Aggregation models with limited choice and the multiplicative coalescent

The percolation phase transition and the mechanism of the emergence of the giant component through the critical scaling window for random graph models, has been a topic of great interest in many different communities ranging from statistical physics, combinatorics, computer science, social networks and probability theory. The last few years have witnessed an explosion of models which couple random aggregation rules, that specify how one adds edges to existing configurations, and choice, wherein one selects from a “limited” set of edges at random to use in the configuration. While an intense study of such models has ensued, understanding the actual emergence of the giant component and merging dynamics in the critical scaling window has remained impenetrable to a rigorous analysis. In this work we take an important step in the analysis of such models by studying one of the standard examples of such processes, namely the Bohman‐Frieze model, and provide first results on the asymptotic dynamics, through the critical scaling window, that lead to the emergence of the giant component for such models. We identify the scaling window and show that through this window, the component sizes properly rescaled converge to the standard multiplicative coalescent. Proofs hinge on a careful analysis of certain infinite‐type branching processes with types taking values in the space of cadlag paths, and stochastic analytic techniques to estimate susceptibility functions of the components all the way through the scaling window where these functions explode. Previous approaches for analyzing random graphs at criticality have relied largely on classical breadth‐first search techniques that exploit asymptotic connections with Brownian excursions. For dynamic random graph models evolving via general Markovian rules, such approaches fail and we develop a quite different set of tools that can potentially be used for the study of critical dynamics for all bounded size rules. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46, 55–116, 2015     

Semi-synthesis of a novel hybrid isoxazolidino withaferin via chemoselective and diastereoselective 1,3-dipolar nitrone cycloaddition reaction

Abstract

A facile, atom-economic synthesis of isoxazilidino withaferin, a novel hybrid of withaferin A, has been accomplished via two-step reaction of nitrone synthesis followed by nitrone 1,3-dipolar cycloaddition. The reaction is highly chemoselective (preferential reaction only on one of the two double bonds present on withaferin A) and diastereoselective affording exclusively the cis-fused products. The structure was determined by detailed analysis of 1D, 2D NMR and mass spectral data.     

Polymer-ligand interaction studies. Part I. Binding of some drugs to poly(N-vinyl-2-pyrrolidone)

A physico-chemical investigation on the binding of some nonsteroidal anti-inflammatory drugs, Naproxen (NP) and Ketoprofen (KP) and a drug model compound, salicylic acid (SA) to poly(N-vinyl-2-pyrrolidone) (PVP, molecular weight = 360,000), was performed at pH 7.1 by the fluorescence competition method employing 1-anilinonaphthalene-8-sulphonate (ANS) as the fluorescent probe. The binding affinities of these substrates to PVP are in the order KP < SA < NP which has been explained on the basis of their structural features and the consequent effect on the interacting forces. Theπ-π interaction between the carbonyl group of PVP and theπ-ring system of the substrate molecule seems to be crucial in deciding the binding affinities of the substrates     

Slow magnetic relaxation and electron delocalization in an S = 9/2 iron(II∕III) complex with two crystallographically inequivalent iron sites

The magnetic, electronic, and Mo?ssbauer spectral properties of [Fe(2)L(μ-OAc)(2)]ClO(4), 1, where L is the dianion of the tetraimino-diphenolate macrocyclic ligand, H(2)L, indicate that 1 is a class III mixed valence iron(II∕III) complex with an electron that is fully delocalized between two crystallographically inequivalent iron sites to yield a [Fe(2)](V) cationic configuration with a S(t) = 9∕2 ground state. Fits of the dc magnetic susceptibility between 2 and 300 K and of the isofield variable-temperature magnetization of 1 yield an isotropic magnetic exchange parameter, J, of -32(2) cm(-1) for an electron transfer parameter, B, of 950 cm(-1), a zero-field uniaxial D(9∕2) parameter of -0.9(1) cm(-1), and g = 1.95(5). In agreement with the presence of uniaxial magnetic anisotropy, ac susceptibility measurements reveal that 1 is a single-molecule magnet at low temperature with a single molecule magnetic effective relaxation barrier, U(eff), of 9.8 cm(-1). At 5.25 K the Mo?ssbauer spectra of 1 exhibit two spectral components, assigned to the two crystallographically inequivalent iron sites with a static effective hyperfine field; as the temperature increases from 7 to 310 K, the spectra exhibit increasingly rapid relaxation of the hyperfine field on the iron-57 Larmor precession time of 5 × 10(-8) s. A fit of the temperature dependence of the average effective hyperfine field yields |D(9∕2)| = 0.9 cm(-1). An Arrhenius plot of the logarithm of the relaxation frequency between 5 and 85 K yields a relaxation barrier of 17 cm(-1).     

On Levitin–Polyak well-posedness and stability in set optimization

Positivity - In this paper, Levitin–Polyak (in short LP) well-posedness in the set and scalar sense are defined for a set optimization problem and a relationship between them is found....     

Assessment of genetic purity of bulked-seed of rice CMS lines using capillary electrophoresis

Genetically pure cytoplasmic male sterile line (A-line) is essential to generate pure hybrid seeds in order to harness the yield heterosis in rice. Conventionally, seed purity testing is carried by grow-out test, which has many limitations. Seed purity assessments based on molecular markers reduce the time required for analysis significantly. However, it is very tedious as at least 200–400 seeds/seedlings are needed to be analyzed individually. An assay based on bulked-seed and molecular markers will be an ideal system. Keeping these points in view, in the present study, a co-dominant mitochondrial marker was used to test the purity of bulked parental line (A-line) seed utilizing CE system in a genetic analyzer. The results indicate that this method is very simple, accurate, and can be used to test purity of large number of samples rapidly in a cost-effective way compared to grow-out test and conventional molecular marker analysis.     

Evaluation of nanomaterials-grafted enzymes for application in contaminants degradation: Need of the hour with proposed IoT synchronized nanosensor fit sustainable clean water technology in en masse

Increased water pollution and challenges in ultrafast recognition of water pollutants poses considerable burden to the public health. The issue of providing clean water to rural people is always a daunting yet challenging task wherein building a centralized water treatment system along with proper pipeline to connect dispersed population is not at all feasible. Amongst different water treatment technologies, sustainable nanozyme based materials have made an exceptional contribution towards providing contaminants free potable water to mankind due to its strong activity and sensitivity towards chemical substances thus facilitating use in advanced point-of-use (POU) system. In this article, we have briefly highlighted the way by which silica, carbon and MOF based nano support stabilizes the enzyme with its improved selectivity and sensitivity towards water decontamination. The strength of nanozymes and its potential use in POU devices has also been discussed for future research endeavor. Additionally, development of various nano-chemo-sensors with advanced machine learning approach is an added advantage towards detecting various contaminants from real samples with its implementation in POU devices. We have also proposed the implementing strategies of these nanozyme based water technologies so that early adopters can be given an informed decision about its way of implementation in coming days in India.