Robust Dynamics and Control of a Partially Observed Markov Chain

In a seminal paper, Martin Clark (Communications Systems and Random Process Theory, Darlington, 1977, pp. 721–734, 1978) showed how the filtered dynamics giving the optimal estimate of a Markov chain observed in Gaussian noise can be expressed using an ordinary differential equation. These results offer substantial benefits in filtering and in control, often simplifying the analysis and an in some settings providing numerical benefits, see, for example Malcolm et al. (J. Appl. Math. Stoch. Anal., 2007, to appear). Clark’s method uses a gauge transformation and, in effect, solves the Wonham-Zakai equation using variation of constants. In this article, we consider the optimal control of a partially observed Markov chain. This problem is discussed in Elliott et al. (Hidden Markov Models Estimation and Control, Applications of Mathematics Series, vol. 29, 1995). The innovation in our results is that the robust dynamics of Clark are used to compute forward in time dynamics for a simplified adjoint process. A stochastic minimum principle is established.     

Raman spectroscopy of acoustic phonons in periodic and Fibonacci superlattices

Results of Raman scattering experiments on (a) periodic superlattices made up of GaAs/In_xGa_1−xAs layers with high indium concentrations, (b) GaAs/Ga_1−xAl_xAs Fibonacci superlattices, are presented. We discuss the observed peak positions and intensities using the continuum theory of acoustic wave propagation in layered media and the photo-elastic coupling model.     

Self-assembly of nanoparticles on the surface of ionic crystals: Structural properties

With a suitable combination of ligand-stabilised nanoparticle suspension and ionic salt solutions, it is possible to produce microcrystals that are coated with nanoparticles. The self-assembly process of coating microcrystals by gold nanoparticles (NP) is mediated by the crystal lattice. This is the so-called CLAMS process - a generic process for self-organisation of nanoparticles on the surface of crystals [M. Murugeshan, D. Cunningham, J.-L. Martnez-Albertos, R. Vrcelj, B.D. Moore, Chem. Commun. (2005) 2677]. We are exploring here the structural properties of these self-assembled structures by using different imaging techniques.     

Equivalence of Toda-Hopf invariants

In this paper it is shown that various existing constructions of ‘Hopf invariant’ are equivalent to each other. In consequence one gets that the oneToda-Hopf invariant enjoys various properties. Both authors supported in part by the NSF.     

Development and validation of a Monte Carlo simulation of photon transport in an Anger camera

The geometric component of the point spread function (PSF) of a gamma camera collimator can be determined analytically, and the penetration component can be calculated readily by numerical ray-tracing. A Monte Carlo simulation of photon transport which includes collimator scatter is developed. The simulation was implemented with an array processor which propagates up to 1024 photons in parallel, allowing accurate estimates of the total radial PSF in less than a day. The simulation was tested by imaging monoenergetic point sources of Tc-99m, Cr-51, and Sr-85 (140, 320, and 514 keV, respectively) on a General Electric Star Cam with low-energy, general-purpose, and medium-energy collimators. Comparisons of measured and simulated PSFs demonstrate the validity of the model and the significance of collimator scatter in the degradation of image quality.     

Optimization of a portable microanalytical system to reduce electrode fouling from proteins associated with biomonitoring of lead (Pb) in saliva

There is a need to develop reliable portable analytical systems for on-site and real-time biomonitoring of lead (Pb) from both occupational and environmental exposures. Saliva is an appealing matrix since it is easily obtainable, and therefore a potential substitute for blood due to existing reasonably good correlation between Pb levels in blood and saliva. The microanalytical system is based on flow-injection/stripping voltammetry with a wall-jet (flow-onto) microelectrochemical cell. Samples that contain as little as 1% saliva can cause electrode fouling, resulting in significantly reduced responsiveness and irreproducible quantitations. In addition, incomplete Pb release from salivary protein can also yield a lower Pb response than expected. This paper evaluates the extent of in vitro Pb-protein binding and the optimal pretreatment for releasing Pb from the saliva samples. Even in 50% by volume of rat saliva, the electrode fouling was not observed, due to the appropriate sample pretreatment and the constant flow of the sample and acidic carrier that prevented passivation by the protein. The system offered a linear response over a low Pb range of 1-10 ppb, low detection limit of 1 ppb, excellent reproducibility, and reliability. It also yielded the same Pb concentrations in unknown samples as did the ICP-MS. These encouraging results suggest that the microanalytical system represents an important analytical advancement for real-time non-invasive biomonitoring of Pb.     

PHOTOLYTIC REARRANGEMENT OF METRONIDAZOLE TO 1-HYDROXYETHYL-2-METHYL-4-HYDROXYIMINO-5-OXO-IMIDAZOLE AND THE FORMATION OF COPPER COMPLEXES OF THESE COMPOUNDS

Abstract— A labile intermediate in the photolytic rearrangement of the antibacterial drug, metronidazole, was identified by isolating the product of photolysis of metronidazole benzoate in methanol. The intermediate, 1-hydroxyethyl-2-methyl-4-hydroxyimino-5-oxo-imidazole, was shown to act as a bidentate chelating agent for copper(II) ions, whereas metronidazole forms a weak monodentate complex. The intermediate may be relevant to the bioactivation mechanism of metronidazole.     

Transient masking and the temporal course of simultaneous tone-on-tone masking

Previous studies have shown that threshold for a signal in tone-on-tone simultaneous masking is sometimes lower when the masker is continuous than when it is gated. Threshold may also decline as signal onset is delayed relative to the onset of a longer duration masker, though it may increase again near masker offset. In the present study, the level of a 1250-Hz sinusoidal masker was found which would just mask a 20-ms, 1000-Hz sinusoid presented at 10-dB sensation level (SL). Masker duration was 20 or 400 ms; in the latter case, the signal was presented in one of three temporal positions within the masker. The level of the 1250-Hz masker necessary to mask the signal was reduced, sometimes by as much as 20-25 dB, by a 20-ms, 500-Hz sinusoid (transient masker) presented at the times when the signal might occur, but at a level 30 dB below that at which it would mask the 10-dB SL signal. This suggests that, in the earlier studies, at least some of the elevation in threshold in the presence of a short-duration masker or at the beginning (or end) of a longer duration masker may have been due to the transient responses to the masker affecting detection of the signal, but not necessarily masking the signal in terms of excitation in the signal "channel."