Complexity Analysis of Accelerated MCMC Methods for Bayesian Inversion

We study Bayesian inversion for a model elliptic PDE with unknown diffusion coefficient. We provide complexity analyses of several Markov Chain-Monte Carlo (MCMC) methods for the efficient numerical evaluation of expectations under the Bayesian posterior distribution, given data $\delta$. Particular attention is given to bounds on the overall work required to achieve a prescribed error level $\varepsilon$. Specifically, we first bound the computational complexity of "plain" MCMC, based on combining MCMC sampling with linear complexity multilevel solvers for elliptic PDE. Our (new) work versus accuracy bounds show that the complexity of this approach can be quite prohibitive. Two strategies for reducing the computational complexity are then proposed and analyzed: first, a sparse, parametric and deterministic generalized polynomial chaos (gpc) "surrogate" representation of the forward response map of the PDE over the entire parameter space, and, second, a novel Multi-Level Markov Chain Monte Carlo (MLMCMC) strategy which utilizes sampling from a multilevel discretization of the posterior and of the forward PDE. For both of these strategies we derive asymptotic bounds on work versus accuracy, and hence asymptotic bounds on the computational complexity of the algorithms. In particular we provide sufficient conditions on the regularity of the unknown coefficients of the PDE, and on the approximation methods used, in order for the accelerations of MCMC resulting from these strategies to lead to complexity reductions over "plain" MCMC algorithms for Bayesian inversion of PDEs.

Redox Modulation at Work: Natural Phytoprotective Polysulfanes From Alliums Based on Redox-Active Sulfur

Purpose of review: This article provides a brief overview of natural phytoprotective products of allium with a special focus on the therapeutic potential of diallyl polysulfanes from garlic, their molecular targets and their fate in the living organisms. A comprehensive overview of antimicrobial and anticancer properties of published literature is presented for the reader to understand the effective concentrations of polysulfanes and their sensitivity towards different human pathogenic microbes, fungi, and cancer cell lines. Recent findings: The article finds polysulfanes potentials as new generation novel antibiotics and chemo preventive agent. The effective dose rates of polysulfanes for antimicrobial properties are in the range of 0.5–40 mg/L and for anticancer 20–100 μM. The molecular targets for these redox modulators are mainly cellular thiols as well as inhibition and/or activation of certain cellular proteins in cancer cell lines. Summary: Antimicrobial and anticancer activities of polysulfanes published in the literature indicate that with further development, they could be promising candidates for cancer prevention due to their selectivity towards abnormal cells

Genetic determinants of risk in pulmonary arterial hypertension: international genome-wide association studies and meta-analysis

Background Rare genetic variants cause pulmonary arterial hypertension, but the contribution of common genetic variation to disease risk and natural history is poorly characterised. We tested for genome-wide association for pulmonary arterial hypertension in large international cohorts and assessed the contribution of associated regions to outcomes. Methods We did two separate genome-wide association studies (GWAS) and a meta-analysis of pulmonary arterial hypertension. These GWAS used data from four international case-control studies across 11744 individuals with European ancestry (including 2085 patients). One GWAS used genotypes from 5895 whole-genome sequences and the other GWAS used genotyping array data from an additional 5849 individuals. Cross-validation of loci reaching genome-wide significance was sought by meta-analysis. Conditional analysis corrected for the most significant variants at each locus was used to resolve signals for multiple associations. We functionally annotated associated variants and tested associations with duration of survival. All-cause mortality was the primary endpoint in survival analyses. Findings A locus near SOX17 (rs10103692, odds ratio 1·80 [95% CI 1·55–2·08], p=5·13×10– ¹⁵) and a second locus in HLA-DPA1 and HLA-DPB1 (collectively referred to as HLA-DPA1/DPB1 here; rs2856830, 1·56 [1·42–1·71], p=7·65×10– ²⁰) within the class II MHC region were associated with pulmonary arterial hypertension. The SOX17 locus had two independent signals associated with pulmonary arterial hypertension (rs13266183, 1·36 [1·25–1·48], p=1·69×10– ¹²; and rs10103692). Functional and epigenomic data indicate that the risk variants near SOX17 alter gene regulation via an enhancer active in endothelial cells. Pulmonary arterial hypertension risk variants determined haplotype-specific enhancer activity, and CRISPR-mediated inhibition of the enhancer reduced SOX17 expression. The HLA-DPA1/DPB1 rs2856830 genotype was strongly associated with survival. Median survival from diagnosis in patients with pulmonary arterial hypertension with the C/C homozygous genotype was double (13·50 years [95% CI 12·07 to >13·50]) that of those with the T/T genotype (6·97 years [6·02–8·05]), despite similar baseline disease severity. Interpretation This is the first study to report that common genetic variation at loci in an enhancer near SOX17 and in HLA-DPA1/DPB1 is associated with pulmonary arterial hypertension. Impairment of SOX17 function might be more common in pulmonary arterial hypertension than suggested by rare mutations in SOX17. Further studies are needed to confirm the association between HLA typing or rs2856830 genotyping and survival, and to determine whether HLA typing or rs2856830 genotyping improves risk stratification in clinical practice or trials. Funding UK NIHR, BHF, UK MRC, Dinosaur Trust, NIH/NHLBI, ERS, EMBO, Wellcome Trust, EU, AHA, ACClinPharm, Netherlands CVRI, Dutch Heart Foundation, Dutch Federation of UMC, Netherlands OHRD and RNAS, German DFG, German BMBF, APH Paris, INSERM, Université Paris-Sud, and French ANR

Material properties and RF applications of high k and ferrite LTCC ceramics

\u3cp\u3eThe continuous trend in modern electronic applications towards smaller size, higher integration density and enhanced functionality requires new materials, which allow embedding passive functions into the substrate. In this paper an LTCC material system with specialized dielectric and magnetic LTCC tapes cofireable in a low-shrinkage process for RF-passive integration is reported. An LTCC dielectric with a dielectric constant of up to 80 is presented. The material is successfully used in a cofired multi-material stack to realize a fully integrated band-pass filter for Bluetooth applications of 1.3 mm\u3csup\u3e3\u3c/sup\u3e volume. A ferroelectric LTCC ceramic with a maximum dielectric constant of 3000 is presented and the reduction of the dielectric constant to a maximum value of 1100 under constrained-sintering is discussed. Magnetic permeabilities of 14 for a NiZnCo-ferrite and 3.5 for a Ba\u3csub\u3e3\u3c/sub\u3eCo \u3csub\u3e2\u3c/sub\u3eFe\u3csub\u3e24\u3c/sub\u3eO\u3csub\u3e41\u3c/sub\u3e (Co\u3csub\u3e2\u3c/sub\u3eZ) ferrite have been realized under LTCC processing conditions, with gyromagnetic resonance frequencies above 1 GHz and 3 GHz respectively. The permeability of these materials is determined for constrained and unconstrained sintering conditions. A maximum absorption of 27 dB/cm and 30 dB/cm is measured for an embedded stripline in NiZnCo- and Co\u3csub\u3e2\u3c/sub\u3eZ ferrite respectively. Two-winding planar RF-chokes in different multi-layer stacks are compared. A maximum of 14.3 nH inductance is realized for a 1.8 mm × 2 mm coil in an LTCC research pilot line.\u3c/p\u3