Inapproximability of Edge-Disjoint Paths and low congestion routing on undirected graphs

In the undirected Edge-Disjoint Paths problem with Congestion (EDPwC), we are given an undirected graph with V nodes, a set of terminal pairs and an integer c. The objective is to route as many terminal pairs as possible, subject to the constraint that at most c demands can be routed through any edge in the graph. When c = 1, the problem is simply referred to as the Edge-Disjoint Paths (EDP) problem. In this paper, we study the hardness of EDPwC in undirected graphs.     

Application of multilayered strategy for variable selection in QSAR modeling of PET and SPECT imaging agents as diagnostic agents for Alzheimer’s disease

Structural Chemistry - Non-invasive imaging of amyloid beta (Aβ) and tau fibrils in the brain may support an early and precise diagnosis of Alzheimer’s disease. Molecular imaging...     

Graphical balanced allocations and the (1 + β)‐choice process

Suppose m balls are sequentially thrown into n bins where each ball goes into a random bin. It is well‐known that the gap between the load of the most loaded bin and the average is , for large m. If each ball goes to the lesser loaded of two random bins, this gap dramatically reduces to independent of m. Consider a constrained setting where not all pairs of bins can be sampled. We are given a graph where each node corresponds to a bin. The process sequentially samples an edge from the graph and places a ball in the lesser loaded of its endpoints. We show the gap is at most where σ is the edge expansion of the graph. Our results extend naturally to the hypergraph version of this question. Our technique involves a tight analysis of what we call the “‐choice” process for some parameter : each ball goes to a random bin with probability and the lesser loaded of two random bins with probability β. For this process we show that the gap is , irrespective of m. Moreover the gap stays at in the weighted case for a large class of weight distributions. No non‐trivial bounds were previously known in the weighted case, even for the 2‐choice case. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 760–775, 2015     

Reaction of barbituric acid with organic azides and phosphonium ylides

Amination by organic azides has been carried out to provide aminobarbiturates by fusion of a triazole ring to the 5,6-positions of barbituric acid followed by cleavage and thermal elimination of nitrogen, whereas aza-Wittig reaction gave phosphoranylidene barbituric acid salts.      

Exploration of nitroimidazoles as radiosensitizers: application of multilayered feature selection approach in QSAR modeling

Structural Chemistry - Radiosensitizers are aimed to augment tumor cell killing by radiation while having much less effect on normal tissues. Nitroimidazoles and related analogues are efficient...     

Chemometric modeling of PET imaging agents for diagnosis of Parkinson’s disease: a QSAR approach

Structural Chemistry - Recently, adenosine A2A receptor antagonists have been identified as an interesting drug target for the treatment of Parkinson’s disease (PD). Radiolabelled molecular...     

A rapid and simple ultra high performance liquid chromatography method for the simultaneous determination of methoxyphenol derivatives involved in the eugenol catabolic pathway

An efficient ultra high performance liquid chromatography method of separation was developed for the analysis of six important methoxyphenol derivatives involved in the eugenol catabolic pathway. In the present study, an Acquity UPLC BEH C₁₈ column was used for the chromatographic separation of the industrially important phenolic compounds such as vanillin, vanillic acid, ferulic acid, coniferyl alcohol, and coniferyl aldehyde obtained during microbial transformation of eugenol. Eluted components were identified using the dual wavelength (254 and 310 nm) UV detector. A gradient method of elution using mobile phase of aqueous 1 mM trifluoroacetic acid (Solvent A) and methanol (Solvent B) at a flow rate of 0.3 mL/min separated all the five intermediate methoxyphenol derivatives along with their precursor eugenol within 15 min with stable baseline resolution. Method validation was performed for the accurate quantification of vanillin, coniferyl aldehyde, and eugenol using the parameters of linearity, specificity, precision, limit of detection, limit of quantification, and robustness. The developed method would be helpful for clear separation and identification of the five most important intermediate metabolites of the eugenol catabolism pathway.     

Biofunctionalized block copolymer nanoparticles based on ring‐opening metathesis polymerization

We present an approach to the synthesis of biofunctionalized block copolymer nanoparticles based on ring‐opening metathesis polymerization; these nanoparticles may serve as novel scaffolds for the multivalent display of ligands. The nanoparticles are formed by the self‐assembly of diblock copolymers composed of a hydrophobic block and a hydrophilic activated block that can be functionalized with thiolated ligands in aqueous media. The activated block enables control over the orientation of the displayed ligands, which may be sugars, peptides, or proteins engineered to contain cysteine residues at suitable locations. The nanoparticle diameter can be varied over a wide range through changes in the composition of the block copolymer, and biofunctionalization of the nanoparticles has been demonstrated by the attachment of a peptide previously shown to inhibit the assembly of anthrax toxin. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 928–939, 2006