Packing in honeycomb networks

Molecules arranging themselves into predictable patterns on silicon chips could lead to microprocessors with much smaller circuit elements. Mathematically, assembling in predictable patterns is equivalent to packing in graphs. An H-packing of a graph G is a set of vertex disjoint subgraphs of G, each of which is isomorphic to a fixed graph H. If H is the complete graph K ₂, the maximum H-packing problem becomes the familiar maximum matching problem. In this paper we give algorithms to find a perfect packing of HC(n) with P ₆ and K _1,3 when n is even and thus determines their packing numbers. Further we also study the packing of HC(n) with 1, 3-dimethyl cyclohexane.     

A novel content-based active contour model for brain tumor segmentation

Brain tumor segmentation is a crucial step in surgical and treatment planning. Intensity-based active contour models such as gradient vector flow (GVF), magneto static active contour (MAC) and fluid vector flow (FVF) have been proposed to segment homogeneous objects/tumors in medical images. In this study, extensive experiments are done to analyze the performance of intensity-based techniques for homogeneous tumors on brain magnetic resonance (MR) images. The analysis shows that the state-of-art methods fail to segment homogeneous tumors against similar background or when these tumors show partial diversity toward the background. They also have preconvergence problem in case of false edges/saddle points. However, the presence of weak edges and diffused edges (due to edema around the tumor) leads to oversegmentation by intensity-based techniques. Therefore, the proposed method content-based active contour (CBAC) uses both intensity and texture information present within the active contour to overcome above-stated problems capturing large range in an image. It also proposes a novel use of Gray-Level Co-occurrence Matrix to define texture space for tumor segmentation. The effectiveness of this method is tested on two different real data sets (55 patients - more than 600 images) containing five different types of homogeneous, heterogeneous, diffused tumors and synthetic images (non-MR benchmark images). Remarkable results are obtained in segmenting homogeneous tumors of uniform intensity, complex content heterogeneous, diffused tumors on MR images (T1-weighted, postcontrast T1-weighted and T2-weighted) and synthetic images (non-MR benchmark images of varying intensity, texture, noise content and false edges). Further, tumor volume is efficiently extracted from 2-dimensional slices and is named as 2.5-dimensional segmentation.     

Intramolecular Cyclization of 9,11‐Seco‐Estrane under Friedel–Crafts Reaction Conditions

An intramolecular cyclization of 17β‐acetoxy‐3‐methoxy‐9,11‐seco‐1,3,5(10)‐estratriene‐11‐oic acid under different Friedel–Crafts reaction conditions is described.     

Analyzing coordination preferences of Mg2+ complexes: insights from computational and database study

Solvation of metal cations has attracted substantial interest on account of its functional importance in biological systems. In the present study, we undertake a comprehensive analysis of hydrated complexes of Mg²⁺ with up to 20 water molecules using MP2/cc-pVTZ and density functional theory (DFT) calculations. The effect of first, second, and higher solvation shells on magnesium coordination has been systematically analyzed by considering Mg²⁺(H₂O) _n complexes. Numerous competing conformations for each of the metal ion complexes have been explored and the minima structures obtained were further analyzed. The study probes the relative preferences among various coordination numbers and unambiguously establishes that coordination number 6 is the most optimal choice. The relative abundance of Mg²⁺ ion and its coordination with water and other ligands has been analyzed in the Protein Data Bank and Cambridge Structural Database. It is noted that the M–O distance and charge transfer to metal ion increase as the number of solvating water molecules increases. The computational studies are in excellent agreement with the experimental observations, and provide support to multiple coordinate site preferences for Mg²⁺.     

Designing Self‐Supported Metal‐Organic Framework Derived Catalysts for Electrochemical Water Splitting

To achieve efficient water splitting, it is essential to develop catalysts with high electrochemical performance, enhanced durability and tunable properties. Most of the transition metal‐based catalysts employed for the water splitting have been fabricated on the solid‐electrode support by using binder, which decreases the activity and durability of the catalyst system. In this respect, self‐supported metal organic framework (MOF) derived catalysts have been introduced with enhanced catalytic activity and mechanical stability for the electrochemical water splitting. The self‐supported MOF derived catalysts exhibit improved electronic conductivity, high electrochemical surface area, enhanced mechanical stability and strong catalyst‐support interaction. Moreover, these catalysts possess highly porous and hollow structure with designed morphology and multi‐metallic composition. Recently, a tremendous effort has been provided to explore this newly growing field and new dimensions and directions have been achieved. Looking at this point, we have described here the basic principles of catalyst design from self‐supported MOF, structural and interface engineering by controlling the electronic structure of the catalysts to improve the water splitting activity. In addition, the challenges and difficulties associated with this field have been pointed out and addressed for the future progress in this field.     

Two minor diterpene glycosides from the leaves of Stevia rebaudiana

Two new new diterpene glycosides, 13-[(2-O-(6-O-beta-D-glucopyranosyl)-beta-D-glucopyranosyl-beta-D-glucopyranosyl)oxy] kaur-16-en-18-oic acid beta-D-glucopyranosyl ester (1) and 13-[(2-O-beta-D-glucopyranosyl-3-O-beta-D-fructofuranosyl-beta-D-glucopyranosyl)oxy] kaur-16-en-18-oic acid beta-D-glucopyranosyl ester (2) were isolated from the leaves of Stevia rebaudiana, along with the known steviol glycosides stevioside, rebaudiosides A-F and dulcoside A. The structures of the two new compounds were established on the basis of extensive 2D NMR (COSY, HSQC, and HMBC), MS and chemical studies.     

Kernel logistic regression using truncated Newton method

Kernel logistic regression (KLR) is a powerful nonlinear classifier. The combination of KLR and the truncated-regularized iteratively re-weighted least-squares (TR-IRLS) algorithm, has led to a powerful classification method using small-to-medium size data sets. This method (algorithm), is called truncated-regularized kernel logistic regression (TR-KLR). Compared to support vector machines (SVM) and TR-IRLS on twelve benchmark publicly available data sets, the proposed TR-KLR algorithm is as accurate as, and much faster than, SVM and more accurate than TR-IRLS. The TR-KLR algorithm also has the advantage of providing direct prediction probabilities.     

Embedding hypercubes into cylinders, snakes and caterpillars for minimizing wirelength

We consider the problem of embedding hypercubes into cylinders to minimize the wirelength. Further, we show that the edge isoperimetric problem solves the wirelength problem of regular graphs and, in particular, hypercubes into triangular snakes and caterpillars.     

Enhancement of dielectric constant in PVDF polymer using dendrite-shaped PbS nanostructures

Dendrite-shaped PbS has been successfully synthesized using hydrothermal method on a large scale. The formation of dendrite-shaped PbS was confirmed by scanning electron microscopy (SEM). A detailed study of variations in dielectric properties on frequency and temperature shows that composites of PVDF and dendrite-shaped PbS have significantly higher dielectric constant than PVDF/PbS nanoparticles (NP) nanocomposites due to low percolation threshold.