Bayesian analysis of the scatterometer wind retrieval inverse problem:Some new approaches

The retrieval of wind vectors from satellite scatterometer observations is a non-linear inverse problem. A common approach to solving inverse problems is to adopt a Bayesian framework and to infer the posterior distribution of the parameters of interest given the observations by using a likelihood model relating the observations to the parameters, and a prior distribution over the parameters. We show how Gaussian process priors can be used efficiently with a variety of likelihood models, using local forward (observation) models and direct inverse models for the scatterometer. We present an enhanced Markov chain Monte Carlo method to sample from the resulting multimodal posterior distribution. We go on to show how the computational complexity of the inference can be controlled by using a sparse, sequential Bayes algorithm for estimation with Gaussian processes. This helps to overcome the most serious barrier to the use of probabilistic, Gaussian process methods in remote sensing inverse problems, which is the prohibitively large size of the data sets. We contrast the sampling results with the approximations that are found by using the sparse, sequential Bayes algorithm.

Typical performance of generalised vector channels

We introduce a general matrix formulation for multiuser channels and analyse the special cases of Multiple-Input Multiple-Output channels, channels with interference and relay arrays under LDPC coding using methods developed for the statistical mechanics of disordered systems. We use the replica method to provide results for the typical overlaps of the original and recovered messages and discuss their implications. The results obtained are consistent with belief propagation and density evolution results but also complement them giving additional insights into the information dynamics of these channels with unexpected effects in some cases.

Brain mechanisms of altered consciousness in generalised seizures

In spite of the inherent difficulties in achieving a biologically meaningful definition of consciousness, recent neurophysiological studies are starting to provide some insight in fundamental mechanisms associated with impaired consciousness in neurological disorders. Generalised seizures are associated with disruption of the default state network, a functional network of discrete brain areas, which include the fronto-parietal cortices. Subcortical contribution through activation of thalamocortical structures, as well as striate nuclei are also crucial to produce impaired consciousness in generalised seizures.

A method of fundamental solutions for the one-dimensional inverse Stefan problem

We investigate an application of the method of fundamental solutions (MFS) to the one-dimensional inverse Stefan problem for the heat equation by extending the MFS proposed in [5] for the one-dimensional direct Stefan problem. The sources are placed outside the space domain of interest and in the time interval (-T, T). Theoretical properties of the method, as well as numerical investigations, are included, showing that accurate and stable results can be obtained efficiently with small computational cost.

Numerical approximation of the one-dimensional inverse Cauchy–Stefan problem using a method of fundamental solutions

We investigate an application of the method of fundamental solutions (MFS) to the one-dimensional parabolic inverse Cauchy–Stefan problem, where boundary data and the initial condition are to be determined from the Cauchy data prescribed on a given moving interface. In [B.T. Johansson, D. Lesnic, and T. Reeve, A method of fundamental solutions for the one-dimensional inverse Stefan Problem, Appl. Math Model. 35 (2011), pp. 4367–4378], the inverse Stefan problem was considered, where only the boundary data is to be reconstructed on the fixed boundary. We extend the MFS proposed in Johansson et al. (2011) and show that the initial condition can also be simultaneously recovered, i.e. the MFS is appropriate for the inverse Cauchy-Stefan problem. Theoretical properties of the method, as well as numerical investigations, are included, showing that accurate results can be efficiently obtained with small computational cost.

Boundary integral equations for acoustical inverse sound-soft scattering

The shape of a plane acoustical sound-soft obstacle is detected from knowledge of the far field pattern for one time-harmonic incident field. Two methods based on solving a system of integral equations for the incoming wave and the far field pattern are investigated. Properties of the integral operators required in order to apply regularization, i.e. injectivity and denseness of the range, are proved.

Effect of solute segregation on the strength of nanocrystalline alloys:Inverse Hall-Petch relation

We have used a high-energy ball mill to prepare single-phased nanocrystalline Fe, Fe90Ni10, Fe85Al4Si11, Ni99Fe1 and Ni90Fe10 powders. We then increased their grain sizes by annealing. We found that a low-temperature anneal (T < 0.4 Tm) softens the elemental nanocrystalline Fe but hardens both the body-centered cubic iron- and face-centered cubic nickel-based solid solutions, leading in these alloys to an inverse Hall–Petch relationship. We explain this abnormal Hall–Petch effect in terms of solute segregation to the grain boundaries of the nanocrystalline alloys. Our analysis can also explain the inverse Hall–Petch relationship found in previous studies during the thermal anneal of ball-milled nanocrystalline Fe (containing ∼1.5 at.% impurities) and electrodeposited nanocrystalline Ni (containing ∼1.0 at.% impurities).

Nonlinear inverse synthesis and eigenvalue division multiplexing in optical fiber channels

We scrutinize the concept of integrable nonlinear communication channels, resurrecting and extending the idea of eigenvalue communications in a novel context of nonsoliton coherent optical communications. Using the integrable nonlinear Schrödinger equation as a channel model, we introduce a new approach - the nonlinear inverse synthesis method - for digital signal processing based on encoding the information directly onto the nonlinear signal spectrum. The latter evolves trivially and linearly along the transmission line, thus, providing an effective eigenvalue division multiplexing with no nonlinear channel cross talk. The general approach is illustrated with a coherent optical orthogonal frequency division multiplexing transmission format. We show how the strategy based upon the inverse scattering transform method can be geared for the creation of new efficient coding and modulation standards for the nonlinear channel. © Published by the American Physical Society.

A meshless method for an inverse two-phase one-dimensional nonlinear Stefan problem

We extend a meshless method of fundamental solutions recently proposed by the authors for the one-dimensional two-phase inverse linear Stefan problem, to the nonlinear case. In this latter situation the free surface is also considered unknown which is more realistic from the practical point of view. Building on the earlier work, the solution is approximated in each phase by a linear combination of fundamental solutions to the heat equation. The implementation and analysis are more complicated in the present situation since one needs to deal with a nonlinear minimization problem to identify the free surface. Furthermore, the inverse problem is ill-posed since small errors in the input measured data can cause large deviations in the desired solution. Therefore, regularization needs to be incorporated in the objective function which is minimized in order to obtain a stable solution. Numerical results are presented and discussed. © 2014 IMACS.

Digital signal processing based on inverse scattering transform

Through numerical modeling, we illustrate the possibility of a new approach to digital signal processing in coherent optical communications based on the application of the so-called inverse scattering transform. Considering without loss of generality a fiber link with normal dispersion and quadrature phase shift keying signal modulation, we demonstrate how an initial information pattern can be recovered (without direct backward propagation) through the calculation of nonlinear spectral data of the received optical signal. © 2013 Optical Society of America.

Phenol methylation over nanoparticulate Co2FeO4 inverse spinel catalysts:the effect of morphology on catalytic performance

A series of CoFe2O4 nanoparticles have been prepared via co-precipitation and controlled thermal sintering, with tunable diameters spanning 7–50 nm. XRD confirms that the inverse spinel structure is adopted by all samples, while XPS shows their surface compositions depend on calcination temperature and associated particle size. Small (<20 nm) particles expose Fe3+ enriched surfaces, whereas larger (∼50 nm) particles formed at higher temperatures possess Co:Fe surface compositions close to the expected 1:2 bulk ratio. A model is proposed in which smaller crystallites expose predominately (1 1 1) facets, preferentially terminated in tetrahedral Fe3+ surface sites, while sintering favours (1 1 0) and (1 0 0) facets and Co:Fe surface compositions closer to the bulk inverse spinel phase. All materials were active towards the gas-phase methylation of phenol to o-cresol at temperatures as low as 300 °C. Under these conditions, materials calcined at 450 and 750 °C exhibit o-cresol selectivities of ∼90% and 80%, respectively. Increasing either particle size or reaction temperature promotes methanol decomposition and the evolution of gaseous reductants (principally CO and H2), which may play a role in CoFe2O4 reduction and the concomitant respective dehydroxylation of phenol to benzene. The degree of methanol decomposition, and consequent H2 or CO evolution, appears to correlate with surface Co2+ content: larger CoFe2O4 nanoparticles have more Co rich surfaces and are more active towards methanol decomposition than their smaller counterparts. Reduction of the inverse spinel surface thus switches catalysis from the regio- and chemo-selective methylation of phenol to o-cresol, towards methanol decomposition and phenol dehydroxylation to benzene. At 300 °C sub-20 nm CoFe2O4 nanoparticles are less active for methanol decomposition and become less susceptible to reduction than their 50 nm counterparts, favouring a high selectivity towards methylation.

Visualisation of heterogeneous data with the generalised generative topographic mapping

Heterogeneous and incomplete datasets are common in many real-world visualisation applications. The probabilistic nature of the Generative Topographic Mapping (GTM), which was originally developed for complete continuous data, can be extended to model heterogeneous (i.e. containing both continuous and discrete values) and missing data. This paper describes and assesses the resulting model on both synthetic and real-world heterogeneous data with missing values.