and entropy indices of n-dimensional hypercubes.

Abstract: We obtain the characteristic polynomials and a number of spectral-based indices such as the Riemann-Zeta functional indices and spectral entropies of n-dimensional hypercubes using recursive Hadamard transforms. The computed numerical results are constructed for up to 23-dimensional hypercubes. While the graph energies exhibit a J-curve as a function of the dimension of the n-cubes, the spectra-based entropies exhibit a linear dependence on the dimension.

Topological Entropy Characterization, NMR and ESR Spectral Patterns of Coronene-Based Transition Metal Organic Frameworks.

Metal organic frameworks (MOFs) are topical crystalline materials with high porosity and inner surface areas synthesized from naturally occurring minerals. Such MOFs with transition metals have attracted considerable attention because of their fascinating morphological diversity and tunable characteristics. The coronene-based structural frameworks with transition metal atoms are synthesized by repeating a fixed coronene unit at several levels.

Topological and Spectral Properties of Wavy Zigzag Nanoribbons.

Low-dimensional graphene-based nanomaterials are interesting due to their cutting-edge electronic and magnetic properties. Their large surface area, strong mechanical resistance, and electronic properties have enabled potential pharmaceutical and opto-electronic applications. Graphene nanoribbons (GNRs) are graphene strips of nanometer size possessing zigzag and armchair edge geometries with tunable widths.

Nanoporous and nano thickness film-forming bioactive composition for biomedical applications.

Unmanageable bleeding is one of the significant causes of mortality. Attaining rapid hemostasis ensures subject survivability as a first aid during combats, road accidents, surgeries that reduce mortality. Nanoporous fibers reinforced composite scaffold (NFRCS) developed by a simple hemostatic film-forming composition (HFFC) (as a continuous phase) can trigger and intensify hemostasis.

Topological Characterization and Graph Entropies of Tessellations of Kekulene Structures: Existence of Isentropic Structures and Applications to Thermochemistry, Nuclear Magnetic Resonance, and Electron Spin Resonance.

Tessellations of kekulenes and cycloarenes are of considerable interest as nanomolecular belts in trapping and transportation of heavy metal ions and chloride ions, as they possess optimal electronic features and pore sizes. A class of cycloarenes called kekulenes have been the focus of several experimental and theoretical studies from the stand point of aromaticity, superaromaticity, chirality, and novel electrical and magnetic properties. In the present study, we investigate the entropies and topological characterization of different tessellations of kekulenes through topological computations of superaromatic structures with pores.

Biochemical and phylogenetic networks-II: -trees and phylogenetic trees.

The present study, which is a continuation of the previous paper, augments a recent work on the use of phylogenetic networks. We develop techniques to characterize the topology of various X-trees and binary trees of biological and phylogenetic interests. We have obtained the results for various -level -trees and phylogenetic networks with variants of Zagreb, Szeged, Padmakar-Ivan, Schultz and Atom Bond Connectivity topological indices.

Beam forming of shear horizontal guided waves by multi-row staggered magnet configurations.

This paper introduces the wave interferences effects of staggering multiple rows of Periodically Permanent Magnets (PPM) in an Electromagnetic Acoustic Transducer (EMAT) configuration to achieve selective beam forming effects such as steering, focusing and de-focusing of guided ultrasonic waves. The shear horizontal (SH) guided ultrasonic wave in a metal plate was used to demonstrate these effects using numerical Finite Element Model (FEM) that were validated using experiments.

Biochemical and phylogenetic networks-I: hypertrees and corona products.

We have obtained graph-theoretically based topological indices for the characterization of certain graph theoretical networks of biochemical interest. We have derived certain distance, degree and eccentricity based topological indices for various -level hypertrees and corona product of hypertrees. We have also pointed out errors in a previous study.

Combinatorics of Supergiant Fullerenes: Enumeration of Polysubstituted Isomers, Chirality, Nuclear Magnetic Resonance, Electron Spin Resonance Patterns, and Vibrational Modes from C to C.

We have developed combinatorial techniques for the enumeration of isomers of polysubstituted giant fullerenes through icosahedral C and applied the techniques to chirality of the isomers, NMR spectroscopy, and group theoretical analysis of the vibrational modes of supergiant fullerenes. We have employed a combination of distance-degree vectorial sequences, self-returning walk sequences followed by our generalization of Sheehan's version of Pólya's theorem, and Möbius inversion technique extended to all irreducible representations of the point groups of giant fullerenes. The concept of shell equivalence classes was utilized to analyze supergiant fullerenes.

An Overview of Ovarian Cancer: Molecular Processes Involved and Development of Target-based Chemotherapeutics.

Ovarian cancer is one of the leading gynecologic diseases with a high mortality rate worldwide. Current statistical studies on cancer reveal that over the past two decades, the fifth most common cause of death related to cancer in females of the western world is ovarian cancer. In spite of significant strides made in genomics, proteomics and radiomics, there has been little progress in transitioning these research advances into effective clinical administration of ovarian cancer.

Nonrigid water octamer: Computations with the 8-cube.

A 8-cube model of the fully nonrigid water octamer is considered within the 8-dimensional hyperoctahedral wreath product group with 10,321,920 operations and 185 irreducible representations by employing computational and mathematical techniques. For the two lowest-lying isomers of (H O) with D and S symmetries of a rigid (H O) , correlation tables and nuclear spin statistics are constructed for the tunneling splittings of the rotational levels are computed by a computational matrix polynomial generating function technique combined with Möbius inversion, and the relationship to the 8-cube multinomials are pointed out. Multinomial generating functions combined with the induced representation techniques are employed to compute and construct the nuclear spin species, nuclear spin statistical weights and tunneling splittings of rovibronic levels.

Computations of Colorings 7D-Hypercube's Hyperplanes for All Irreducible Representations.

In the present study, we compute and enumerate the colorings of 7D-hypercube for all of its hyperplanes (q = 1-7) for all 110 irreducible representations (IRs) of the seventh-dimensional hyperoctahedral group consisting of 645,120 symmetry operations. The computations of colorings of the 7D-hypercube are motivated by a number of chemical and biological applications such as the 7D-hypercube representation of the periodic table, hypercube representations of water heptamer clusters, genetic regulatory networks, isomerization graphs, massively large data representations, and so forth. We have employed the Möbius inversion technique combined with generalized character cycle indices for 110 IRs to compute the generating functions for colorings of seven different types of hyperplanes of the 7D-hypercube varying from the vertices (q = 7) to hexeracts (q = 1) of the 7D-hypercube.

Edge Distance-based Topological Indices of Strength-weighted Graphs and their Application to Coronoid Systems, Carbon Nanocones and SiO Nanostructures.

The edge-Wiener index is conceived in analogous to the traditional Wiener index and it is defined as the sum of distances between all pairs of edges of a graph G. In the recent years, it has received considerable attention for determining the variations of its computation. Motivated by the method of computation of the traditional Wiener index based on canonical metric representation, we present the techniques to compute the edge-Wiener and vertex-edge-Wiener indices of G by dissecting the original graph G into smaller strength-weighted quotient graphs with respect to Djoković-Winkler relation.

Quantum Molecular Dynamics, Topological, Group Theoretical and Graph Theoretical Studies of Protein-Protein Interactions.

Background: Protein-protein interactions (PPIs) are becoming increasingly important as PPIs form the basis of multiple aggregation-related diseases such as cancer, Creutzfeldt-Jakob, and Alzheimer's diseases. This mini-review presents hybrid quantum molecular dynamics, quantum chemical, topological, group theoretical, graph theoretical, and docking studies of PPIs. We also show how these theoretical studies facilitate the discovery of some PPI inhibitors of therapeutic importance.

Mathematical and Computational Techniques for Drug Discovery: Promises and Developments.

We review various mathematical and computational techniques for drug discovery exemplifying some recent works pertinent to group theory of nested structures of relevance to phylogeny, topological, computational and combinatorial methods for drug discovery for multiple viral infections. We have reviewed techniques from topology, combinatorics, graph theory and knot theory that facilitate topological and mathematical characterizations of protein-protein interactions, molecular-target interactions, proteomics, genomics and statistical data reduction procedures for a large set of starting chemicals in drug discovery. We have provided an overview of group theoretical techniques pertinent to phylogeny, protein dynamics especially in intrinsically disordered proteins, DNA base permutations and related algorithms.

Combinatorial Enumeration of Isomers of Superaromatic Polysubstituted Cycloarenes and Coronoid Hydrocarbons with Applications to NMR.

We have employed combinatorial techniques based on character cycle indices, Pólya's theory, and Euler totem function to enumerate isomers of polysubstituted cycloarenes and coronoid hydrocarbons which have been receiving considerable attention because of their superaromaticity, ring currents, and interesting magnetic properties. Systematic enumeration and construction of tables of polysubstituted isomers such as fluoro-chloro superaromatic hydrocarbons are considered as they are of interest in the study of environmental pollutants and toxicity. Isomers of fluoro-chloro polysubstituted donut shaped circumkekulenes, circumseptulenes, circumoctulenes, etc.

Psychological Consequences of Maxillofacial Trauma in the Indian Population: A Preliminary Study.

The aim of this article is to identify the prevalence of posttraumatic psychological symptoms following maxillofacial trauma among an Indian population sample and assess changes in these symptoms over a period of time. Forty-eight adult patients were assessed within 2 weeks of injury with two follow-up visits (4-6 weeks and 12-14 weeks). Patients were administered three self-reporting questionnaires in local language (GHQ-12; HADS; TSQ) on all occasions.

Quantum molecular modeling of hepatitis C virus inhibition through non-structural protein 5B polymerase receptor binding of C-arylidene rhodanines.

We have carried out high-level quantum chemical computations followed by molecular docking studies on a set of 17C-arylidene rhodanine isomers to provide insights into the binding modes with different reported binding pockets of the nonstructural protein 5B (NS5B) polymerase that contribute to the hepatitis C virus (HCV) inhibition. We optimized the multi-target profile of the selected rhodanine analogs to investigate potential non-nucleotide inhibitors (NNIs) by quantum chemical optimization of the 18 isomers followed by docking with quantum chemically optimized structures of each isomer with NS5B polymerase at multiple binding pockets. The binding affinities of the PP-I, PP-II and TP-II pockets of NS5B polymerase were analyzed for all the 17 isomers of 2-[(5Z)-5-(2,4-dichlorobenzylidene)-4-oxo-2-thioxo-1,3-thiazolidin-3-yl]-3-phenylpropanoic acid.

Unexpected Blooming Artifact in Brain Magnetic Resonance Imaging.

Unexpected foreign bodies are occasionally discovered during magnetic resonance imaging (MRI). These are often present unknown to the patient, missed during routine pre-MRI screening and result in unnecessary delay during MRI. The authors present a patient with traumatically embedded foreign body in the scalp that escaped pre-MRI screening and caused susceptibility artifacts during brain MRI.