Algorithms for Kullback-Leibler Approximation of Probability Measures in Infinite Dimensions

In this paper we study algorithms to find a Gaussian approximation to a target measure defined on a Hilbert space of functions; the target measure itself is defined via its density with respect to a reference Gaussian measure. We employ the Kullback-Leibler divergence as a distance and find the best Gaussian approximation by minimizing this distance. It then follows that the approximate Gaussian must be equivalent to the Gaussian reference measure, defining a natural function space setting for the underlying calculus of variations problem. We introduce a computational algorithm which is well-adapted to the required minimization, seeking to find the mean as a function, and parameterizing the covariance in two different ways: through low rank perturbations of the reference covariance; and through Schr\"odinger potential perturbations of the inverse reference covariance. Two applications are shown: to a nonlinear inverse problem in elliptic PDEs, and to a conditioned diffusion process. We also show how the Gaussian approximations we obtain may be used to produce improved pCN-MCMC methods which are not only well-adapted to the high-dimensional setting, but also behave well with respect to small observational noise (resp. small temperatures) in the inverse problem (resp. conditioned diffusion).Comment: 28 page

Sonochemically fabricated microelectrode arrays for biosensors. Part II. Modification with a polysiloxane coating

A polymer modified sonochemically fabricated glucose oxidase microelectrode array with microelectrode population densities of up to 2.5 x 105 microelectrodes cm-2 is reported. These microelectrode sensors were formed by first depositing an insulating film on commercial screen printed electrodes which was subsequently sonicated to form cavities of regular sizes in the film. Electropolymerisation of aniline at the microelectrode cavities formed polyaniline protrusions containing entrapped glucose oxidase. Chemical deposition of polysiloxane from dichlorodimethysilane was used to deposit a thin protective and diffusion mass transport controlling coating over the electrodes. The physical and electrochemical properties of these films were studied. The performance of the final glucose oxidase based microelectrode sensor array is reported

Flexible Ultrathin PolyDVB/EVB Composite Membranes for the Optimization of a Whole Blood Glucose Sensor.

An ultrathin composite membrane has been developed as the outer covering barrier in a model amperometric glucose oxidase enzyme electrode. The membrane was formed by cathodic electropolymerization of divinylbenzene/ethylvinylbenzene at the surface of a gold coated polyester support membrane. Permeability coefficients were determined for O2 and glucose across membranes with a range of polymer thicknesses. Anionic interferents (such as ascorbate), were screened from the working electrode via a charge exclusion mechanism. The enzyme electrode showed an initial 10% signal drift when first exposed to whole human blood over a period of 2 hours, after which responses remained essentially stable. Whole blood patient glucose determinations yielded a correlation coefficient of r2=0.99 compared to standard hospital analyses

A Function Space HMC Algorithm With Second Order Langevin Diffusion Limit

We describe a new MCMC method optimized for the sampling of probability measures on Hilbert space which have a density with respect to a Gaussian; such measures arise in the Bayesian approach to inverse problems, and in conditioned diffusions. Our algorithm is based on two key design principles: (i) algorithms which are well-defined in infinite dimensions result in methods which do not suffer from the curse of dimensionality when they are applied to approximations of the infinite dimensional target measure on \bbR^N; (ii) non-reversible algorithms can have better mixing properties compared to their reversible counterparts. The method we introduce is based on the hybrid Monte Carlo algorithm, tailored to incorporate these two design principles. The main result of this paper states that the new algorithm, appropriately rescaled, converges weakly to a second order Langevin diffusion on Hilbert space; as a consequence the algorithm explores the approximate target measures on \bbR^N in a number of steps which is independent of $N$. We also present the underlying theory for the limiting non-reversible diffusion on Hilbert space, including characterization of the invariant measure, and we describe numerical simulations demonstrating that the proposed method has favourable mixing properties as an MCMC algorithm.Comment: 41 pages, 2 figures. This is the final version, with more comments and an extra appendix adde

Electrochemical detection of TNT at cobalt phthalocyanine mediated screen-printed electrodes and application to detection of airborne vapours

We describe the use of cobalt phthalocyanine as a mediator to improve the sensitivity for the electrochemical detection of TNT. Commercial screen-printed electrodes containing cobalt phthalocyanine were employed for determination of TNT. Improved sensitivities compared to screen-printed carbon electrodes without phthalocyanine were observed, current response for cyclic voltammetric measurements at modified electrodes being at least double that of unmodified electrodes. A synergistic effect between oxygen and TNT reduction was also observed. Correlation between TNT concentrations and sensor output was observed between 0–200 µM TNT. Initial proof-of-concept experiments combining electrochemical determinations, with the use of an air-sampling cyclone, are also reported

Differential Tissue Response to Growth Hormone in Mice

Growth hormone (GH) has been shown to act directly on multiple tissues throughout the body. Historically, it was believed that GH acted directly in the liver and only indirectly in other tissues via insulin‐like growth hormone 1 (IGF‐1). Despite extensive work to describe GH action in individual tissues, a comparative analysis of acute GH signaling in key metabolic tissues has not been performed. Herein, we address this knowledge gap. Acute tissue response to human recombinant GH was assessed in mice by measuring signaling via phospho‐STAT5 immunoblotting. STAT5 activation is an easily and reliably detected early marker of GH receptor engagement. We found differential tissue sensitivities; liver and kidney were equally GH‐sensitive and more sensitive than white adipose tissue, heart, and muscle (gastrocnemius). Gastrocnemius had the greatest maximal response compared to heart, liver, white adipose tissue, and whole kidney. Differences in maximum responsiveness were positively correlated with tissue STAT5 abundance, while differences in sensitivity were not explained by differences in GH receptor levels. Thus, GH sensitivity and responsiveness of distinct metabolic tissues differ and may impact physiology and disease

A Hybrid Compressive Approach to Noise Source Visualization: Application to a Diesel Engine

To identify sound source locations by using Fourier-based Near-field Acoustical Holography (NAH), a large number of microphone measurements is generally required to span the source region and ensure a sufficiently high spatial sampling rate. As a result, such measurements are costly, a fact which has discouraged the industrial application of NAH to identify sound source locations. However, recently, compressive sensing approaches have made it feasible to identify concentrated sound sources with a limited number of microphone measurements. In the present work, sound radiation from the front face of a diesel engine was measured by using one set of measurements from a 35-channel combo-array. The locations of significant noise sources were then identified by using three compressive sensing algorithms: Wideband Acoustical Holography (WBH), l1-norm minimization, and a hybrid approach which combined WBH and l1-norm minimization. The latter approach takes advantage of the l1’ norm’s ability to locate spatially distinct sources, and WBH’s ability to suppress “ghost” sources. It was found that the hybrid algorithm can localize and visualize the major noise sources over a broad range of frequencies, even though using a relatively small number of microphones. Finally, comments are made regarding sound field reconstruction differences between the algorithms

Diesel Engine Noise Source Visualization with Wideband Acoustical Holography

Wideband Acoustical Holography (WBH), which is a monopole-based, equivalent source procedure (J. Hald, “Wideband Acoustical Holography,” INTER-NOISE 2014), has proven to offer accurate noise source visualization results in experiments with a simple noise source: e.g., a loudspeaker (T. Shi, Y. Liu, J.S. Bolton, ”The Use of Wideband Holography for Noise Source Visualization”, NOISECON 2016). From a previous study, it was found that the advantage of this procedure is the ability to optimize the solution in the case of an under-determined system: i.e., when the number of measurements is much smaller than the number of parameters that must be estimated in the model. In the present work, a diesel engine noise source was measured by using one set of measurements from a thirty-five channel combo-array placed in front of the engine. The noise source distribution was reconstructed at the front face of diesel engine and it was possible to successfully localize and visualize the major noise sources over a broad range of frequencies, even when using a relatively small number of microphones, as in this case