On Bipartite and Multipartite Clique Problems

In this paper, we introduce the maximum edge biclique problem in bipartite graphs and the edge/node weighted multipartite clique problem in multipartite graphs. Our motivation for studying these problems came from abstractions of real manufacturing problems in the computer industry and from formal concept analysis. We show that the weighted version and four variants of the unweighted version of the biclique problem are NP-complete. For random bipartite graphs, we show that the size of the maximum balanced biclique is considerably smaller than the size of the maximum edge cardinality biclique, thus highlighting the difference between the two problems. For multipartite graphs, we consider three versions each for the edge and node weighted problems which differ in the structure of the multipartite clique (MPC) required. We show that all the edge weighted versions are NP-complete in general. We also provide a special case in which edge weighted versions are polynomially solvable.     

Application of ring-rearrangement metathesis in organic synthesis: A grand design

In this report, we compiled various strategies involving a ring-rearrangement metathesis as a key step to assemble diverse molecules. Popular name reactions such as Grignard reaction, Overman rearrangement, Fischer indolization, Beckmann rearrangement and Diels–Alder reaction were used in combination with ring-rearrangement metathesis to construct complex targets. Additionally, CH activation and RRM strategy has been used to assemble azacycles. In some instances, the ring-rearrangement metathesis was expected to occur; however, ring-opening metathesis products were realized. These methods were included in the miscellaneous section. We anticipate that the lessons learned here are useful in designing complex polycyclic and heterocyclic targets suitable for biological and material science applications. Beside our work, we have also included others work as a background information.     

Molecular Tailoring Approach for the Estimation of Intramolecular Hydrogen Bond Energy

Hydrogen bonds (HBs) play a crucial role in many physicochemical and biological processes. Theoretical methods can reliably estimate the intermolecular HB energies. However, the methods for the quantification of intramolecular HB (IHB) energy available in the literature are mostly empirical or indirect and limited only to evaluating the energy of a single HB. During the past decade, the authors have developed a direct procedure for the IHB energy estimation based on the molecular tailoring approach (MTA), a fragmentation method. This MTA-based method can yield a reliable estimate of individual IHB energy in a system containing multiple H-bonds. After explaining and illustrating the methodology of MTA, we present its use for the IHB energy estimation in molecules and clusters. We also discuss the use of this method by other researchers as a standard, state-of-the-art method for estimating IHB energy as well as those of other noncovalent interactions.     

LC Determination of Isosorbide-5-Mononitrate in Human Plasma

A simple, sensitive, selective and cost effective LC–UV method was developed for determination of isosorbide mononitrate in human plasma using guaifenesin as an internal standard. Isosorbide mononitrate in plasma was extracted by a single step liquid extraction using tert-butyl methyl ether and chromatographed on a C18 column using water and acetonitrile (80:20 v/v) as mobile phase. The method was validated and exhibited a linear range from 51.6 to 2064.4 ng mL^?1. The inter- and intra-assay accuracy ranged from 97.2–102.7 to 94.2–105.5%, respectively, with precision less than 10% in both the cases. The LLQ was 51.6 ng mL^?1. The validated method was applied to the quantitation of isosorbide mononitrate from plasma samples in a pharmacokinetic study.     

Assessment of immune response to repeat stimulation with BCG vaccine using in vitro PBMC model

Background  

Tuberculosis (TB) is one of the most prevalent cause of death due to a single pathogen. Bacillus Calmette Guérin (BCG) is the only vaccine available for clinical use that protects against miliary TB; however, this vaccine has shown variable levels of efficacy against pulmonary TB. In India, a single dose of BCG vaccine is given and there are few countries where repeated doses of BCG are given. The incidence of TB in India is very high inspite of primary vaccination in neonatal period and therefore requires consideration for repeated immunization.     

Supply planning models for a remanufacturer under just-in-time manufacturing environment with reverse logistics

We study a supply planning problem in a manufacturing system with two stages. The first stage is a remanufacturer that supplies two closely-related components to the second (manufacturing) stage, which uses each component as the basis for its respective product. The used products are recovered from the market by a third-party logistic provider through an established reverse logistics network. The remanufacturer may satisfy the manufacturer’s demand either by purchasing new components or by remanufacturing components recovered from the returned used products. The remanufacturer’s costs arise from product recovery, remanufacturing components, purchasing original components, holding inventories of recovered products and remanufactured components, production setups (at the first stage and at each component changeover), disposal of recovered products that are not remanufactured, and coordinating the supply modes. The objective is to develop optimal production plans for different production strategies. These strategies are differentiated by whether inventories of recovered products or remanufactured components are carried, and by whether the order in which retailers are served during the planning horizon may be resequenced. We devise production policies that minimize the total cost at the remanufacturer by specifying the quantity of components to be remanufactured, the quantity of new components to be purchased from suppliers, and the quantity of recovered used products that must be disposed. The effects of production capacity are also explored. A comprehensive computational study provides insights into this closed-loop supply chain for those strategies that are shown to be NP-hard.     

Energetic Ordering of Hydrogen Bond Strengths in Methanol-Water Clusters: Insights via Molecular Tailoring Approach

In this work, we examine the strength of various types of individual hydrogen bond (HB) in mixed methanol-water M_nW_m, (n+m=2 to 7) clusters, with an aim to understand the relative order of their strength, using our recently proposed molecular tailoring-based approach (MTA). Among all the types of HB, it is observed that the O_M−H…O_W HBs are the strongest (6.9 to 12.4 kcal mol⁻¹). The next ones are O_M−H…O_M HBs (6.5 to 11.6 kcal mol⁻¹). The O_W−H…O_W (0.2 to 10.9 kcal mol⁻¹) and O_W−H…O_M HBs (0.3 to 10.3 kcal mol⁻¹) are the weakest ones. This energetic ordering of HBs is seen to be different from the respective HB energies in the dimer i. e., O_M−H…O_M (5.0 to 6.0 kcal mol⁻¹)>O_W−H…O_M (1.5 to 6.0 kcal mol⁻¹)>O_M−H…O_W (3.8 to 5.6 kcal mol⁻¹)>O_W−H…O_W (1.2 to 5.0 kcal mol⁻¹). The plausible reason for the difference in the HB energy ordering may be attributed to the increase or decrease in HB strengths due to the formation of cooperative or anti-cooperative HB networks. For instance, the cooperativity contribution towards the different types of HB follows: O_M−H…O_W (2.4 to 8.6 kcal mol⁻¹)>O_M−H…O_M (1.3 to 6.3 kcal mol⁻¹)>O_W−H…O_W (−1.0 to 6.5 kcal mol⁻¹)>O_W−H…O_M (−1.2 to 5.3 kcal mol⁻¹). This ordering of cooperativity contribution is similar to the HB energy ordering obtained by the MTA-based method. It is emphasized here that, the interplay between the cooperative and anti-cooperative contributions are indispensable for the correct energetic ordering of these HBs.     

Ultrafast,electric field-induced fingers in an anticlinic liquid crystal

Propagating fingers of synclinic liquid crystalline phase were observed to invade the anticlinic phase for applied electric fields E larger than a characteristic threshold field E_th. The front velocity was found to be highly non-linear in E, with enormous velocities of at least 10 cm s^-1, and perhaps as high as 400 cm s^-1 for the maximum applied field. These are by far the largest velocities ever observed for a liquid crystal. The results are discussed theoretically, including the possibilities of a field-dependent molecular interaction coefficient and shear thinning.     

Semi-analytical solution for a system with clearance nonlinearity and periodic excitation

Many dynamical systems such as gears, tire-pavement, automotive brakes, and cam-follower have clearance nonlinearity and excitation, which are periodic in nature. It is essential to accurately predict the steady-state response of these systems using contact-mechanics-based model for understanding their nonlinear dynamic behavior. Among the methods available to theoretically solve the system’s nonlinear governing equation(s), a semi-analytical technique such as the harmonic balance method (HBM) is preferred over numerical approaches for various reasons, including accuracy. An HBM formulation that can predict the fundamental, sub-, and super-harmonic solutions is presented here. As multiple variants of HBM exist in the literature, this work focuses on comparatively evaluating the most appropriate variant for the system under consideration. Since the system has multiple discontinuities in terms of contact stiffness and damping forces, these have to be smoothed precisely to be utilized in the HBM. Hence, a novel smoothing function was proposed and evaluated against other existing smoothing functions in literature based on various criteria. Next, the most applicable HBM variant was selected with reference to steady-state solutions from numerical methods. The predictions from the selected HBM variant were validated against the results furnished in the literature for a similar system. Finally, the nonlinear frequency response of the system with multiple discontinuities was estimated using the selected HBM and found to be in good agreement with numerical results.