Maximum likelihood analysis of multi-stress accelerated life test data of series systems with competing log-normal causes of failure

This article presents frequentist inference of accelerated life test data of series systems with independent log-normal component lifetimes. The means of the component log-lifetimes are assumed to depend on the stress variables through a linear stress translation function that can accommodate the standard stress translation functions in the literature. An expectation-maximization algorithm is developed to obtain the maximum likelihood estimates of model parameters. The maximum likelihood estimates are then further refined by bootstrap, which is also used to infer about the component and system reliability metrics at usage stresses. The developed methodology is illustrated by analyzing a real as well as a simulated dataset. A simulation study is also carried out to judge the effectiveness of the bootstrap. It is found that in this model, application of bootstrap results in significant improvement over the simple maximum likelihood estimates.

B-Spline potential function for maximum a-posteriori image reconstruction in fluorescence microscopy

An iterative image reconstruction technique employing B-Spline potential function in a Bayesian framework is proposed for fluorescence microscopy images. B-splines are piecewise polynomials with smooth transition, compact support and are the shortest polynomial splines. Incorporation of the B-spline potential function in the maximum-a-posteriori reconstruction technique resulted in improved contrast, enhanced resolution and substantial background reduction. The proposed technique is validated on simulated data as well as on the images acquired from fluorescence microscopes (widefield, confocal laser scanning fluorescence and super-resolution 4Pi microscopy). A comparative study of the proposed technique with the state-of-art maximum likelihood (ML) and maximum-a-posteriori (MAP) with quadratic potential function shows its superiority over the others. B-Spline MAP technique can find applications in several imaging modalities of fluorescence microscopy like selective plane illumination microscopy, localization microscopy and STED. (C) 2015 Author(s).

MRT Letter: A Unified Accelerated Maximum Likelihood Technique for Widefield, Confocal, and Super-Resolution 4Pi Microscopy

We propose an algorithmic technique for accelerating maximum likelihood (ML) algorithm for image reconstruction in fluorescence microscopy. This is made possible by integrating Biggs-Andrews (BA) method with ML approach. The results on widefield, confocal, and super-resolution 4Pi microscopy reveal substantial improvement in the speed of 3D image reconstruction (the number of iterations has reduced by approximately one-half). Moreover, the quality of reconstruction obtained using accelerated ML closely resembles with nonaccelerated ML method. The proposed technique is a step closer to realize real-time reconstruction in 3D fluorescence microscopy. Microsc. Res. Tech. 78:331-335, 2015. (c) 2015 Wiley Periodicals, Inc.

Probable maximum precipitation estimation for catchments in Mahanadi river basin

Probable maximum precipitation (PMP) is a theoretical concept that is widely used by hydrologists to arrive at estimates for probable maximum flood (PMF) that find use in planning, design and risk assessment of high-hazard hydrological structures such as flood control dams upstream of populated areas. The PMP represents the greatest depth of precipitation for a given duration that is meteorologically possible for a watershed or an area at a particular time of year, with no allowance made for long-term climatic trends. Various methods are in use for estimation of PMP over a target location corresponding to different durations. Moisture maximization method and Hershfield method are two widely used methods. The former method maximizes the observed storms assuming that the atmospheric moisture would rise up to a very high value estimated based on the maximum daily dew point temperature. On the other hand, the latter method is a statistical method based on a general frequency equation given by Chow. The present study provides one-day PMP estimates and PMP maps for Mahanadi river basin based on the aforementioned methods. There is a need for such estimates and maps, as the river basin is prone to frequent floods. Utility of the constructed PMP maps in computing PMP for various catchments in the river basin is demonstrated. The PMP estimates can eventually be used to arrive at PMF estimates for those catchments. (C) 2015 The Authors. Published by Elsevier B.V.

Variational approach to homogenization of doubly-nonlinear flow in a periodic structure

This work deals with the homogenization of an initial- and boundary-value problem for the doubly-nonlinear system D(t)w - del.(z) over right arrow = g(x, t, x/epsilon) (0.1) w is an element of alpha(u, x/epsilon) (0.2) (z) over right arrow is an element of (gamma) over right arrow (del u, x/epsilon) (0.3) Here epsilon is a positive parameter; alpha and (gamma) over right arrow are maximal monotone with respect to the first variable and periodic with respect to the second one. The inclusions (0.2) and (0.3) are here formulated as null-minimization principles, via the theory of Fitzpatrick MR 1009594]. As epsilon -> 0, a two-scale formulation is derived via Nguetseng's notion of two-scale convergence, and a (single-scale) homogenized problem is then retrieved. (C) 2015 Elsevier Ltd. All rights reserved.

Variational approach to homogenization of doubly-nonlinear flow in a periodic structure

This work deals with the homogenization of an initial- and boundary-value problem for the doubly-nonlinear system D(t)w - del.(z) over right arrow = g(x, t, x/epsilon) (0.1) w is an element of alpha(u, x/epsilon) (0.2) (z) over right arrow is an element of (gamma) over right arrow (del u, x/epsilon) (0.3) Here epsilon is a positive parameter; alpha and (gamma) over right arrow are maximal monotone with respect to the first variable and periodic with respect to the second one. The inclusions (0.2) and (0.3) are here formulated as null-minimization principles, via the theory of Fitzpatrick MR 1009594]. As epsilon -> 0, a two-scale formulation is derived via Nguetseng's notion of two-scale convergence, and a (single-scale) homogenized problem is then retrieved. (C) 2015 Elsevier Ltd. All rights reserved.

On the superposition principle in interference experiments

The superposition principle is usually incorrectly applied in interference experiments. This has recently been investigated through numerics based on Finite Difference Time Domain (FDTD) methods as well as the Feynman path integral formalism. In the current work, we have derived an analytic formula for the Sorkin parameter which can be used to determine the deviation from the application of the principle. We have found excellent agreement between the analytic distribution and those that have been earlier estimated by numerical integration as well as resource intensive FDTD simulations. The analytic handle would be useful for comparing theory with future experiments. It is applicable both to physics based on classical wave equations as well as the non-relativistic Schrodinger equation.

Maximum magnitude estimation considering the regional rupture character

The main objective of the paper is to develop a new method to estimate the maximum magnitude (M (max)) considering the regional rupture character. The proposed method has been explained in detail and examined for both intraplate and active regions. Seismotectonic data has been collected for both the regions, and seismic study area (SSA) map was generated for radii of 150, 300, and 500 km. The regional rupture character was established by considering percentage fault rupture (PFR), which is the ratio of subsurface rupture length (RLD) to total fault length (TFL). PFR is used to arrive RLD and is further used for the estimation of maximum magnitude for each seismic source. Maximum magnitude for both the regions was estimated and compared with the existing methods for determining M (max) values. The proposed method gives similar M (max) value irrespective of SSA radius and seismicity. Further seismicity parameters such as magnitude of completeness (M (c) ), ``a'' and ``aEuro parts per thousand b `` parameters and maximum observed magnitude (M (max) (obs) ) were determined for each SSA and used to estimate M (max) by considering all the existing methods. It is observed from the study that existing deterministic and probabilistic M (max) estimation methods are sensitive to SSA radius, M (c) , a and b parameters and M (max) (obs) values. However, M (max) determined from the proposed method is a function of rupture character instead of the seismicity parameters. It was also observed that intraplate region has less PFR when compared to active seismic region.

Maximum group velocity in a one-dimensional model with a sinusoidally varying staggered potential

We use Floquet theory to study the maximum value of the stroboscopic group velocity in a one-dimensional tight-binding model subjected to an on-site staggered potential varying sinusoidally in time. The results obtained by numerically diagonalizing the Floquet operator are analyzed using a variety of analytical schemes. In the low-frequency limit we use adiabatic theory, while in the high-frequency limit the Magnus expansion of the Floquet Hamiltonian turns out to be appropriate. When the magnitude of the staggered potential is much greater or much less than the hopping, we use degenerate Floquet perturbation theory; we find that dynamical localization occurs in the former case when the maximum group velocity vanishes. Finally, starting from an ``engineered'' initial state where the particles (taken to be hard-core bosons) are localized in one part of the chain, we demonstrate that the existence of a maximum stroboscopic group velocity manifests in a light-cone-like spreading of the particles in real space.

VAM Applied to Dimensional Reduction of Nonlinear Multifunctional Film-fabric Laminates

This work aims at asymptotically accurate dimensional reduction of non-linear multi-functional film-fabric laminates having specific application in design of envelopes for High Altitude Airships (HAA). The film-fabric laminate for airship envelope consists of a woven fabric core coated with thin films on each face. These films provide UV protection and Helium leakage prevention, while the core provides required structural strength. This problem is both geometrically and materially non-linear. To incorporate the geometric non-linearity, generalized warping functions are used and finite deformations are allowed. The material non-linearity is handled by using hyper-elastic material models for each layer. The development begins with three-dimensional (3-D) nonlinear elasticity and mathematically splits the analysis into a one-dimensional through-the-thickness analysis and a two-dimensional (2-D) plate analysis. The through-the-thickness analysis provides the 2-D constitutive law which is then given as an input to the 2-D reference surface analysis. The dimensional reduction is carried out using Variational Asymptotic Method (VAM) for moderate strains and very small thickness-to-wavelength ratio. It features the identification and utilization of additional small parameters such as ratio of thicknesses and stiffness coefficients of core and films. Closed form analytical expressions for warping functions and 2-D constitutive law of the film-fabric laminate are obtained.

Nonlinear Optical Properties and Temperature-Dependent UV-Vis Absorption and Photoluminescence Emission in 2D Hexagonal Boron Nitride Nanosheets

Recently, a lot of interest has been centred on the optical properties of hexagonal boron nitride (h-BN), which has a similar lattice structure to graphene. Interestingly, h-BN has a wide bandgap and is biocompatible, so it has potential applications in multiphoton bioimaging, if it can exhibit large nonlinear optical (NLO) properties. However, extensive investigation into the NLO properties of h-BN have not been done so far. Here, NLO properties of 2D h-BN nanosheets (BNNS) are reported for the first time, using 1064-nm NIR laser radiation with a pulse duration of 10 ns using the Z-scan technique. The reverse saturable absorption occurs in aqueous colloidal solutions of BNNS with a very large two-photon absorption cross section (sigma(2PA)) of approximate to 57 x 10(-46) cm(4) s(-1) photon(-1). Also, by using UV-Vis absorption spectroscopy, the temperature coefficient of the bandgap (dE(g)/dT) of BNNS is determined to be 5.9 meV K-1. Further defect-induced photoluminescence emission in the UV region is obtained in the 283-303 K temperature range, under excitations of different wavelengths. The present report of large sigma(2PA) combined with stability and biocompatibility could open up new possibilities for the application of BNNS as a potential optical material for multiphoton bioimaging and advanced photonic devices.

Investigations on growth, structure, optical properties and laser damage threshold of organic nonlinear optical crystals of Guanidinium L-Ascorbate

Single crystals of Guanidinium L-Ascorbate (GuLA) were grown and crystal structure was determined by direct methods. GuLA crystallizes in orthorhombic, non-centrosymmetric space group P2(1)2(1)2(1). The UV-cutoff was determined as 325 nm. The morphology was generated and the interplanar angles estimated and compared with experimental values. Second harmonic generation conversion efficiency was measured and compared with other salts of L-Ascorbic acid. Surface laser damage threshold was calculated as 11.3GW/cm(2) for a single shot of laser of 1064 nm wavelength.

Nonlinear Differential Games-Based Impact-Angle-Constrained Guidance Law

The problem of intercepting a maneuvering target at a prespecified impact angle is posed in nonlinear zero-sum differential games framework. A feedback form solution is proposed by extending state-dependent Riccati equation method to nonlinear zero-sum differential games. An analytic solution is obtained for the state-dependent Riccati equation corresponding to the impact-angle-constrained guidance problem. The impact-angle-constrained guidance law is derived using the states line-of-sight rate and projected terminal impact angle error. Local asymptotic stability conditions for the closed-loop system corresponding to these states are studied. Time-to-go estimation is not explicitly required to derive and implement the proposed guidance law. Performance of the proposed guidance law is validated using two-dimensional simulation of the relative nonlinear kinematics as well as a thrust-driven realistic interceptor model.

Comparison of a priori and a posteriori meshes for singularly perturbed nonlinear parameterized problems

This paper deals with the adaptive mesh generation for singularly perturbed nonlinear parameterized problems with a comparative research study on them. We propose an a posteriori error estimate for singularly perturbed parameterized problems by moving mesh methods with fixed number of mesh points. The well known a priori meshes are compared with the proposed one. The comparison results show that the proposed numerical method is highly effective for the generation of layer adapted a posteriori meshes. A numerical experiment of the error behavior on different meshes is carried out to highlight the comparison of the approximated solutions. (C) 2015 Elsevier B.V. All rights reserved.

Energy Harvesting WSNs for Accurately Estimating the Maximum Sensor Reading: Trade-Offs and Optimal Design

Computing the maximum of sensor readings arises in several environmental, health, and industrial monitoring applications of wireless sensor networks (WSNs). We characterize the several novel design trade-offs that arise when green energy harvesting (EH) WSNs, which promise perpetual lifetimes, are deployed for this purpose. The nodes harvest renewable energy from the environment for communicating their readings to a fusion node, which then periodically estimates the maximum. For a randomized transmission schedule in which a pre-specified number of randomly selected nodes transmit in a sensor data collection round, we analyze the mean absolute error (MAE), which is defined as the mean of the absolute difference between the maximum and that estimated by the fusion node in each round. We optimize the transmit power and the number of scheduled nodes to minimize the MAE, both when the nodes have channel state information (CSI) and when they do not. Our results highlight how the optimal system operation depends on the EH rate, availability and cost of acquiring CSI, quantization, and size of the scheduled subset. Our analysis applies to a general class of sensor reading and EH random processes.