Speeding up MCMC by Delayed Acceptance and Data Subsampling

The complexity of the Metropolis–Hastings (MH) algorithm arises from the requirement of a likelihood evaluation for the full dataset in each iteration. One solution has been proposed to speed up the algorithm by a delayed acceptance approach where the acceptance decision proceeds in two stages. In the first stage, an estimate of the likelihood based on a random subsample determines if it is likely that the draw will be accepted and, if so, the second stage uses the full data likelihood to decide upon final acceptance. Evaluating the full data likelihood is thus avoided for draws that are unlikely to be accepted. We propose a more precise likelihood estimator that incorporates auxiliary information about the full data likelihood while only operating on a sparse set of the data. We prove that the resulting delayed acceptance MH is more efficient. The caveat of this approach is that the full dataset needs to be evaluated in the second stage. We therefore propose to substitute this evaluation by an estimate and construct a state-dependent approximation thereof to use in the first stage. This results in an algorithm that (i) can use a smaller subsample m by leveraging on recent advances in Pseudo-Marginal MH (PMMH) and (ii) is provably within O(m^{? 2}) of the true posterior.     

Some properties of k-Delaunay and k-Gabriel graphs

We consider two classes of higher order proximity graphs defined on a set of points in the plane, namely, the k-Delaunay graph and the k-Gabriel graph. We give bounds on the following combinatorial and geometric properties of these graphs: spanning ratio, diameter, connectivity, chromatic number, and minimum number of layers necessary to partition the edges of the graphs so that no two edges of the same layer cross.     

Controlled Uptake and Release of Metal Cations by Vanadium Oxide Nanotubes

Vanadium oxide nanotubes (C_n‐VO_x‐NTs) contain α‐monoamines (C_nH_2n+1NH₂ with 4≤n≤22) as templates intercalated between crystalline VO_x layers comprising multilayer tube walls. The present study reveals that a large proportion of the amines can easily be exchanged by metal cations. The tubular morphology is not affected by this reaction, but the distance between the VO_x layers, i.e., 2.8 nm in C₁₂‐VO_xNTs, decreases in the reaction product to 0.9 – 1.2 nm, depending on the metal salt actually applied. Alkali (Na⁺, K⁺), alkaline‐earth (Mg²⁺, Ca²⁺, Sr²⁺), and transition‐metal salts (Fe²⁺, Co²⁺, Ni²⁺, Cu²⁺) have successfully been intercalated. This reaction is partly reversible since intercalated sodium cations can be resubstituted by dodecylamine. This exchange produces again C₁₂‐VO_x‐NTs with the original inter‐layer spacing. However, this release is successful only when sodium is complexed by a crown ether. Under these reaction conditions, even a cyclic uptake and release of Na⁺ and amine, respectively, accompanied by a corresponding shrinkage and widening of the inter‐layer distance, is observed while the tubular structure is widely preserved. Furthermore, a distinct selectivity of the metal‐cation exchange has been observed.     

Thermal Shift Assay as a Tool to Evaluate the Release of Breakdown Peptides from Cowpea β-Vignin during Seed Germination

The present work aimed to characterize the molecular relationships between structure and function of the seed storage protein β-vignin, the vicilin storage protein of cowpea (Vigna unguiculata, l. Walp) seeds. The molecular characterization of β-vignin was carried out firstly by assessing its thermal stability, under different conditions of pH and ionic strength, by thermal shift assay (TSA) using SYPRO Orange fluorescent dye. Secondly, its aggregation propensity was evaluated using a combination of chromatographic and electrophoretic techniques. Two forms of β-vignin were considered: the native form purified from mature quiescent seeds, and a stable breakdown intermediate of 27 kDa produced while seeds germinate. TSA is a useful tool for determining and following over time the structural changes that occur to the protein during germination. The main result was the molecular characterization of the 27 kDa intermediate breakdown polypeptide, which, to the best of our knowledge, has never been described before. β-vignin seems to retain its trimeric conformation despite the evident degradation of its polypeptides.     

pH‐Responsive Pharmacological Chaperones for Rescuing Mutant Glycosidases

A general approach is reported for the design of small‐molecule competitive inhibitors of lysosomal glycosidases programmed to 1) promote correct folding of mutant enzymes at the endoplasmic reticulum, 2) facilitate trafficking, and 3) undergo dissociation and self‐inactivation at the lysosome. The strategy is based on the incorporation of an orthoester segment into iminosugar conjugates to switch the nature of the aglycone moiety from hydrophobic to hydrophilic in the pH 7 to pH 5 window, which has a dramatic effect on the enzyme binding affinity. As a proof of concept, new highly pH‐responsive glycomimetics targeting human glucocerebrosidase or α‐galactosidase with strong potential as pharmacological chaperones for Gaucher or Fabry disease, respectively, were developed.     

Measuring the small-scale power spectrum of cosmic density fluctuations through 21 cm tomography prior to the epoch of structure formation

The thermal evolution of the cosmic gas decoupled from that of the cosmic microwave background (CMB) at a redshift z approximately 200. Afterwards and before the first stars had formed, the cosmic neutral hydrogen absorbed the CMB flux at its resonant 21 cm spin-flip transition. We calculate the evolution of the spin temperature for this transition and the resulting anisotropies that are imprinted on the CMB sky due to linear density fluctuations during this epoch. These anisotropies, at an observed wavelength of 10.56[(1+z)/50] m, contain an amount of information that is orders of magnitude larger than any other cosmological probe.     

Refined shell-model matrix elements for muon-capture processes

Recently many shell-model calculations have been performed in order to extract the value of the ratio C _P/C _A in light nuclei. Most of these calculations fail to reproduce the value given by the partially conserved axial vector hypothesis, roughly 7. We show, that by using the effective transition operators, calculated by the perturbative techniques, this discrepancy can be, at least partly, solved. New angular correlation data for ²⁸Si is used for the extraction of C _P/C _A. In the case of ²⁰Ne, the capture rate data is used for extraction.     

ID29: a high‐intensity highly automated ESRF beamline for macromolecular crystallography experiments exploiting anomalous scattering

ID29 is an ESRF undulator beamline with a routinely accessible energy range of between 20.0 keV and 6.0 keV (λ = 0.62 Å to 2.07 Å) dedicated to the use of anomalous dispersion techniques in macromolecular crystallography. Since the beamline was first commissioned in 2001, ID29 has, in order to provide an improved service to both its academic and proprietary users, been the subject of almost continuous upgrade and refurbishment. It is now also the home to the ESRF Cryobench facility, ID29S. Here, the current status of the beamline is described and plans for its future are briefly outlined.