Generalized Direct Sampling for Hierarchical Bayesian Models

We develop a new method to sample from posterior distributions in hierarchical models without using Markov chain Monte Carlo. This method, which is a variant of importance sampling ideas, is generally applicable to high-dimensional models involving large data sets. Samples are independent, so they can be collected in parallel, and we do not need to be concerned with issues like chain convergence and autocorrelation. Additionally, the method can be used to compute marginal likelihoods

Scalable Rejection Sampling for Bayesian Hierarchical Models

Bayesian hierarchical modeling is a popular approach to capturing unobserved heterogeneity across individual units. However, standard estimation methods such as Markov chain Monte Carlo (MCMC) can be impracticable for modeling outcomes from a large number of units. We develop a new method to sample from posterior distributions of Bayesian models, without using MCMC. Samples are independent, so they can be collected in parallel, and we do not need to be concerned with issues like chain convergence and autocorrelation. The algorithm is scalable under the weak assumption that individual units are conditionally independent, making it applicable for large datasets. It can also be used to compute marginal likelihoods

Dense ceramic cathodes for lithium and sodium batteries

Electrodeposition of dense ceramic electrode materials has the potential to enhance secondary battery performance and mechanics, and broaden the scope of available electrode form factors. I will present our work on the electrodeposition of high performance LiCoO2, NaCoO2, LiMn2O4, and Al-doped LiCoO2-based Na and Li-ion cathodes as well as related materials. The electrolytically active materials were formed as solid films, with densities as high as 95%, and in thicknesses as great as 200 µm. The capacities are near-theoretical and the crystallinities and electrochemical capacities are comparable to powders synthesized at much higher temperatures. By using electrodeposition to grow the materials, the growth temperature was reduced from 700-1000 °C, the typical temperature for the solid-state synthesis of most cathode materials to 200-300 °C, which both enabled the direct growth of the nearly solid cathode on a metal current collector, and reduces the overall energy input required to grow the cathodes. We also find the electrodeposited films can be high textured, and in some cases, the crystals can be oriented such that the fast ion and electron diffusion pathways are normal to the substrate, which results in electrodes with unexpectedly good rate performances. Please click Additional Files below to see the full abstract

Porcine pancreatic α-amylase hydrolysis of modified substrates and the specificity of subsite binding

The effect of substrate modification on the action of PPA has been determined for five (alpha)-(1(---\u3e)4)-glucans in which a small proportion of the glucose residues (15% or less) contained modified functional groups. Chemical and enzymatic techniques were used to synthesize four substrates (6-deoxyamylose, mono-6-deoxy-6-fluoro-(beta)-cyclodextrin, mono-2-deoxy-(beta)-cyclodextrin, and amylose containing D-allose residues) in which hydrogen bond-forming capabilities were altered or removed. Hydrolysis of these substrates by PPA produced two isomers of modified disaccharides and modified monosaccharide. These results indicate that modifications of this type may be productively bound at subsites 1 through 4 of the five-subsite active site. Evidence for productive binding at subsite 5 was also obtained for substrates containing D-allose and 2-deoxy-D-glucose. For each of these modified substrates, formation of the modified disaccharide substituted in the nonreducing residue is favored over formation of the disaccharide substituted in the reducing residue, suggesting that modified residues are bound less readily than D-glucose at subsite 3, the subsite where catalytic attack occurs. Kinetic data for 2-deoxy-oligosaccharides indicated that PPA hydrolysis of glucosidic linkages of 2-deoxy-D-glucose is slower than enzymolysis of normal glucosidic bonds. A modified glycogen which contained 2-amino-2-deoxy-D-glucose was also hydrolyzed by PPA. This reaction produced no modified monosaccharide, a single disaccharide in the nonreducing residue, two trisaccharides modified in the nonreducing and middle residues, and larger products. Analysis of the substituted products indicated that 2-amino-2-deoxy-D-glucose may be productively bound at subsites 1, 2, 4, and 5, but not at subsite 3. These results are compared with data obtained from other modified PPA substrates and interpreted in terms of the enzyme-substrate binding requirements

Three-dimensional single gyroid photonic crystals with a mid-infrared bandgap

A gyroid structure is a distinct morphology that is triply periodic and consists of minimal isosurfaces containing no straight lines. We have designed and synthesized amorphous silicon (a-Si) mid-infrared gyroid photonic crystals that exhibit a complete bandgap in infrared spectroscopy measurements. Photonic crystals were synthesized by deposition of a-Si/Al2O3 coatings onto a sacrificial polymer scaffold defined by two-photon lithography. We observed a 100% reflectance at 7.5 \mum for single gyroids with a unit cell size of 4.5 \mum, in agreement with the photonic bandgap position predicted from full-wave electromagnetic simulations, whereas the observed reflection peak shifted to 8 um for a 5.5 \mum unit cell size. This approach represents a simulation-fabrication-characterization platform to realize three-dimensional gyroid photonic crystals with well-defined dimensions in real space and tailored properties in momentum space

First passage times in integrate-and-fire neurons with stochastic thresholds

We consider a leaky integrate--and--fire neuron with deterministic subthreshold dynamics and a firing threshold that evolves as an Ornstein-Uhlenbeck process. The formulation of this minimal model is motivated by the experimentally observed widespread variation of neural firing thresholds. We show numerically that the mean first passage time can depend non-monotonically on the noise amplitude. For sufficiently large values of the correlation time of the stochastic threshold the mean first passage time is maximal for non-vanishing noise. We provide an explanation for this effect by analytically transforming the original model into a first passage time problem for Brownian motion. This transformation also allows for a perturbative calculation of the first passage time histograms. In turn this provides quantitative insights into the mechanisms that lead to the non-monotonic behaviour of the mean first passage time. The perturbation expansion is in excellent agreement with direct numerical simulations. The approach developed here can be applied to any deterministic subthreshold dynamics and any Gauss-Markov processes for the firing threshold. This opens up the possibility to incorporate biophysically detailed components into the subthreshold dynamics, rendering our approach a powerful framework that sits between traditional integrate-and-fire models and complex mechanistic descriptions of neural dynamics

Enriched surface acidity for surfactant-free suspensions of carboxylated carbon nanotubes purified by centrifugation

AbstractIt is well known that surfactant-suspended carbon nanotube (CNT) samples can be purified by centrifugation to decrease agglomerates and increase individually-dispersed CNTs. However, centrifugation is not always part of protocols to prepare CNT samples used in biomedical applications. Herein, using carboxylated multi-walled CNTs (cMWCNTs) suspended in water without a surfactant, we developed a Boehm titrimetric method for the analysis of centrifuged cMWCNT suspensions and used it to show that the surface acidity of oxidized carbon materials in aqueous cMWCNT suspensions was enriched by ∼40% by a single low-speed centrifugation step. This significant difference in surface acidity between un-centrifuged and centrifuged cMWCNT suspensions has not been previously appreciated and is important because the degree of surface acidity is known to affect the interactions of cMWCNTs with biological systems