Pruning 2-Connected Graphs

Given an undirected graph G with edge costs and a specified set of terminals, let the density of any subgraph be the ratio of its cost to the number of terminals it contains. If G is 2-connected, does it contain smaller 2-connected subgraphs of density comparable to that of?G? We answer this question in the affirmative by giving an algorithm to pruneG and find such subgraphs of any desired size, incurring only a logarithmic factor increase in density (plus a small additive term). We apply our pruning techniques to give algorithms for two NP-Hard problems on finding large 2-vertex-connected subgraphs of low cost; no previous approximation algorithm was known for either problem. In the k-2VC problem, we are given an undirected graph G with edge costs and an integer k; the goal is to find a minimum-cost 2-vertex-connected subgraph of G containing at least k vertices. In the Budget-2VC problem, we are given a graph G with edge costs, and a budget B; the goal is to find a 2-vertex-connected subgraph H of G with total edge cost at most B that maximizes the number of vertices in H. We describe an O(log?nlog?k) approximation for the k-2VC problem, and a bicriteria approximation for the Budget-2VC problem that gives an $O(\frac{1}{\epsilon}\log^{2} n)$ approximation, while violating the budget by a factor of at most 2+ε.     

Summarization of Visual Content in Instructional Videos

In instructional videos of chalk board presentations, the visual content refers to the text and figures written on the boards. Existing methods on video summarization are not effective for this video domain because they are mainly based on low-level image features such as color and edges. In this work, we present a novel approach to summarizing the visual content in instructional videos using middle-level features. We first develop a robust algorithm to extract content text and figures from instructional videos by statistical modelling and clustering. This algorithm addresses the image noise, nonuniformity of the board regions, camera movements, occlusions, and other challenges in the instructional videos that are recorded in real classrooms. Using the extracted text and figures as the middle level features, we retrieve a set of key frames that contain most of the visual content. We further reduce content redundancy and build a mosaicked summary image by matching extracted content based on K-th Hausdorff distance and connected component decomposition. Performance evaluation on four full-length instructional videos shows that our algorithm is highly effective in summarizing instructional video content.     

Synthesis of 1,4-dihydropyridine derivatives using nanocrystalline copper(II) oxide catalyst

Nanocrystalline copper(II) oxide catalyzed three-component coupling of aromatic amines, β-ketoesters and cinnamaldehyde to afford the corresponding 1,4-dihydropyridines in moderate to good yields under mild conditions is described. The catalyst can be recovered and reused for four cycles with almost consistent activity.     

Microwave-hydrothermal synthesis and characterization of Co-VSB-5 microporous framework

The crystallization of cobalt metal incorporated microporous nickel phosphate framework, Co-VSB-5, with initial Ni/P gel ratio of about 1.0, 1.5 and 2.5, respectively, has been investigated under microwave-hydrothermal conditions. Attempts are made to incorporate metal ion in the range of 2.5–10 atomic % in the VSB-5 framework having varied Ni/P ratio by varying gel pH. The prepared samples were characterized by means of X-ray diffraction, scanning electron microscopy, UV-visible diffuse reflectance spectroscopy (UV-visible DRS), and nitrogen adsorption–desorption measurements at 77 K. The prepared samples are found to be crystalline in nature. The initial gel pH is found to be critical for crystallization of nickel phosphate framework with varied Ni/P ratio. Like wise, isomorphic substitution is favored with an increase in Ni/P gel ratio. The results for UVDRS demonstrated the incorporation of transition metal ions in the octahedral position for nickel sites in VSB-5 framework. The textural properties, such as surface area and micropore volume, of the Co-VSB-5 samples crystallized from initial Ni/P gel ratio of 2.5, were found to lower than those crystallized from initial Ni/P gel ratio of 1.5 at equivalent metal content level. Interestingly, crystallization of framework having micro-mesoporosity is favored with an increase in Ni/P gel ratio. Furthermore, scanning electron microscopy revealed the crystallization of samples with rod shaped morphology irrespective of the nature of metal ion and its concentration from gel comprising of Ni/P of 1.5 and 2.5. The results of UV-Vis DRS demonstrated the incorporation of transition metal ions in the octahedral position for nickel sites in VSB-5 framework.     

Molecular recognition of geometrical isomers in montmorillonite

cis-alkenes are hydrogenated preferentially followed by trans-alkenes sequentially from the mixture of geometrical isomers by the montmorillonitebipyridylpalladium(II) acetate catalyst. Such molecular recognition in montmorillonite is unusual and remarkable, and forms an advanced model to enzymes.IICT Communication No. 3187.     

Alumina supported copper nanoparticles for aziridination and cyclopropanation reactions

Alumina supported copper (Cu–Al₂O₃) nanoparticles were prepared and applied for the aziridination of olefins employing [N-(p-tolylsulfonyl)imino]phenyliodinane (PhI = NTs) as nitrene source to afford the corresponding 3-membered cyclic compounds in moderate to excellent yields. Cyclopropanation of several olefins was also carried out by using Cu–Al₂O₃ nanoparticles and ethyl diazoacetate as a carbene source. The catalyst was recovered by simple centrifugation and reused for four cycles.     

Aerobic Alcohol Oxidation by Ruthenium Species Stabilized on Nanocrystalline Magnesium Oxide by Basic Ionic Liquids

The selective oxidation of various alcohols into their corresponding aldehydes and ketones was achieved by ruthenium species stabilized on the nanocrystalline magnesium oxide (NAP‐MgO) by the incorporation of choline hydroxide, a basic ionic liquid, in excellent yields. The procedure is simple, efficient and environmentally benign. The catalyst can be used for four cycles with almost consistent activity.     

The One‐Pot Wittig Reaction: A Facile Synthesis of α,β‐Unsaturated Esters and Nitriles by Using Nanocrystalline Magnesium Oxide

Nanocrystalline magnesium oxide was found to be an effective heterogeneous, solid base catalyst for the one‐pot Wittig reaction to afford α,β‐unsaturated esters and nitriles in excellent yields with high E‐stereoselectivity in the presence of triphenylphosphine under mild conditions.     

Cloning, sequencing and expression of the Fab fragment of a monoclonal antibody to the herbicide atrazine

The Fab region of an IgG2b antibody (AM7B2.1) reactive to theherbicide atrazine was cloned into a plasmid vector using thepolymerase chain reaction and two sets of degenerate oligonucleotideprimers designed to mimic the amino acid variation at the N-terminiof _L-chains and TH-chains. These primers also provide a secretionsignal fused precisely to the antibody gene sequence for secretionof the mature antibody. A further set of universal oligonucleotideprimers was developed for the direct sequencing of the V_H andC_m regions of _B-chains and the V_L and C_L regions of _L-chainswithout subcloning and were used to determine the sequence ofthis antibody. The _L-chain was found to not possess a conservedCys residue at position 23 and the implications of this observationare discussed. The cloned genes were expressed in Escherichiacoli using a commercially available T7 RNA polymerase-basedplasmid. The clones were also expressed in a 17 RNA polymerasebasedsystem containing an attenuated version of the T7 RNA polymerasepromoter, plus a lac promoter placed in an antisense orientation,to enhance plasmid stability. The expressed products were confirmedas atrazine reactive by binding to an atrazine derivative conjugatedwith alkaline phosphatase.     

Cyclopropanation of Olefins Using a Silica Gel Anchored Palladium Phosphine Complex

A silica gel anchored palladium phosphine complex is synthesized and used as a catalyst for the first time in the cyclopropanation of several olefins using ethyl diazoacetate as a carbene source.