Non-standard asymptotics in an inhomogeneous gamma process

Nonhomogeneous Poisson process (NHPP) is a commonly used stochastic model that is utilized to describe the pattern of repeated occurrence of certain events or conditions. Aninhomogeneous gamma process evolves as a generalization to NHPP, where the observed failure epochs correspond to every successive κ-th event of the underlying Poisson process, κ being an unknown parameter to be estimated from the data. This article focuses on a special class of inhomogeneous gamma process, calledmodulated power law process (MPLP) that assumes the Weibull form of the intensity function. The traditional power law process is a popular stochastic formulation of certain empirical relationships between the time to failure and the cumulative number of failures, often observed in industrial experiments. The MPLP retains this underlying physical basis and provides a more flexible modeling environment potentially leading to a better fit to the failure data at hand. In this paper, we investigate inference issues related to MPLP. The maximum likelihood estimators (MLE’s) of the model parameters are not in closed form and enjoy the curious property that they are asymptotically normal with a singular variance-covariance matrix. Consequently, the derivation of the large-sample results requires non-standard modifications of the usual arguments. We also propose a set of simple closed-form estimators that are asymptotically equivalent to the MLE’s. Extensive simulation results are carried out to supplement the theoretical findings. Finally, we implement our inference results to a failure dataset arising from a repairable system.     

Analysis of a model scheme incorporating reactant inhibition: Instability of homogeneous solution and formation of spatio–temporal structures

A model scheme incorporating reactant inhibition in the rate process has been analyzed with a view to study the instability of homogeneous solution due to diffusion. Conditions for the occurrence of Turing as well as phase instability are derived and show the existence of multiplicity in the parameter space. The Ginzburg-Landau equation for the system is developed and solved numerically in various regions of the parameter space. The simple model system shows the existence of very rich behavior including normal and inverted bifurcations in the super and subcritical regimes. The various results are analyzed and discussed. © 1993 John Wiley & Sons, Inc.     

Exploration of the secondary structure specific differential solvation dynamics between the native and molten globule states of the protein HP-36

Recent experiments have shown that the time dependence of fluorescence Stokes shift of a chromophore is substantially different when the chromophore is located in a molten globule (MG) state and in the native state of the same protein. To understand the origin of this difference, particularly the role of water in the differential solvation of the protein in the native and the MG states, we have carried out fully atomistic molecular dynamics simulations with explicit water of a partially unfolded MG state of the protein HP-36 and compared the results with the solvation dynamics of the protein in the folded native state. It is observed that the polar solvation dynamics of the three helical segments of the protein is influenced in a nonuniform heterogeneous manner in the MG state. While the equilibrium solvation time correlation function for helix-3 has been found to relax faster in the MG state as compared to that in the native state, the decay of the corresponding function for the other two helices slows down in the MG state. A careful analysis shows that the origin of such heterogeneous relative solvation behavior lies in the differential location of the polar probe residues and their exposure to bulk solvent. We find a significant negative cross-correlation between the contribution (to the solvation energy of a tagged amino acid residue) of water and the other groups of the protein, indicating a competing role in solvation. The sensitivity of solvation dynamics to the secondary structure and the immediate environment can be used to discriminate the partially unfolded and folded states. These results therefore should be useful in explaining recent solvation dynamics experiments on native and MG states of proteins.     

Global tuning of local molecular phenomena: an alternative approach to bionanoelectronics

We have applied simultaneous horizontal and vertical bias to a single molecule (2 nm(2)) in an ordered and disordered matrix to virtually isolate and tune its property without taking it out physically from its environment. Using a dedicated electrode system, we have locally tuned nanoscale properties vertically by STM, while stabilizing its environment by applying a global electric field horizontally. Using this technique, we report tuning of molecular conformations in room temperature, whose evolution of states has been statistically investigated. We have also shown control on switching of a few selected conformations by applying dual bias simultaneously. As we avoid any direct injection of charge into the system via electrode contact, this technique could be used as a generalized method to tune phenomena evolved in an environment of weak interaction from a large distance without destroying the property.     

Role of aspartic acid in collagen structure and stability: A molecular dynamics investigation

A molecular dynamics (MD) simulation study has been carried out to understand the stability of the triple helical collagen models. The calculations show that the presence of the aspartic acid residue in different positions leads to the local variation in the structure. Analyses of root-mean-square deviation (RMSD), radial distribution function (RDF), puckering effect, dihedral angle variation, hydrogen bond (H-bond), and conformational changes during molecular dynamics simulation reveal that the local perturbation in the sequences, increase in chain flexibility due to removal of five membered rings in the collagen by aspartic acid, change of intermolecular H-bonding pattern, and differences in the association of water are mainly influencing the nature of stabilization of collagen by aspartic acid.     

Molecular dynamics study of surfactant monolayers adsorbed at the oil/water and air/water interfaces

Atomistic molecular dynamics (MD) simulations have been carried out to investigate the physical properties of monolayers of monododecyl diethylene glycol (C(12)E(2)) surfactants adsorbed at the oil/water and air/water interfaces. The study shows that the surfactant molecules exhibit more extended conformations with a consequent increase of the thickness of the monolayer in the presence of the oil medium. It is noticed that the hydrocarbon tails of the surfactants are more vertically oriented at the oil/water interface. Interestingly, we notice that the presence of the oil medium has a strong influence in restricting both the translational and reorientational motions of the water molecules present in the hydration layer close to the surfactant headgroups.     

Effect of regulation on efficiency: evidence from Indian cement industry

The main objective of the paper is to analyze the impact of environmental regulation on technical efficiencies of Indian cement producing firms. It derives the technical efficiency (TE) scores of firms in the presence and absence of regulation and brings out the differences in their magnitudes in two scenarios: one in which the firms take initiatives to comply with the set standards by investing additional resources for pollution abatement and the other in which the firms do not take the necessary initiatives. The paper uses establishment level data from Annual Survey of Industries on cement for two years, the most recent data published for 2003–2004 and a previous year for 1999–2000 when the environmental regulations in India were in the initial phases of implementation. A non-parametric deterministic method of data envelopment analysis (DEA) is used to derive the TE scores of firms. The traditional DEA framework is modified by introducing weak disposability of bad outputs to characterize ‘effective environmental regulation’, which ensures that reducing pollution is not costless. For both years it has been found that the TE scores of firms under ‘effective regulation’ scenario are either higher than or equal to those derived under ‘ineffective regulation’ scenario resulting in a higher average TE at the industry level in the ‘effective regulation’ scenario.