A numerical study of variable coefficient elliptic Cauchy problem via projection method

In this paper, we investigate a numerical method for the solution of an inverse problem of recovering lacking data on some part of the boundary of a domain from the Cauchy data on other part for a variable coefficient elliptic Cauchy problem. In the process, the Cauchy problem is transformed into the problem of solving a compact linear operator equation. As a remedy to the ill-posedness of the problem, we use a projection method which allows regularization solely by discretization. The discretization level plays the role of regularization parameter in the case of projection method. The balancing principle is used for the choice of an appropriate discretization level. Several numerical examples show that the method produces a stable good approximate solution.

A pseudo-time EnKF incorporating shape based reconstruction for diffuse optical tomography

Purpose: The authors aim at developing a pseudo-time, sub-optimal stochastic filtering approach based on a derivative free variant of the ensemble Kalman filter (EnKF) for solving the inverse problem of diffuse optical tomography (DOT) while making use of a shape based reconstruction strategy that enables representing a cross section of an inhomogeneous tumor boundary by a general closed curve. Methods: The optical parameter fields to be recovered are approximated via an expansion based on the circular harmonics (CH) (Fourier basis functions) and the EnKF is used to recover the coefficients in the expansion with both simulated and experimentally obtained photon fluence data on phantoms with inhomogeneous inclusions. The process and measurement equations in the pseudo-dynamic EnKF (PD-EnKF) presently yield a parsimonious representation of the filter variables, which consist of only the Fourier coefficients and the constant scalar parameter value within the inclusion. Using fictitious, low-intensity Wiener noise processes in suitably constructed ``measurement'' equations, the filter variables are treated as pseudo-stochastic processes so that their recovery within a stochastic filtering framework is made possible. Results: In our numerical simulations, we have considered both elliptical inclusions (two inhomogeneities) and those with more complex shapes (such as an annular ring and a dumbbell) in 2-D objects which are cross-sections of a cylinder with background absorption and (reduced) scattering coefficient chosen as mu(b)(a)=0.01mm(-1) and mu('b)(s)=1.0mm(-1), respectively. We also assume mu(a) = 0.02 mm(-1) within the inhomogeneity (for the single inhomogeneity case) and mu(a) = 0.02 and 0.03 mm(-1) (for the two inhomogeneities case). The reconstruction results by the PD-EnKF are shown to be consistently superior to those through a deterministic and explicitly regularized Gauss-Newton algorithm. We have also estimated the unknown mu(a) from experimentally gathered fluence data and verified the reconstruction by matching the experimental data with the computed one. Conclusions: The PD-EnKF, which exhibits little sensitivity against variations in the fictitiously introduced noise processes, is also proven to be accurate and robust in recovering a spatial map of the absorption coefficient from DOT data. With the help of shape based representation of the inhomogeneities and an appropriate scaling of the CH expansion coefficients representing the boundary, we have been able to recover inhomogeneities representative of the shape of malignancies in medical diagnostic imaging. (C) 2012 American Association of Physicists in Medicine. [DOI: 10.1118/1.3679855]

Photo, thermal, and ultrasonic degradation of EGDMA-crosslinked poly(acrylic acid-co-sodium acrylate-co-acrylamide) superabsorbents

Superabsorbent polymers (SAPs) based on acrylic acid (AA), sodium acrylate (SA), and acrylamide (AM) were synthesized by inverse suspension polymerization using ethylene glycol dimethacrylate as the crosslinking agent. The equilibrium swelling capacities and the rates of swelling of SAPs varied with the AM content and followed first-order kinetics. The photodegradation of SAPs in their equilibrium swollen state was carried out by monitoring their swelling capacity and the residual weight fraction. The SAPs degraded in two stages, wherein the swelling capacity increased to a maximum and then subsequently decreased. Thermogravimetric analysis of the SAPs indicated that the copolymeric superabsorbents had intermediate thermal stability between the homopolymeric superabsorbents. The activation energies of SAPs with 0, 20, and 100 mol % AM content were determined by Kissinger method and were found to be 299, 248, and 147 kJ mol-1, respectively. The ultrasonic degradation of the superabsorbents was carried out in their equilibrium swollen state, and the change in the viscosity with ultrasonication time was used to quantify the degradation. The ultrasonic degradation of AA/SA superabsorbent was also investigated at various ultrasound intensities. The degradation rate coefficients were found to increase with the intensity of ultrasound. The ultrasonic degradation of AA/SA/AM (20% AM) was also carried out, and degradation rate was found to be more than that of the AA/SA superabsorbent. (C) 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012

Linearization and Reconstruction of Non-linear Diffuse Optical Tomographic Image

Diffuse optical tomography (DOT) is one of the ways to probe highly scattering media such as tissue using low-energy near infra-red light (NIR) to reconstruct a map of the optical property distribution. The interaction of the photons in biological tissue is a non-linear process and the phton transport through the tissue is modelled using diffusion theory. The inversion problem is often solved through iterative methods based on nonlinear optimization for the minimization of a data-model misfit function. The solution of the non-linear problem can be improved by modeling and optimizing the cost functional. The cost functional is f(x) = x(T)Ax - b(T)x + c and after minimization, the cost functional reduces to Ax = b. The spatial distribution of optical parameter can be obtained by solving the above equation iteratively for x. As the problem is non-linear, ill-posed and ill-conditioned, there will be an error or correction term for x at each iteration. A linearization strategy is proposed for the solution of the nonlinear ill-posed inverse problem by linear combination of system matrix and error in solution. By propagating the error (e) information (obtained from previous iteration) to the minimization function f(x), we can rewrite the minimization function as f(x; e) = (x + e)(T) A(x + e) - b(T)(x + e) + c. The revised cost functional is f(x; e) = f(x) + e(T)Ae. The self guided spatial weighted prior (e(T)Ae) error (e, error in estimating x) information along the principal nodes facilitates a well resolved dominant solution over the region of interest. The local minimization reduces the spreading of inclusion and removes the side lobes, thereby improving the contrast, localization and resolution of reconstructed image which has not been possible with conventional linear and regularization algorithm.

Robust solver based on modified particle swarm optimization for improved solution of diffusion transport through containment facilities

Accurate estimation of mass transport parameters is necessary for overall design and evaluation processes of the waste disposal facilities. The mass transport parameters, such as effective diffusion coefficient, retardation factor and diffusion accessible porosity, are estimated from observed diffusion data by inverse analysis. Recently, particle swarm optimization (PSO) algorithm has been used to develop inverse model for estimating these parameters that alleviated existing limitations in the inverse analysis. However, PSO solver yields different solutions in successive runs because of the stochastic nature of the algorithm and also because of the presence of multiple optimum solutions. Thus the estimated mean solution from independent runs is significantly different from the best solution. In this paper, two variants of the PSO algorithms are proposed to improve the performance of the inverse analysis. The proposed algorithms use perturbation equation for the gbest particle to gain information around gbest region on the search space and catfish particles in alternative iterations to improve exploration capabilities. Performance comparison of developed solvers on synthetic test data for two different diffusion problems reveals that one of the proposed solvers, CPPSO, significantly improves overall performance with improved best, worst and mean fitness values. The developed solver is further used to estimate transport parameters from 12 sets of experimentally observed diffusion data obtained from three diffusion problems and compared with published values from the literature. The proposed solver is quick, simple and robust on different diffusion problems. (C) 2012 Elsevier Ltd. All rights reserved.

Kinetics of adsorption of methylene blue and rhodamine 6G on acrylic acid-based superabsorbents

Superabsorbent polymers (SAPs) of acrylic acid, sodium acrylate, and acrylamide (AM), crosslinked with ethylene glycol dimethacrylate, were synthesized by inverse suspension polymerization. The equilibrium swelling capacities of the SAPs were determined and these decreased with increasing AM content. The adsorption of the two cationic dyes, methylene blue and rhodamine 6G, on the dry as well as equilibrium swollen SAPs was investigated. The amount of the dye adsorbed at equilibrium per unit weight of the SAPs and the rate constants of adsorption were determined. The amount of the dye adsorbed at equilibrium by the SAPs decreased with increasing mol % of AM in the SAPs. The amount of the dye adsorbed at equilibrium was almost equal for the dry and equilibrium swollen SAPs. However, the equilibrium swollen SAPs adsorbed dyes at a higher rate than the dry SAPs. The higher rate of adsorption was attributed to the availability of all the anionic groups present in the fully elongated conformation of the SAPs in the equilibrium swollen state. The effect of initial dye concentration on the adsorption was also investigated and the adsorption was described by Langmuir adsorption isotherms. (C) 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012

The Hinge Region of Human Thyroid-Stimulating Hormone (TSH) Receptor Operates as a Tunable Switch between Hormone Binding and Receptor Activation

The mechanism by which the hinge regions of glycoprotein hormone receptors couple hormone binding to activation of downstream effecters is not clearly understood. In the present study, agonistic (311.62) and antagonistic (311.87) monoclonal antibodies (MAbs) directed against the TSH receptor extracellular domain were used to elucidate role of the hinge region in receptor activation. MAb 311.62 which identifies the LRR/Cb-2 junction (aa 265-275), increased the affinity of TSHR for the hormone while concomitantly decreasing its efficacy, whereas MAb 311.87 recognizing LRR 7-9 (aa 201-259) acted as a non-competitive inhibitor of Thyroid stimulating hormone (TSH) binding. Binding of MAbs was sensitive to the conformational changes caused by the activating and inactivating mutations and exhibited differential effects on hormone binding and response of these mutants. By studying the effects of these MAbs on truncation and chimeric mutants of thyroid stimulating hormone receptor (TSHR), this study confirms the tethered inverse agonistic role played by the hinge region and maps the interactions between TSHR hinge region and exoloops responsible for maintenance of the receptor in its basal state. Mechanistic studies on the antibody-receptor interactions suggest that MAb 311.87 is an allosteric insurmountable antagonist and inhibits initiation of the hormone induced conformational changes in the hinge region, whereas MAb 311.62 acts as a partial agonist that recognizes a conformational epitope critical for coupling of hormone binding to receptor activation. The hinge region, probably in close proximity with the alpha-subunit in the hormone-receptor complex, acts as a tunable switch between hormone binding and receptor activation.

AIWIN - A fast and jigless inspection technique for machined parts

Precision inspection of manufactured components having multiple complex surfaces and variable tolerance definition is an involved, complex and time-consuming function. In routine practice, a jig is used to present the part in a known reference frame to carry out the inspection process. Jigs involve both time and cost in their development, manufacture and use. This paper describes 'as is where is inspection' (AIWIN), a new automated inspection technique that accelerates the inspection process by carrying out a fast registration procedure and establishing a quick correspondence between the part to inspect and its CAD geometry. The main challenge in doing away with a jig is that the inspection reference frame could be far removed from the CAD frame. Traditional techniques based on iterative closest point (ICP) or Newton methods require either a large number of iterations for convergence or fail in such a situation. A two-step coarse registration process is proposed to provide a good initial guess for a modified ICP algorithm developed earlier (Ravishankar et al., Int J Adv Manuf Technol 46(1-4):227-236, 2010). The first step uses a calibrated sphere for local hard registration and fixing the translation error. This transformation locates the centre for the sphere in the CAD frame. In the second step, the inverse transformation (involving pure rotation about multiple axes) required to align the inspection points measured on the manufactured part with the CAD point dataset of the model is determined and enforced. This completes the coarse registration enabling fast convergence of the modified ICP algorithm. The new technique has been implemented on complex freeform machined components and the inspection results clearly show that the process is precise and reliable with rapid convergence. © 2011 Springer-Verlag London Limited.

Quantum corrections to screening at strong coupling

We compute a certain class of corrections to (specific) screening lengths in strongly coupled non-abelian plasmas using the AdS/CFT correspondence. In this holographic framework, these corrections arise from various higher curvature interactions modifying the leading Einstein gravity action. The changes in the screening lengths are perturbative in inverse powers of the `t Hooft coupling or of the number of colors, as can be made precise in the context where the dual gauge theory is superconformal. We also compare the results of these holographic calculations to lattice results for the analogous screening lengths in QCD. In particular, we apply these results within the program of making quantitative comparisons between the strongly coupled quark-gluon plasma and holographic descriptions of conformal field theory. (c) 2012 Elsevier B.V. All rights reserved.

Parameter estimation of a two-horizon soil profile by combining crop canopy and surface soil moisture observations using GLUE

Estimation of soil parameters by inverse modeling using observations on either surface soil moisture or crop variables has been successfully attempted in many studies, but difficulties to estimate root zone properties arise when heterogeneous layered soils are considered. The objective of this study was to explore the potential of combining observations on surface soil moisture and crop variables - leaf area index (LAI) and above-ground biomass for estimating soil parameters (water holding capacity and soil depth) in a two-layered soil system using inversion of the crop model STICS. This was performed using GLUE method on a synthetic data set on varying soil types and on a data set from a field experiment carried out in two maize plots in South India. The main results were (i) combination of surface soil moisture and above-ground biomass provided consistently good estimates with small uncertainity of soil properties for the two soil layers, for a wide range of soil paramater values, both in the synthetic and the field experiment, (ii) above-ground biomass was found to give relatively better estimates and lower uncertainty than LAI when combined with surface soil moisture, especially for estimation of soil depth, (iii) surface soil moisture data, either alone or combined with crop variables, provided a very good estimate of the water holding capacity of the upper soil layer with very small uncertainty whereas using the surface soil moisture alone gave very poor estimates of the soil properties of the deeper layer, and (iv) using crop variables alone (else above-ground biomass or LAI) provided reasonable estimates of the deeper layer properties depending on the soil type but provided poor estimates of the first layer properties. The robustness of combining observations of the surface soil moisture and the above-ground biomass for estimating two layer soil properties, which was demonstrated using both synthetic and field experiments in this study, needs now to be tested for a broader range of climatic conditions and crop types, to assess its potential for spatial applications. (C) 2012 Elsevier B.V. All rights reserved.

Mesh Simplification Based on Edge Collapsing Could Improve Computational Efficiency in Near Infrared Optical Tomographic Imaging

The diffusion equation-based modeling of near infrared light propagation in tissue is achieved by using finite-element mesh for imaging real-tissue types, such as breast and brain. The finite-element mesh size (number of nodes) dictates the parameter space in the optical tomographic imaging. Most commonly used finite-element meshing algorithms do not provide the flexibility of distinct nodal spacing in different regions of imaging domain to take the sensitivity of the problem into consideration. This study aims to present a computationally efficient mesh simplification method that can be used as a preprocessing step to iterative image reconstruction, where the finite-element mesh is simplified by using an edge collapsing algorithm to reduce the parameter space at regions where the sensitivity of the problem is relatively low. It is shown, using simulations and experimental phantom data for simple meshes/domains, that a significant reduction in parameter space could be achieved without compromising on the reconstructed image quality. The maximum errors observed by using the simplified meshes were less than 0.27% in the forward problem and 5% for inverse problem.

Zero-crossing approach to high-resolution reconstruction in frequency-domain optical-coherence tomography

We address the problem of high-resolution reconstruction in frequency-domain optical-coherence tomography (FDOCT). The traditional method employed uses the inverse discrete Fourier transform, which is limited in resolution due to the Heisenberg uncertainty principle. We propose a reconstruction technique based on zero-crossing (ZC) interval analysis. The motivation for our approach lies in the observation that, for a multilayered specimen, the backscattered signal may be expressed as a sum of sinusoids, and each sinusoid manifests as a peak in the FDOCT reconstruction. The successive ZC intervals of a sinusoid exhibit high consistency, with the intervals being inversely related to the frequency of the sinusoid. The statistics of the ZC intervals are used for detecting the frequencies present in the input signal. The noise robustness of the proposed technique is improved by using a cosine-modulated filter bank for separating the input into different frequency bands, and the ZC analysis is carried out on each band separately. The design of the filter bank requires the design of a prototype, which we accomplish using a Kaiser window approach. We show that the proposed method gives good results on synthesized and experimental data. The resolution is enhanced, and noise robustness is higher compared with the standard Fourier reconstruction. (c) 2012 Optical Society of America

Minimal residual method provides optimal regularization parameter for diffuse optical tomography

The inverse problem in the diffuse optical tomography is known to be nonlinear, ill-posed, and sometimes under-determined, requiring regularization to obtain meaningful results, with Tikhonov-type regularization being the most popular one. The choice of this regularization parameter dictates the reconstructed optical image quality and is typically chosen empirically or based on prior experience. An automated method for optimal selection of regularization parameter that is based on regularized minimal residual method (MRM) is proposed and is compared with the traditional generalized cross-validation method. The results obtained using numerical and gelatin phantom data indicate that the MRM-based method is capable of providing the optimal regularization parameter. (C) 2012 Society of Photo-Optical Instrumentation Engineers (SPIE). DOI: 10.1117/1.JBO.17.10.106015]

Effective contrast recovery in rapid dynamic near-infrared diffuse optical tomography using l(1)-norm-based linear image reconstruction method

Traditional image reconstruction methods in rapid dynamic diffuse optical tomography employ l(2)-norm-based regularization, which is known to remove the high-frequency components in the reconstructed images and make them appear smooth. The contrast recovery in these type of methods is typically dependent on the iterative nature of method employed, where the nonlinear iterative technique is known to perform better in comparison to linear techniques (noniterative) with a caveat that nonlinear techniques are computationally complex. Assuming that there is a linear dependency of solution between successive frames resulted in a linear inverse problem. This new framework with the combination of l(1)-norm based regularization can provide better robustness to noise and provide better contrast recovery compared to conventional l(2)-based techniques. Moreover, it is shown that the proposed l(1)-based technique is computationally efficient compared to its counterpart (l(2)-based one). The proposed framework requires a reasonably close estimate of the actual solution for the initial frame, and any suboptimal estimate leads to erroneous reconstruction results for the subsequent frames.

A numerical approach to determine the sufficiency of given boundary data sets for uniquely estimating interior elastic properties

We consider an inverse elasticity problem in which forces and displacements are known on the boundary and the material property distribution inside the body is to be found. In other words, we need to estimate the distribution of constitutive properties using the finite boundary data sets. Uniqueness of the solution to this problem is proved in the literature only under certain assumptions for a given complete Dirichlet-to-Neumann map. Another complication in the numerical solution of this problem is that the number of boundary data sets needed to establish uniqueness is not known even under the restricted cases where uniqueness is proved theoretically. In this paper, we present a numerical technique that can assess the sufficiency of given boundary data sets by computing the rank of a sensitivity matrix that arises in the Gauss-Newton method used to solve the problem. Numerical experiments are presented to illustrate the method.