Expectation Propagation for Nonlinear Inverse Problems -- with an Application to Electrical Impedance Tomography

In this paper, we study a fast approximate inference method based on expectation propagation for exploring the posterior probability distribution arising from the Bayesian formulation of nonlinear inverse problems. It is capable of efficiently delivering reliable estimates of the posterior mean and covariance, thereby providing an inverse solution together with quantified uncertainties. Some theoretical properties of the iterative algorithm are discussed, and the efficient implementation for an important class of problems of projection type is described. The method is illustrated with one typical nonlinear inverse problem, electrical impedance tomography with complete electrode model, under sparsity constraints. Numerical results for real experimental data are presented, and compared with that by Markov chain Monte Carlo. The results indicate that the method is accurate and computationally very efficient.Comment: Journal of Computational Physics, to appea

An Analysis of Finite Element Approximation in Electrical Impedance Tomography

We present a finite element analysis of electrical impedance tomography for reconstructing the conductivity distribution from electrode voltage measurements by means of Tikhonov regularization. Two popular choices of the penalty term, i.e., $H^1(\Omega)$-norm smoothness penalty and total variation seminorm penalty, are considered. A piecewise linear finite element method is employed for discretizing the forward model, i.e., the complete electrode model, the conductivity, and the penalty functional. The convergence of the finite element approximations for the Tikhonov model on both polyhedral and smooth curved domains is established. This provides rigorous justifications for the ad hoc discretization procedures in the literature.Comment: 20 page

Gradient-based estimation of Manning's friction coefficient from noisy data

We study the numerical recovery of Manning's roughness coefficient for the diffusive wave approximation of the shallow water equation. We describe a conjugate gradient method for the numerical inversion. Numerical results for one-dimensional model are presented to illustrate the feasibility of the approach. Also we provide a proof of the differentiability of the weak form with respect to the coefficient as well as the continuity and boundedness of the linearized operator under reasonable assumptions using the maximal parabolic regularity theory.Comment: 19 pages, 3 figure

New Biotite and Muscovite Isotopic Reference Materials, USGS57 and USGS58, for δ2H Measurements–A Replacement for NBS 30

The advent of continuous-flow isotope-ratio mass spectrometry (CF-IRMS) coupled with a high temperature conversion (HTC) system enabled faster, more cost effective, and more precise δ2H analysis of hydrogen-bearing solids. Accurate hydrogen isotopic analysis by on-line or off-line techniques requires appropriate isotopic reference materials (RMs). A strategy of two-point calibrations spanning δ2H range of the unknowns using two RMs is recommended. Unfortunately, the supply of the previously widely used isotopic RM, NBS 30 biotite, is exhausted. In addition, recent measurements have shown that the determination of δ2H values of NBS 30 biotite on the VSMOW-SLAP isotope-delta scale by on-line HTC systems with CF-IRMS may be unreliable because hydrogen in this biotite may not be converted quantitatively to molecular hydrogen. The δ2HVSMOW-SLAP values of NBS 30 biotite analyzed by on-line HTC systems can be as much as 21 mUr (or ‰) too positive compared to the accepted value of −65.7 mUr, determined by only a few conventional off-line measurements. To ensure accurate and traceable on-line hydrogen isotope-ratio determinations in mineral samples, we here propose two isotopically homogeneous, hydrous mineral RMs with well-characterized isotope-ratio values, which are urgently needed. The U.S. Geological Survey (USGS) has prepared two such RMs, USGS57 biotite and USGS58 muscovite. The δ2H values were determined by both glassy carbon-based on-line conversion and chromium-based on-line conversion, and results were confirmed by off-line conversion. The quantitative conversion of hydrogen from the two RMs using the on-line HTC method was carefully evaluated in this study. The isotopic compositions of these new RMs with 1-σ uncertainties and mass fractions of hydrogen are: USGS57 (biotite) δ2HVSMOW-SLAP = −91.5 ± 2.4 mUr (n =24) Mass fraction hydrogen = 0.416 ± 0.002% (n=4) Mass fraction water = 3.74 ± 0.02% (n=4) USGS58 (muscovite) δ2HVSMOW-SLAP = −28.4 ± 1.6 mUr (n =24) Mass fraction hydrogen = 0.448 ± 0.002% (n=4) Mass fraction water = 4.03 ± 0.02% (n =4). These δ2HVSMOW-SLAP values encompass typical ranges for solid unknowns of crustal and mantle origin and are available to users for recommended two-point calibration

Organic Reference Materials for Hydrogen, Carbon, and Nitrogen Stable Isotope-Ratio Measurements: Caffeines, n-Alkanes, Fatty Acid Methyl Esters, Glycines, L-Valines, Polyethylenes, and Oils

An international project developed, quality-tested, and determined isotope−δ values of 19 new organic reference materials (RMs) for hydrogen, carbon, and nitrogen stable isotope-ratio measurements, in addition to analyzing pre-existing RMs NBS 22 (oil), IAEA-CH-7 (polyethylene foil), and IAEA-600 (caffeine). These new RMs enable users to normalize measurements of samples to isotope−δ scales. The RMs span a range of δ^2H_(VSMOW-SLAP) values from −210.8 to +397.0 mUr or ‰, for δ^(13)C_(VPDB-LSVEC) from −40.81 to +0.49 mUr and for δ^(15)N_(Air) from −5.21 to +61.53 mUr. Many of the new RMs are amenable to gas and liquid chromatography. The RMs include triads of isotopically contrasting caffeines, C_(16) n-alkanes, n-C_(20)-fatty acid methyl esters (FAMEs), glycines, and L-valines, together with polyethylene powder and string, one n-C_(17)-FAME, a vacuum oil (NBS 22a) to replace NBS 22 oil, and a ^2H-enriched vacuum oil. A total of 11 laboratories from 7 countries used multiple analytical approaches and instrumentation for 2-point isotopic normalization against international primary measurement standards. The use of reference waters in silver tubes allowed direct normalization of δ2H values of organic materials against isotopic reference waters following the principle of identical treatment. Bayesian statistical analysis yielded the mean values reported here. New RMs are numbered from USGS61 through USGS78, in addition to NBS 22a. Because of exchangeable hydrogen, amino acid RMs currently are recommended only for carbon- and nitrogen-isotope measurements. Some amino acids contain ^(13)C and carbon-bound organic ^2H-enrichments at different molecular sites to provide RMs for potential site-specific isotopic analysis in future studies

Isotopic evidence (⁸⁷Sr/⁸⁶Sr, δ⁷Li) for alteration of the oceanic crust at deep-rooted mud volcanoes in the Gulf of Cadiz, NE Atlantic Ocean [(Sr-87/Sr-86, delta Li-7) ]

The chemical and isotopic composition of pore fluids is presented for five deep-rooted mud volcanoes aligned on a transect across the Gulf of Cadiz continental margin at water depths between 350 and 3860 m. Generally decreasing interstitial Li concentrations and Sr-87/Sr-86 ratios with increasing distance from shore are attributed to systematically changing fluid sources across the continental margin. Although highest Li concentrations at the near-shore mud volcanoes coincide with high salinities derived from dissolution of halite and late-stage evaporites, clayey, terrigenous sediments are identified as the ultimate Li source to all pore fluids investigated. Light delta Li-7 values, partly close to those of hydrothermal vent fluids (delta Li-7: +11.9 parts per thousand), indicate that Li has been mobilized during high-temperature fluid/sediment or fluid/rock interactions in the deep sub-surface. Intense leaching of terrigenous clay has led to radiogenic Sr-87/Sr-86 ratios (similar to 0.7106) in pore fluids of the near-shore mud volcanoes. In contrast, non-radiogenic Sr-87/Sr-86 ratios (similar to 0.7075) at the distal locations are attributed to admixing of a basement-derived fluid component, carrying an isotopic signature from interaction with the basaltic crust. This inference is substantiated by temperature constraints from Li isotope equilibrium calculations suggesting exchange processes at particularly high temperatures (>200 degrees C) for the least radiogenic pore fluids of the most distal location.Advective pore fluids in the off-shore reaches of the Gulf of Cadiz are influenced by successive exchange processes with both oceanic crust and terrigenous, fine-grained sediments, resulting in a chemical and isotopic signature similar to that of fluids in near-shore ridge flank hydrothermal systems. This suggests that deep-rooted mud volcanoes in the Gulf of Cadiz represent a fluid pathway intermediate between mid-ocean ridge hydrothermal vent and shallow, marginal cold seep. Due to the thicker sediment coverage and slower fluid advection rates, the overall geochemical signature is shifted towards the sediment-diagenetic signal compared to ridge flank hydrothermal environments. (C) 2009 Elsevier Ltd. All rights reserved

Adjunctive Dexamethasone Affects the Expression of Genes Related to Inflammation, Neurogenesis and Apoptosis in Infant Rat Pneumococcal Meningitis

Streptococcus pneumoniae is the most common pathogen causing non-epidemic bacterial meningitis worldwide. The immune response and inflammatory processes contribute to the pathophysiology. Hence, the anti-inflammatory dexamethasone is advocated as adjuvant treatment although its clinical efficacy remains a question at issue. In experimental models of pneumococcal meningitis, dexamethasone increased neuronal damage in the dentate gyrus. Here, we investigated expressional changes in the hippocampus and cortex at 72 h after infection when dexamethasone was given to infant rats with pneumococcal meningitis. Nursing Wistar rats were intracisternally infected with Streptococcus pneumoniae to induce experimental meningitis or were sham-infected with pyrogen-free saline. Besides antibiotics, animals were either treated with dexamethasone or saline. Expressional changes were assessed by the use of GeneChip® Rat Exon 1.0 ST Arrays and quantitative real-time PCR. Protein levels of brain-derived neurotrophic factor, cytokines and chemokines were evaluated in immunoassays using Luminex xMAP® technology. In infected animals, 213 and 264 genes were significantly regulated by dexamethasone in the hippocampus and cortex respectively. Separately for the cortex and the hippocampus, Gene Ontology analysis identified clusters of biological processes which were assigned to the predefined categories “inflammation”, “growth”, “apoptosis” and others. Dexamethasone affected the expression of genes and protein levels of chemokines reflecting diminished activation of microglia. Dexamethasone-induced changes of genes related to apoptosis suggest the downregulation of the Akt-survival pathway and the induction of caspase-independent apoptosis. Signalling of pro-neurogenic pathways such as transforming growth factor pathway was reduced by dexamethasone resulting in a lack of pro-survival triggers. The anti-inflammatory properties of dexamethasone were observed on gene and protein level in experimental pneumococcal meningitis. Further dexamethasone-induced expressional changes reflect an increase of pro-apoptotic signals and a decrease of pro-neurogenic processes. The findings may help to identify potential mechanisms leading to apoptosis by dexamethasone in experimental pneumococcal meningitis