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

Development of novel routes to pyridines

Pyridines occupy a central part in modern day organic chemistry. Recent studies in various fields of chemistry, biology and physics have featured numerous examples and applications of these compounds. The purpose of this study was to produce a library of polysubstituted pyridines, 2,2'-bipyridines and 2,2':6',2"-terpyridines via pathways that allowed unusual or even unique substitution patterns. To achieve a generic pyridine synthesis that delivers a diversity of products tailored to different industrial needs, a strategy by which the target molecule is constructed in a [2+2+2]-manner was chosen, i.e. the six atoms of the pyridine ring and their pendant functionalities are traced back to three building blocks, each delivering two atoms to the pyridine ring. A range of a-acetoxy-a-chloro-P-keto esters were prepared in three steps from commercially available P-keto esters through a-chlorination with sulfuryl chloride, a-acetoxylation with acetic acid and triethylamine and a second a-chlorination in good overall yields (69 — 89 %) without the need for chromatographic purification. These a-acetoxy-a-chloro-j3-keto esters served as equivalents for a,[3-diketo esters (building block 1) in the synthesis of various 1,2,4- triazines through condensation with picolinohydrazonamides or thiosemicarbazides (building block 2). A subsequent aza Diels-Alder reaction of these 1,2,4-triazines with electron-rich dienophiles (building block 3) such as 2,5-norbornadiene, 1-pyrrolidino- 1 -cyclopentene and 2,3-dihydrofuran furnished an array of novel polysubstitued (bi)pyridines. The two-step sequence of condensation and aza Diels-Alder reaction could be advanced into a 'one-pot' synthesis on several occasions. Furthermore, we devised a feasible synthetic alternative towards a,(3-diketo esters. Alpha-picolinoyl-3-keto esters were prepared from the same starting materials as the a-acetoxy-a¬chloro-P-keto esters in a shortened two-step sequence of a-chlorination of P-keto esters with sulfuryl chloride and replacement of the chloro group by a picolinoyl group using picolinic acid and KHCO3. The overall yields of a-picolinoyl-f3-keto esters (55 — 91 %) were comparable to those of the a-acetoxy-a-chloro-P-keto esters. Copper(II) acetate-facilitated methanolysis of a-picolinoyl-P-keto esters and immediate oxidation of the in situ generated a-hydroxy-P-keto esters by excess copper(II) acetate afforded a,(3-diketo esters which reacted with hydrazonamides in the same manner as the a-chloro-a-acetoxy-P-keto esters. However, in terms of product purity and yield the `chloroacetate route' remains the superior strategy

Lignin dynamics in two13C-labelled arable soils during 18 years

Lignin has long been considered a relatively stable component of soil organic matter. However, recent studies suggest that lignin may turn over within years to decades in arable soil. Here we analyzed lignin concentrations in an 18 year field experiment under continuous silage maize where two soils were sampled at six points in time. Our objectives were to examine the long-term dynamics of (i) lignin derived from a previous C3-vegetation and (ii) lignin derived from maize, as influenced by two levels of maize biomass input. Total lignin concentrations in soil were quantified by gas chromatography of lignin cupric oxide oxidation products. Compound-specific 13C isotope analysis allowed discrimination between C3-derived lignin and maize-derived lignin. Degradation dynamics of C3-derived lignin were independent of biomass input level, suggesting that priming did not affect soil lignin concentrations over almost two decades. After 18 years approximately two thirds of the initial C3-derived lignin remained in the soils, whereas, on average, 10 % of the recent maize-derived lignin input was retained. We suggest that lignin is effectively stabilized in these arable soils, although the mechanisms involved remain unclear

The transverse field Richtmyer-Meshkov instability in magnetohydrodynamics

The magnetohydrodynamic Richtmyer-Meshkov instability is investigated for the case where the initial magnetic field is unperturbed and aligned with the mean interface location. For this initial condition, the magnetic field lines penetrate the perturbed density interface, forbidding a tangential velocity jump and therefore the presence of a vortex sheet. Through simulation, we find that the vorticity distribution present on the interface immediately after the shock acceleration breaks up into waves traveling parallel and anti-parallel to the magnetic field, which transport the vorticity. The interference of these waves as they propagate causes the perturbation amplitude of the interface to oscillate in time. This interface behavior is accurately predicted over a broad range of parameters by an incompressible linearized model derived presently by solving the corresponding impulse driven, linearized initial value problem. Our use of an equilibrium initial condition results in interface motion produced solely by the impulsive acceleration. Nonlinear compressible simulations are used to investigate the behavior of the transverse field magnetohydrodynamic Richtmyer-Meshkov instability, and the performance of the incompressible model, over a range of shock strengths, magnetic field strengths, perturbation amplitudes and Atwood numbers

Pulse-shape discrimination of surface events in CdZnTe detectors for the COBRA experiment

Events near the cathode and anode surfaces of a coplanar grid CdZnTe detector are identifiable by means of the interaction depth information encoded in the signal amplitudes. However, the amplitudes cannot be used to identify events near the lateral surfaces. In this paper a method is described to identify lateral surface events by means of their pulse shapes. Such identification allows for discrimination of surface alpha particle interactions from more penetrating forms of radiation, which is particularly important for rare event searches. The effectiveness of the presented technique in suppressing backgrounds due to alpha contamination in the search for neutrinoless double beta decay with the COBRA experiment is demonstrated.Comment: 15 pages, 13 figure

Comprehensive inter-laboratory calibration of reference materials for δ18O versus VSMOW using various on-line high-temperature conversion techniques

Internationally distributed organic and inorganic oxygen isotopic reference materials have been calibrated by six laboratories carrying out more than 5300 measurements using a variety of high-temperature conversion techniques (HTC) in an evaluation sponsored by the International Union of Pure and Applied Chemistry (IUPAC). To aid in the calibration of these reference materials, which span more than 125‰, an artificially enriched reference water (δ18O of +78.91‰) and two barium sulfates (one depleted and one enriched in 18O) were prepared and calibrated relative to VSMOW2 and SLAP reference waters. These materials were used to calibrate the other isotopic reference materials in this study. The seemingly large estimated combined uncertainties arise from differences in instrumentation and methodology and difficulty in accounting for all measurement bias. They are composed of the 3-fold standard errors directly calculated from the measurements and provision for systematic errors discussed in this paper. A primary conclusion of this study is that nitrate samples analyzed for δ18O should be analyzed with internationally distributed isotopic nitrates, and likewise for sulfates and organics. Authors reporting relative differences of oxygen-isotope ratios (δ18O) of nitrates, sulfates, or organic material should explicitly state in their reports the δ18O values of two or more internationally distributed nitrates (USGS34, IAEA-NO-3, and USGS35), sulfates (IAEA-SO-5, IAEA-SO-6, and NBS 127), or organic material (IAEA-601 benzoic acid, IAEA-602 benzoic acid, and IAEA-600 caffeine), as appropriate to the material being analyzed, had these reference materials been analyzed with unknowns. This procedure ensures that readers will be able to normalize the δ18O values at a later time should it become necessary. The high-temperature reduction technique for analyzing δ18O and δ2H is not as widely applicable as the well-established combustion technique for carbon and nitrogen stable isotope determination. To obtain the most reliable stable isotope data, materials should be treated in an identical fashion; within the same sequence of analyses, samples should be compared with working reference materials that are as similar in nature and in isotopic composition as feasible.

Deciphering the growth behaviour of Mycobacterium africanum.

BACKGROUND: Human tuberculosis (TB) in West Africa is not only caused by M. tuberculosis but also by bacteria of the two lineages of M. africanum. For instance, in The Gambia, 40% of TB is due to infections with M. africanum West African 2. This bacterial lineage is associated with HIV infection, reduced ESAT-6 immunogenicity and slower progression to active disease. Although these characteristics suggest an attenuated phenotype of M. africanum, no underlying mechanism has been described. From the first descriptions of M. africanum in the literature in 1969, the time to a positive culture of M. africanum on solid medium was known to be longer than the time to a positive culture of M. tuberculosis. However, the delayed growth of M. africanum, which may correlate with the less virulent phenotype in the human host, has not previously been studied in detail. METHODOLOGY/PRINCIPAL FINDINGS: We compared the growth rates of M. tuberculosis and M. africanum isolates from The Gambia in two liquid culture systems. M. africanum grows significantly slower than M. tuberculosis, not only when grown directly from sputa, but also in growth experiments under defined laboratory conditions. We also sequenced four M. africanum isolates and compared their whole genomes with the published M. tuberculosis H37Rv genome. M. africanum strains have several non-synonymous SNPs or frameshift mutations in genes that were previously associated with growth-attenuation. M. africanum strains also have a higher mutation frequency in genes crucial for transport of sulphur, ions and lipids/fatty acids across the cell membrane into the bacterial cell. Surprisingly, 5 of 7 operons, recently described as essential for intracellular survival of H37Rv in the host macrophage, showed at least one non-synonymously mutated gene in M. africanum. CONCLUSIONS/SIGNIFICANCE: The altered growth behaviour of M. africanum might indicate a different survival strategy within host cells

The role of histone H3.3 lysine 4 and lysine 36 residues in mouse embryonic stem cells and neuronal development

Numerous mutations in histone H3 lysine 4 (H3K4) and H3 lysine 36 (H3K36) modifying enzymes have been reported in human disease, yet the role of the H3K4 and H3K36 residues in mammals remain unclear due to the clustered arrays of many histone genes. Replication-dependent canonical H3 (H3.1/H3.2) exists as multiple gene copies and supplies nucleosomes for packaging of newly synthesized DNA during replication. The histone variant H3.3 differs from canonical H3 by only 4 to 5 amino acids, which allow nucleosome assembly independent of DNA replication throughout the cell cycle and in post-mitotic cells. In this study, I set out to investigate the role of the K4 and K36 residues in the histone H3.3 variant, which is enriched at active regions of the mammalian genome and encoded by two isolated genes; therefore amenable to functional analysis. Using CRISPR-Cas9, I mutated the K4 or K36 residue of endogenous H3.3 to unmodifable alanine (A) in mouse embryonic stem cells (ESCs) and revealed that the K4A mutation, but not K36A, resulted in widespread gene expression changes and impairment of neuronal differentiation into glutamatergic neurons. Furthermore, K4A resulted in significant H3.3 protein depletion at transcription start sites and active enhancers of ESCs - without effects at other sites. Genomic regions depleted of H3.3K4A showed concerted alterations of histone modifications (decreased K27 acetylation and increased K4 methylation) regardless of gene expression changes. In differentiated neurons, the K4A mutation impacted protein stability and resulted in widespread proteasomal degradation of the mutant histone. Thus, H3.3K4 is required for site-specific nucleosome maintenance at regulatory regions, histone stability and cellular differentiation of ESCs. H3.3K36 is not required for H3.3 deposition and turnover inside coding regions, and the K36A mutation affected gene expression at later stages of neurodevelopment. Furthermore, the K36A mutation globally depleted H3K36 di-metylation levels in ESCs, which resulted in a spread of the repressive mark H3K27me3, suggesting that H3K36 di-methylation is required to restrict the activity of PRC2. This study demonstrates a direct link between a specific histone residue (H3K4) and histone maintenance at promoters and enhancers, and that H3.3 provides a platform for analyzing the role of histone residues in mammals