Geometric optimization methods for the analysis of gene expression data

DNA microarrays provide such a huge amount of data that unsupervised methods are required to reduce the dimension of the data set and to extract meaningful biological information. This work shows that Independent Component Analysis (ICA) is a promising approach for the analysis of genome-wide transcriptomic data. The paper first presents an overview of the most popular algorithms to perform ICA. These algorithms are then applied on a microarray breast-cancer data set. Some issues about the application of ICA and the evaluation of biological relevance of the results are discussed. This study indicates that ICA significantly outperforms Principal Component Analysis (PCA).

Different methods of manufacturing FE-based oxygen carrier particles for reforming via chemical looping, and their effect on performance

Chemical looping combustion (CLC) is a means of combusting carbonaceous fuels, which inherently separates the greenhouse gas carbon dioxide from the remaining combustion products, and has the potential to be used for the production of high-purity hydrogen. Iron-based oxygen carriers for CLC have been subject to considerable work; however, there are issues regarding the lifespan of iron-based oxygen carriers over repeated cycles. In this work, haematite (Fe2O3) was reduced in an N2+CO+CO2 mixture within a fluidised bed at 850°C, and oxidised back to magnetite (Fe3O4) in a H2O+N2 mixture, with the subsequent yield of hydrogen during oxidation being of interest. Subsequent cycles started from Fe3O4 and two transition regimes were studied; Fe3O4↔Fe0.947O and Fe 3O4↔Fe. Particles were produced by mechanical mixing and co-precipitation. In the case of co-precipitated particles, Al was added such that the ratio of Fe:Al by weight was 9:1, and the final pH of the particles during precipitation was investigated for its subsequent effect on reactivity. This paper shows that co-precipitated particles containing additives such as Al may be able to achieve consistently high H2 yields when cycling between Fe3O4 and Fe, and that these yields are a function of the ratio of [CO2] to [CO] during reduction, where thermodynamic arguments suggest that the yield should be independent of this ratio. A striking feature with our materials was that particles made by mechanical mixing performed much better than those made by co-precipitation when cycling between Fe3O4 and Fe0.947O, but much worse than co-precipitated particles when cycling between Fe3O 4 and Fe.

Methods for enhanced electrical transduction and characterization of micromechanical resonators

This paper details the design and enhanced electrical transduction of a bulk acoustic mode resonator fabricated in a commercial foundry MEMS process utilizing 2.5 μm gaps. The I-V characteristics of electrically addressed silicon resonators are often dominated by capacitive parasitics, inherent to hybrid technologies. This paper benchmarks a variety of drive and detection principles for electrostatically driven square-extensional mode resonators operating in air via analytical models accompanied by measurements of fabricated devices with the primary aim of enhancing the ratio of the motional to feedthrough current at nominal operating voltages. In view of ultimately enhancing the motional to feedthrough current ratio, a new detection technique that combines second harmonic capacitive actuation and piezoresistive detection is presented herein. This new method is shown to outperform previously reported methods utilizing voltages as low as ±3 V in air, providing a promising solution for low voltage CMOS-MEMS integration. To elucidate the basis of this improvement in signal output from measured devices, an approximate analytical model for piezoresistive sensing specific to the resonator topology reported here is also developed and presented. © 2010 Elsevier B.V. All rights reserved.

Enhanced transduction methods for electrostatically driven MEMS resonators

Electrically addressed silicon bulk acoustic wave microresonators offer high Q solutions for applications in sensing and signal processing. However, the electrically transduced motional signal is often swamped by parasitic feedthrough in hybrid technologies. With the aim of enhancing the ratio of the motional to feedthrough current at nominal operating voltages, this paper benchmarks a variety of drive and detection principles for electrostatically driven square-extensional mode resonators operating in air and in a foundry MEMS process utilizing 2μm gaps. A new detection technique, combining second harmonic capacitive actuation and piezoresistive detection, outperforms previously reported methods utilizing voltages as low as ± 3V in air providing a promising solution for low voltage CMOS-MEMS integration. ©2009 IEEE.

Uniform stability of a particle approximation of the optimal filter derivative

Sequential Monte Carlo methods, also known as particle methods, are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. In many applications it may be necessary to compute the sensitivity, or derivative, of the optimal filter with respect to the static parameters of the state-space model; for instance, in order to obtain maximum likelihood model parameters of interest, or to compute the optimal controller in an optimal control problem. In Poyiadjis et al. [2011] an original particle algorithm to compute the filter derivative was proposed and it was shown using numerical examples that the particle estimate was numerically stable in the sense that it did not deteriorate over time. In this paper we substantiate this claim with a detailed theoretical study. Lp bounds and a central limit theorem for this particle approximation of the filter derivative are presented. It is further shown that under mixing conditions these Lp bounds and the asymptotic variance characterized by the central limit theorem are uniformly bounded with respect to the time index. We demon- strate the performance predicted by theory with several numerical examples. We also use the particle approximation of the filter derivative to perform online maximum likelihood parameter estimation for a stochastic volatility model.

Parameter Estimation for Hidden Markov Models with Intractable Likelihoods

Approximate Bayesian computation (ABC) is a popular technique for analysing data for complex models where the likelihood function is intractable. It involves using simulation from the model to approximate the likelihood, with this approximate likelihood then being used to construct an approximate posterior. In this paper, we consider methods that estimate the parameters by maximizing the approximate likelihood used in ABC. We give a theoretical analysis of the asymptotic properties of the resulting estimator. In particular, we derive results analogous to those of consistency and asymptotic normality for standard maximum likelihood estimation. We also discuss how sequential Monte Carlo methods provide a natural method for implementing our likelihood-based ABC procedures.

Filtering via approximate Bayesian computation

Approximate Bayesian computation (ABC) has become a popular technique to facilitate Bayesian inference from complex models. In this article we present an ABC approximation designed to perform biased filtering for a Hidden Markov Model when the likelihood function is intractable. We use a sequential Monte Carlo (SMC) algorithm to both fit and sample from our ABC approximation of the target probability density. This approach is shown to, empirically, be more accurate w.r.t.~the original filter than competing methods. The theoretical bias of our method is investigated; it is shown that the bias goes to zero at the expense of increased computational effort. Our approach is illustrated on a constrained sequential lasso for portfolio allocation to 15 constituents of the FTSE 100 share index.