Sparse polynomial approximation in positive order Sobolev spaces with bounded mixed derivatives and applications to elliptic problems with random loading

In the present paper we study the approximation of functions with bounded mixed derivatives by sparse tensor product polynomials in positive order tensor product Sobolev spaces. We introduce a new sparse polynomial approximation operator which exhibits optimal convergence properties in L2 and tensorized View the MathML source simultaneously on a standard k-dimensional cube. In the special case k=2 the suggested approximation operator is also optimal in L2 and tensorized H1 (without essential boundary conditions). This allows to construct an optimal sparse p-version FEM with sparse piecewise continuous polynomial splines, reducing the number of unknowns from O(p2), needed for the full tensor product computation, to View the MathML source, required for the suggested sparse technique, preserving the same optimal convergence rate in terms of p. We apply this result to an elliptic differential equation and an elliptic integral equation with random loading and compute the covariances of the solutions with View the MathML source unknowns. Several numerical examples support the theoretical estimates.

Dysregulation of REST-regulated coding and non-coding RNAs in a cellular model of Huntington's disease

Huntingtin (Htt) protein interacts with many transcriptional regulators, with widespread disruption to the transcriptome in Huntington's disease (HD) brought about by altered interactions with the mutant Htt (muHtt) protein. Repressor Element-1 Silencing Transcription Factor (REST) is a repressor whose association with Htt in the cytoplasm is disrupted in HD, leading to increased nuclear REST and concomitant repression of several neuronal-specific genes, including brain-derived neurotrophic factor (Bdnf). Here, we explored a wide set of HD dysregulated genes to identify direct REST targets whose expression is altered in a cellular model of HD but that can be rescued by knock-down of REST activity. We found many direct REST target genes encoding proteins important for nervous system development, including a cohort involved in synaptic transmission, at least two of which can be rescued at the protein level by REST knock-down. We also identified several microRNAs (miRNAs) whose aberrant repression is directly mediated by REST, including miR-137, which has not previously been shown to be a direct REST target in mouse. These data provide evidence of the contribution of inappropriate REST-mediated transcriptional repression to the widespread changes in coding and non-coding gene expression in a cellular model of HD that may affect normal neuronal function and survival.

Transcriptional dysregulation of coding and non-coding genes in cellular models of Huntington's disease

HD (Huntington's disease) is a late onset heritable neurodegenerative disorder that is characterized by neuronal dysfunction and death, particularly in the cerebral cortex and medium spiny neurons of the striatum. This is followed by progressive chorea, dementia and emotional dysfunction, eventually resulting in death. HD is caused by an expanded CAG repeat in the first exon of the HD gene that results in an abnormally elongated polyQ (polyglutamine) tract in its protein product, Htt (Huntingtin). Wild-type Htt is largely cytoplasmic; however, in HD, proteolytic N-terminal fragments of Htt form insoluble deposits in both the cytoplasm and nucleus, provoking the idea that mutHtt (mutant Htt) causes transcriptional dysfunction. While a number of specific transcription factors and co-factors have been proposed as mediators of mutHtt toxicity, the causal relationship between these Htt/transcription factor interactions and HD pathology remains unknown. Previous work has highlighted REST [RE1 (repressor element 1)-silencing transcription factor] as one such transcription factor. REST is a master regulator of neuronal genes, repressing their expression. Many of its direct target genes are known or suspected to have a role in HD pathogenesis, including BDNF (brain-derived neurotrophic factor). Recent evidence has also shown that REST regulates transcription of regulatory miRNAs (microRNAs), many of which are known to regulate neuronal gene expression and are dysregulated in HD. Thus repression of miRNAs constitutes a second, indirect mechanism by which REST can alter the neuronal transcriptome in HD. We will describe the evidence that disruption to the REST regulon brought about by a loss of interaction between REST and mutHtt may be a key contributory factor in the widespread dysregulation of gene expression in HD.

Alterations in predicted regulatory and coding regions of the sterol 14α-demethylase gene (CYP51) confer decreased azole sensitivity in the oilseed rape pathogen Pyrenopeziza brassicae

The incidence and severity of light leaf spot epidemics caused by the ascomycete fungus Pyrenopeziza brassicae on UK oilseed rape crops is increasing. The disease is currently controlled by a combination of host resistance, cultural practices and fungicide applications. We report decreases in sensitivities of modern UK P. brassicae isolates to the azole (imidazole and triazole) class of fungicides. By cloning and sequencing the P. brassicae CYP51 (PbCYP51) gene, encoding the azole target sterol 14α-demethylase, we identified two non-synonymous mutations encoding substitutions G460S and S508T associated with reduced azole sensitivity. We confirmed the impact of the encoded PbCYP51 changes on azole sensitivity and protein activity by heterologous expression in a Saccharomyces cerevisiae mutant YUG37::erg11 carrying a controllable promoter of native CYP51 expression. In addition, we identified insertions in the predicted regulatory regions of PbCYP51 in isolates with reduced azole sensitivity. The presence of these insertions was associated with enhanced transcription of PbCYP51 in response to sub-inhibitory concentrations of the azole fungicide tebuconazole. Genetic analysis of in vitro crosses of sensitive and resistant isolates confirmed the impact of PbCYP51 alterations in coding and regulatory sequences on a reduced sensitivity phenotype, as well as identifying a second major gene at another locus contributing to resistance in some isolates. The least sensitive field isolates carry combinations of upstream insertions and non-synonymous mutations, suggesting PbCYP51 evolution is on-going and the progressive decline in azole sensitivity of UK P. brassicae populations will continue. The implications for the future control of light leaf spot are discussed.

Reliability comparison of transmit/receive diversity and error control coding in low-power medium access control protocols

Low-power medium access control (MAC) protocols used for communication of energy constraint wireless embedded devices do not cope well with situations where transmission channels are highly erroneous. Existing MAC protocols discard corrupted messages which lead to costly retransmissions. To improve transmission performance, it is possible to include an error correction scheme and transmit/receive diversity. It is possible to add redundant information to transmitted packets in order to recover data from corrupted packets. It is also possible to make use of transmit/receive diversity via multiple antennas to improve error resiliency of transmissions. Both schemes may be used in conjunction to further improve the performance. In this study, the authors show how an error correction scheme and transmit/receive diversity can be integrated in low-power MAC protocols. Furthermore, the authors investigate the achievable performance gains of both methods. This is important as both methods have associated costs (processing requirements; additional antennas and power) and for a given communication situation it must be decided which methods should be employed. The authors’ results show that, in many practical situations, error control coding outperforms transmission diversity; however, if very high reliability is required, it is useful to employ both schemes together.

Sparse density estimation on the multinomial manifold

A new sparse kernel density estimator is introduced based on the minimum integrated square error criterion for the finite mixture model. Since the constraint on the mixing coefficients of the finite mixture model is on the multinomial manifold, we use the well-known Riemannian trust-region (RTR) algorithm for solving this problem. The first- and second-order Riemannian geometry of the multinomial manifold are derived and utilized in the RTR algorithm. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with an accuracy competitive with those of existing kernel density estimators.

Advances in the stochastic modelling of satellite-derived rainfall estimates using a sparse calibration dataset

As satellite technology develops, satellite rainfall estimates are likely to become ever more important in the world of food security. It is therefore vital to be able to identify the uncertainty of such estimates and for end users to be able to use this information in a meaningful way. This paper presents new developments in the methodology of simulating satellite rainfall ensembles from thermal infrared satellite data. Although the basic sequential simulation methodology has been developed in previous studies, it was not suitable for use in regions with more complex terrain and limited calibration data. Developments in this work include the creation of a multithreshold, multizone calibration procedure, plus investigations into the causes of an overestimation of low rainfall amounts and the best way to take into account clustered calibration data. A case study of the Ethiopian highlands has been used as an illustration.

Sparse space-time boundary element methods for the heat equation

The goal of this work is the efficient solution of the heat equation with Dirichlet or Neumann boundary conditions using the Boundary Elements Method (BEM). Efficiently solving the heat equation is useful, as it is a simple model problem for other types of parabolic problems. In complicated spatial domains as often found in engineering, BEM can be beneficial since only the boundary of the domain has to be discretised. This makes BEM easier than domain methods such as finite elements and finite differences, conventionally combined with time-stepping schemes to solve this problem. The contribution of this work is to further decrease the complexity of solving the heat equation, leading both to speed gains (in CPU time) as well as requiring smaller amounts of memory to solve the same problem. To do this we will combine the complexity gains of boundary reduction by integral equation formulations with a discretisation using wavelet bases. This reduces the total work to O(h

Sparse density estimator with tunable kernels

A new sparse kernel density estimator with tunable kernels is introduced within a forward constrained regression framework whereby the nonnegative and summing-to-unity constraints of the mixing weights can easily be satisfied. Based on the minimum integrated square error criterion, a recursive algorithm is developed to select significant kernels one at time, and the kernel width of the selected kernel is then tuned using the gradient descent algorithm. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing very sparse kernel density estimators with competitive accuracy to existing kernel density estimators.

Sparse density estimation on multinomial manifold combining local component analysis

A new sparse kernel density estimator is introduced based on the minimum integrated square error criterion combining local component analysis for the finite mixture model. We start with a Parzen window estimator which has the Gaussian kernels with a common covariance matrix, the local component analysis is initially applied to find the covariance matrix using expectation maximization algorithm. Since the constraint on the mixing coefficients of a finite mixture model is on the multinomial manifold, we then use the well-known Riemannian trust-region algorithm to find the set of sparse mixing coefficients. The first and second order Riemannian geometry of the multinomial manifold are utilized in the Riemannian trust-region algorithm. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with competitive accuracy to existing kernel density estimators.