Accurate and efficient Monte Carlo solutions to the radiative transport equation in the spatial frequency domain

We present an approach to solving the radiative transport equation (RTE) for layered media in the spatial frequency domain (SFD) using Monte Carlo (MC) simulations. This is done by obtaining a complex photon weight from analysis of the Fourier transform of the RTE. We also develop a modified shortcut method that enables a single MC simulation to efficiently provide RTE solutions in the SFD for any number of spatial frequencies. We provide comparisons between the modified shortcut method and conventional discrete transform methods for SFD reflectance. Further results for oblique illumination illustrate the potential diagnostic utility of the SFD phase-shifts for analysis of layered media.     

Diagnosis of Toxoplasmosis Using a Synthetic Glycosylphosphatidylinositol Glycan

Around 2 billion people worldwide are infected with the apicomplexan parasite Toxoplasma gondii which induces a variety of medical conditions. For example, primary infection during pregnancy can result in fetal death or mental retardation of the child. Diagnosis of acute infections in pregnant women is challenging but crucially important as the drugs used to treat T. gondii infections are potentially harmful to the unborn child. Better, faster, more reliable, and cheaper means of diagnosis by using defined antigens for accurate serological tests are highly desirable. Synthetic pathogen‐specific glycosylphosphatidylinositol (GPI) glycan antigens are diagnostic markers and have been used to distinguish between toxoplasmosis disease states using human sera.     

Study of the base-catalysed oxidation of the anti-bacterial and anti-protozoal agent metronidazole by permanganate ion in alkaline medium

The mechanism of dismutation of MnO₄ ^2? via the complex [MTZ–MnO₄·OH]^2?, formed during the oxidation of metronidazole (MTZ), has been investigated spectrophotometrically at different temperatures. The stoichiometry of the reaction is 1:1, i.e. 1 mol MTZ reacts with 1 mol Mn(VII).The reaction is first order in permanganate, less than first order in [MTZ] and [alkali]. The effects of added products and the dielectric constant and ionic strength of the reaction medium were investigated. The main products were identified by spot test and FT-IR. A mechanism involving a free radical has been proposed. In the equilibrium step MTZ binds to the MnO₄ ^? species to form a complex (C). Investigation of the reaction at different temperatures enabled determination of the activation data for the slow step of proposed mechanism. The proposed mechanism and the derived rate laws are consistent with the observed kinetics.     

Relation between Green’s functions for different potentials

A general relation between the energy-dependent Green’s functions for different potentials is derived in a simple and direct manner. This interesting connection enables the eigenstates of one physical system to be deduced from those of a related system. The derivation is based on the Schrödinger equation and provides an independent justification for the technique of path-dependent time transformation used in path integration.     

A Synergistic Approach towards Optimization of Coupled Cluster Amplitudes by Exploiting Dynamical Hierarchy

The coupled cluster iteration scheme for determining the cluster amplitudes involves a set of nonlinearly coupled difference equations. In the space spanned by the amplitudes, the set of equations are analyzed as a multivariate time-discrete map where the concept of time appears in an implicit manner. With the observation that the cluster amplitudes have difference in their relaxation timescales with respect to the distributions of their magnitudes, the coupled cluster iteration dynamics are considered as a synergistic motion of coexisting slow and fast relaxing modes, manifesting a dynamical hierarchical structure. With the identification of the highly damped auxiliary amplitudes, their time variation can be neglected compared to the principal amplitudes which take much longer time to reach the fixed points. We analytically establish the adiabatic approximation where each of these auxiliary amplitudes are expressed as unique parametric functions of the collective principal amplitudes, allowing us to study the optimization with the latter taken as the independent degrees of freedom. Such decoupling of the amplitudes significantly reduces the computational scaling without sacrificing the accuracy in the ground state energy as demonstrated by a number of challenging molecular applications. A road-map to treat higher order post-adiabatic effects is also discussed.     

Charge regulation as a stabilization mechanism for shell-like assemblies of polyoxometalates

We show that the equilibrium size of single-layer shells composed of polyoxometalate macroions is inversely proportional to the dielectric constant of the medium in which they are dispersed. This behavior is consistent with a stabilization mechanism based on Coulomb repulsion combined with charge regulation. We estimate the cohesive energy per bond between macroions on the shells to be approximately -6kT. This number is extracted from analysis based on a charge regulation model in combination with a model for defects on a sphere. The value of the cohesive bond energy is in agreement with the model-independent critical aggregate concentration. This observation points to a new class of thermodynamically stable shell-like objects. We point out the possible relevance our findings have for certain surfactant systems.     

Evolution and characterization of dynamically recrystallized microstructure in a titanium-modified austenitic stainless steel using ultrasonic and EBSD techniques

A C-scan ultrasonic imaging system was used to investigate the microstructural evolution during dynamic recrystallization (DRX) of a 15Cr–15Ni–2.2Mo–Ti modified austenitic stainless steel (alloy D9). Four specimens were forged at 1273 K to different strains in the range 0.1–0.5. Specimens with true strains of 0.2 or lower did not show any variation in the amplitude of the first back-wall echo. However, a visible variation in the C-scan image was observed at and above the 0.3 strain level. This variation was attributed to the evolution of fine grains. The formation of fine grains was related to DRX, as indicated by electron backscattered diffraction. This study also revealed the characteristics of the DRX or ‘necklace grains’, as opposed to the so-called parent grains or rest of the microstructure.     

Perceptually optimized blind repair of natural images

We define the new idea of blind image repair as a process of correcting one or more different and unknown types of distortions afflicting an image. These distortions could introduce linear or non-linear degradations, compression artifacts, noise, etc., or combinations of these. Thus the concept encompasses denoising, deblurring, deblocking, deringing, and other post-acquisition image improvement processes that address distortions. The problem is distortion-blind when the natures of the distortion processes are unknown prior to analyzing the image. Towards solving this problem, we describe a new framework for repairing an image that has undergone an unknown set of distortions, based on identifying the distortion(s) present in the image (if any) and applying possibly multiple distortion-specific image repair algorithms. Our philosophy is based on the principle that the task of general purpose image repair is one of agglomeration, i.e., the algorithm should embody multiple high-performing distortion-specific repair modules such that seamless general purpose image repair is achieved. Our proposed framework – the GEneral-purpose No-reference Image Improver (GENII) – enables the design of algorithms that are blind to distortion type as well as to distortion parameters, and only requires as input the distorted image to be repaired. The GENII framework is modular and easily extensible to image repair problems beyond those considered here. GENII operates by using natural scene statistic models to identify distortion, to perceptually optimize the distortion parameter(s), to assess the quality of the intermediate repaired images, and to perceptually optimize the repair processes. We explain the general purpose image repair framework and one specific realization, dubbed GENII-1, which assumes that the image has been affected by one or more of four possible distortion types.The performance of GENII-1 is evaluated on 4000 distorted images, and shown to deliver substantial improvements in both quantitative and qualitative visual quality.     

Diophantine exponents and the Khintchine Groshev theorem

We prove the convergence case of the Khintchine–Groshev theorem for affine subspaces and their nondegenerate submanifolds, answering a conjecture of D. Kleinbock.     

Efficient finite-edge diffraction using conservative from-region visibility

We present a fast algorithm to accelerate geometric sound propagation in complex 3D scenes. Our approach computes propagation paths from each source to the listener by taking into account specular reflections and higher-order edge diffractions around finite edges in the scene. We use the well known Biot–Tolstoy–Medwin (BTM) diffraction model along with efficient algorithms for region-based visibility to cull away primitives and significantly reduce the number of edge pairs that need to be processed. The performance of region-based visibility computation is improved by using a fast occluder selection algorithm that can combine small, connected triangles to form large occluders and perform conservative computations at object-space precision. We show that our approach is able to reduce the number of visible primitives considered for sound propagation by a factor of 2–4 for second order edge diffraction as compared to prior propagation algorithms. We demonstrate and analyze its performance on multiple benchmarks. To the best of our knowledge, this is the first algorithm that uses object-space visibility algorithms to improve the performance of finite-edge diffraction computation for geometric sound propagation.