Rank-preserving geometric means of positive semi-definite matrices

The generalization of the geometric mean of positive scalars to positive definite matrices has attracted considerable attention since the seminal work of Ando. The paper generalizes this framework of matrix means by proposing the definition of a rank-preserving mean for two or an arbitrary number of positive semi-definite matrices of fixed rank. The proposed mean is shown to be geometric in that it satisfies all the expected properties of a rank-preserving geometric mean. The work is motivated by operations on low-rank approximations of positive definite matrices in high-dimensional spaces.© 2012 Elsevier Inc. All rights reserved.

Innovation processes within the healthcare industry: Determining critical success factors aligned to product strategies

The impact of differing product strategies on product innovation processes pursued by healthcare firms is discussed. The critical success factors aligned to product strategies are presented. A definite split between pioneering product strategies and late entrant product strategies is also recognised.

Convergence of the auxiliary particle implementation of the PHD filter

Optimal Bayesian multi-target filtering is in general computationally impractical owing to the high dimensionality of the multi-target state. The Probability Hypothesis Density (PHD) filter propagates the first moment of the multi-target posterior distribution. While this reduces the dimensionality of the problem, the PHD filter still involves intractable integrals in many cases of interest. Several authors have proposed Sequential Monte Carlo (SMC) implementations of the PHD filter. However, these implementations are the equivalent of the Bootstrap Particle Filter, and the latter is well known to be inefficient. Drawing on ideas from the Auxiliary Particle Filter (APF), a SMC implementation of the PHD filter which employs auxiliary variables to enhance its efficiency was proposed by Whiteley et. al. Numerical examples were presented for two scenarios, including a challenging nonlinear observation model, to support the claim. This paper studies the theoretical properties of this auxiliary particle implementation. $\mathbb{L}_p$ error bounds are established from which almost sure convergence follows.

Auxiliary particle implementation of the probability hypothesis density filter

Optimal Bayesian multi-target filtering is, in general, computationally impractical owing to the high dimensionality of the multi-target state. The Probability Hypothesis Density (PHD) filter propagates the first moment of the multi-target posterior distribution. While this reduces the dimensionality of the problem, the PHD filter still involves intractable integrals in many cases of interest. Several authors have proposed Sequential Monte Carlo (SMC) implementations of the PHD filter. However, these implementations are the equivalent of the Bootstrap Particle Filter, and the latter is well known to be inefficient. Drawing on ideas from the Auxiliary Particle Filter (APF), we present a SMC implementation of the PHD filter which employs auxiliary variables to enhance its efficiency. Numerical examples are presented for two scenarios, including a challenging nonlinear observation model.

Analytical approximations for the modal acoustic impedances of simply supported, rectangular plates.

Coupling of the in vacuo modes of a fluid-loaded, vibrating structure by the resulting acoustic field, while known to be negligible for sufficiently light fluids, is still only partially understood. A particularly useful structural geometry for the study of this problem is the simply supported, rectangular flat plate, since it exhibits all the relevant physical features while still admitting an analytical description of the modes. Here the influence of the fluid can be expressed in terms of a set of doubly infinite integrals over wave number: the modal acoustic impedances. Closed-form solutions for these impedances do not exist and, while their numerical evaluation is possible, it greatly increases the computational cost of solving the coupled system of modal equations. There is thus a need for accurate analytical approximations. In this work, such approximations are sought in the limit where the modal wavelength is small in comparison with the acoustic wavelength and the plate dimensions. It is shown that contour integration techniques can be used to derive analytical formulas for this regime and that these formulas agree closely with the results of numerical evaluations. Previous approximations [Davies, J. Sound Vib. 15(1), 107-126 (1971)] are assessed in the light of the new results and are shown to give a satisfactory description of real impedance components, but (in general) erroneous expressions for imaginary parts.

Generalised Wishart Processes

We introduce a stochastic process with Wishart marginals: the generalised Wishart process (GWP). It is a collection of positive semi-definite random matrices indexed by any arbitrary dependent variable. We use it to model dynamic (e.g. time varying) covariance matrices. Unlike existing models, it can capture a diverse class of covariance structures, it can easily handle missing data, the dependent variable can readily include covariates other than time, and it scales well with dimension; there is no need for free parameters, and optional parameters are easy to interpret. We describe how to construct the GWP, introduce general procedures for inference and predictions, and show that it outperforms its main competitor, multivariate GARCH, even on financial data that especially suits GARCH. We also show how to predict the mean of a multivariate process while accounting for dynamic correlations.

Probabilistic fault identification using vibration data and neural networks

Bayesian formulated neural networks are implemented using hybrid Monte Carlo method for probabilistic fault identification in cylindrical shells. Each of the 20 nominally identical cylindrical shells is divided into three substructures. Holes of (12±2) mm in diameter are introduced in each of the substructures and vibration data are measured. Modal properties and the Coordinate Modal Assurance Criterion (COMAC) are utilized to train the two modal-property-neural-networks. These COMAC are calculated by taking the natural-frequency-vector to be an additional mode. Modal energies are calculated by determining the integrals of the real and imaginary components of the frequency response functions over bandwidths of 12% of the natural frequencies. The modal energies and the Coordinate Modal Energy Assurance Criterion (COMEAC) are used to train the two frequency-response-function-neural-networks. The averages of the two sets of trained-networks (COMAC and COMEAC as well as modal properties and modal energies) form two committees of networks. The COMEAC and the COMAC are found to be better identification data than using modal properties and modal energies directly. The committee approach is observed to give lower standard deviations than the individual methods. The main advantage of the Bayesian formulation is that it gives identities of damage and their respective confidence intervals.

Feasibility of damage detection using vibration data in a population of cylinders

The feasibility of vibration data to identify damage in a population of cylindrical shells is assessed. Vibration data from a population of cylinders were measured and modal analysis was employed to obtain natural frequencies and mode shapes. The mode shapes were transformed into the Coordinate Modal Assurance Criterion (COMAC). The natural frequencies and the COMAC before and after damage for a population of structures show that modal analysis is a viable route to damage identification in a population of nominally identical cylinders. Modal energies, which are defined as the integrals of the real and imaginary components of the frequency response functions over various frequency ranges, were extracted and transformed into the Coordinate Modal Energy Assurance Criterion (COMEAC). The COMEAC before and after damage show that using modal energies is a viable approach to damage identification in a population of cylinders.

Analytical techniques for indentation of viscoelastic materials

Indentation of linearly viscoelastic materials is explored using elastic-viscoelastic correspondence analysis for both conical-pyramidal and spherical indentation. Boltzmann hereditary integrals are used to generate displacement-time solutions for loading at constant rate and creep following ramp loading. Experimental data for triangle- and trapezoidal-loading are examined for commercially-available polymers and compared with analytical solutions. Emphasis is given to the use of multiple experiments to test the fidelity and predictive capability of the obtained material creep function. Plastic deformation occurs in sharp indentation of glassy polymers and is found to complicate the viscoelastic analysis. A new method is proposed for estimating a material time-constant from peak displacement or hardness data obtained in pyramidal indentation tests performed at different loading rates.

Fracture and energy partitioning in uncooked and cooked noodles

Humans perform fascinating science experiments at home on a daily basis when they undertake the modification of natural and naturally-derived materials by a cooking process prior to consumption. The material properties of such foods are of interest to food scientists (texture is often fundamental to food acceptability), oral biologists (foods modulate feeding behavior), anthropologists (cooking is probably as old as the genus Homo and distinguishes us from all other creatures) and dentists (foods interact with tooth and tooth replacement materials). Materials scientists may be interested in the drastic changes in food properties observed over relatively short cooking times. In the current study, the mechanical properties of one of the most common (and oldest at 4,000+ years) foods on earth, the noodle, were examined as a function of cooking time. Two types of noodles were studied, each made from natural materials (wheat flour, salt, alkali and water) by kneading dough and passing them through a pasta-making machine. These were boiled for between 2-14 min and tested at regular intervals from raw to an overcooked state. Cyclic tensile tests at small strain levels were used to examine energy dissipation characteristics. Energy dissipation was >50% per cycle in uncooked noodles, but decreased by an order of magnitude with cooking. Fractional dissipation values remained approximately constant at cooking times greater than 7 min. Overall, a greater effect of cooking was on viscoplastic dissipation characteristics rather than on fracture resistance. The results of the current study plot the evolution of a viscoplastic mixture into an essentially elastic material in the space of 7 minutes and have broad implications for understanding what cooking does to food materials. In particular, they suggest that textural assessment by consumers of the optimally cooked state of food has a definite physical definition. © 2007 Materials Research Society.

The potential for thermal energy recovery from wastewater treatment works in Southern England

There is potential to extract energy from wastewater in a number of ways, including: kinetic energy using micro-hydro systems, chemical energy through the incineration of sludge, biomass energy from the biogas produced after anaerobic sludge digestion, and thermal energy as heat. This paper considers the last option and asks how much heat could be recovered under UK climatic conditions and can this heat be used effectively by wastewater treatment plants to reduce their carbon footprint? Four wastewater treatment sites in southern England are investigated and the available heat that can be recovered at those sites is quantified. Issues relating to the environmental, economic and practical constraints on how energy can be realistically recovered and utilised are discussed .The results show there is a definite possibility for thermal energy recovery with potential savings at some sites of up to 35,000 tonnes of total long-cycle carbon equivalent (fossil fuel) emissions per year being achievable. The paper also shows that the financial feasibility of three options for using the heat (either for district heating, sludge drying or thermophilic heating in sludge digestion processes) is highly dependant upon the current shadow price of carbon. Without the inclusion of the cost of carbon, the financial feasibility is significantly limited. An environmental constraint for the allowable discharge temperature of effluent after heat-extraction was found to be the major limitation to the amount of energy available for recovery. The paper establishes the true potential of thermal energy recovery from wastewater in English conditions and the economic feasibility of reducing the carbon footprint of wastewater treatment operations using this approach.

Probing the electronic structure of multi-walled carbon nanotubes by transient optical transmittivity

High-resolution time resolved transmittivity measurements on horizontally aligned free-standing multi-walled carbon nanotubes reveal a different electronic transient behavior from that of graphite. This difference is ascribed to the presence of discrete energy states in the multishell carbon nanotube electronic structure. Probe polarization dependence suggests that the optical transitions involve definite selection rules. The origin of these states is discussed and a rate equation model is proposed to rationalize our findings. © 2013 Elsevier Ltd. All rights reserved.

Contraction and observer design on cones

We consider the problem of positive observer design for positive systems defined on solid cones in Banach spaces. The design is based on the Hilbert metric and convergence properties are analyzed in the light of the Birkhoff theorem. Two main applications are discussed: positive observers for systems defined in the positive orthant, and positive observers on the cone of positive semi-definite matrices with a view on quantum systems. © 2011 IEEE.