A generalized collectively compact operator theory with an application to integral equations on unbounded domains

In this paper a generalization of collectively compact operator theory in Banach spaces is developed. A feature of the new theory is that the operators involved are no longer required to be compact in the norm topology. Instead it is required that the image of a bounded set under the operator family is sequentially compact in a weaker topology. As an application, the theory developed is used to establish solvability results for a class of systems of second kind integral equations on unbounded domains, this class including in particular systems of Wiener-Hopf integral equations with L1 convolutions kernels

Error, reproducibility and sensitivity: a pipeline for data processing of Agilent oligonucleotide expression arrays

Background: Expression microarrays are increasingly used to obtain large scale transcriptomic information on a wide range of biological samples. Nevertheless, there is still much debate on the best ways to process data, to design experiments and analyse the output. Furthermore, many of the more sophisticated mathematical approaches to data analysis in the literature remain inaccessible to much of the biological research community. In this study we examine ways of extracting and analysing a large data set obtained using the Agilent long oligonucleotide transcriptomics platform, applied to a set of human macrophage and dendritic cell samples. Results: We describe and validate a series of data extraction, transformation and normalisation steps which are implemented via a new R function. Analysis of replicate normalised reference data demonstrate that intrarray variability is small (only around 2 of the mean log signal), while interarray variability from replicate array measurements has a standard deviation (SD) of around 0.5 log(2) units (6 of mean). The common practise of working with ratios of Cy5/Cy3 signal offers little further improvement in terms of reducing error. Comparison to expression data obtained using Arabidopsis samples demonstrates that the large number of genes in each sample showing a low level of transcription reflect the real complexity of the cellular transcriptome. Multidimensional scaling is used to show that the processed data identifies an underlying structure which reflect some of the key biological variables which define the data set. This structure is robust, allowing reliable comparison of samples collected over a number of years and collected by a variety of operators. Conclusions: This study outlines a robust and easily implemented pipeline for extracting, transforming normalising and visualising transcriptomic array data from Agilent expression platform. The analysis is used to obtain quantitative estimates of the SD arising from experimental (non biological) intra- and interarray variability, and for a lower threshold for determining whether an individual gene is expressed. The study provides a reliable basis for further more extensive studies of the systems biology of eukaryotic cells.

Optimising the analysis of transcript data using high density oligonucleotide arrays and genomic DNA-based probe selection

Background: Affymetrix GeneChip arrays are widely used for transcriptomic studies in a diverse range of species. Each gene is represented on a GeneChip array by a probe- set, consisting of up to 16 probe-pairs. Signal intensities across probe- pairs within a probe-set vary in part due to different physical hybridisation characteristics of individual probes with their target labelled transcripts. We have previously developed a technique to study the transcriptomes of heterologous species based on hybridising genomic DNA (gDNA) to a GeneChip array designed for a different species, and subsequently using only those probes with good homology. Results: Here we have investigated the effects of hybridising homologous species gDNA to study the transcriptomes of species for which the arrays have been designed. Genomic DNA from Arabidopsis thaliana and rice (Oryza sativa) were hybridised to the Affymetrix Arabidopsis ATH1 and Rice Genome GeneChip arrays respectively. Probe selection based on gDNA hybridisation intensity increased the number of genes identified as significantly differentially expressed in two published studies of Arabidopsis development, and optimised the analysis of technical replicates obtained from pooled samples of RNA from rice. Conclusion: This mixed physical and bioinformatics approach can be used to optimise estimates of gene expression when using GeneChip arrays.

Using genomic DNA-based probe-selection to improve the sensitivity of high-density oligonucleotide arrays when applied to heterologous species

High-density oligonucleotide (oligo) arrays are a powerful tool for transcript profiling. Arrays based on GeneChip® technology are amongst the most widely used, although GeneChip® arrays are currently available for only a small number of plant and animal species. Thus, we have developed a method to improve the sensitivity of high-density oligonucleotide arrays when applied to heterologous species and tested the method by analysing the transcriptome of Brassica oleracea L., a species for which no GeneChip® array is available, using a GeneChip® array designed for Arabidopsis thaliana (L.) Heynh. Genomic DNA from B. oleracea was labelled and hybridised to the ATH1-121501 GeneChip® array. Arabidopsis thaliana probe-pairs that hybridised to the B. oleracea genomic DNA on the basis of the perfect-match (PM) probe signal were then selected for subsequent B. oleracea transcriptome analysis using a .cel file parser script to generate probe mask files. The transcriptional response of B. oleracea to a mineral nutrient (phosphorus; P) stress was quantified using probe mask files generated for a wide range of gDNA hybridisation intensity thresholds. An example probe mask file generated with a gDNA hybridisation intensity threshold of 400 removed > 68 % of the available PM probes from the analysis but retained >96 % of available A. thaliana probe-sets. Ninety-nine of these genes were then identified as significantly regulated under P stress in B. oleracea, including the homologues of P stress responsive genes in A. thaliana. Increasing the gDNA hybridisation intensity thresholds up to 500 for probe-selection increased the sensitivity of the GeneChip® array to detect regulation of gene expression in B. oleracea under P stress by up to 13-fold. Our open-source software to create probe mask files is freely available http://affymetrix.arabidopsis.info/xspecies/ webcite and may be used to facilitate transcriptomic analyses of a wide range of plant and animal species in the absence of custom arrays.

Arrays of chiral nanotubes and a layered coordination polymer containing gallium-sulfide supertetrahedral clusters

We report here a unique chiral hybrid gallium sulfide, [NC2H8]2[Ga10S16(N2C12H12)(NC2H7)2] 1, consisting of helical chains of organically-functionalised supertetrahedral clusters which form quadruple-stranded helical nanotubes of ca. 3 nm diameter. This material therefore consists of discrete metal-organic nanotubes which, to the best of our knowledge, are extremely rare. Whilst solvothermal reactions involving 1,2-di(4-pyridyl)ethylene (DPE) resulted in the formation of such single-walled chiral nanotubes, the use of longer 4,4’-trimethylenedipyridine (TMP) ligands resulted in the synthesis of a two-dimensional hybrid gallium sulfide, [C5H6N]3[Ga10S16(OH)(N2C13H14)] 2 in which, for the first time, inorganic and organic linkages between supertetrahedral clusters coexist.

Chaos of Wolbachia Sequences Inside the Compact Fig Syconia of Ficus benjamina (Ficus: Moraceae)

Figs and fig wasps form a peculiar closed community in which the Ficus tree provides a compact syconium (inflorescence) habitat for the lives of a complex assemblage of Chalcidoid insects. These diverse fig wasp species have intimate ecological relationships within the closed world of the fig syconia. Previous surveys of Wolbachia, maternally inherited endosymbiotic bacteria that infect vast numbers of arthropod hosts, showed that fig wasps have some of the highest known incidences of Wolbachia amongst all insects. We ask whether the evolutionary patterns of Wolbachia sequences in this closed syconium community are different from those in the outside world. In the present study, we sampled all 17 fig wasp species living on Ficus benjamina, covering 4 families, 6 subfamilies, and 8 genera of wasps. We made a thorough survey of Wolbachia infection patterns and studied evolutionary patterns in wsp (Wolbachia Surface Protein) sequences. We find evidence for high infection incidences, frequent recombination between Wolbachia strains, and considerable horizontal transfer, suggesting rapid evolution of Wolbachia sequences within the syconium community. Though the fig wasps have relatively limited contact with outside world, Wolbachia may be introduced to the syconium community via horizontal transmission by fig wasps species that have winged males and visit the syconia earlier.

Flow structure and near-field dispersion in arrays of building-like obstacles

Dispersion in the near-field region of localised releases in urban areas is difficult to predict because of the strong influence of individual buildings. Effects include upstream dispersion, trapping of material into building wakes and enhanced concentration fluctuations. As a result, concentration patterns are highly variable in time and mean profiles in the near field are strongly non-Gaussian. These aspects of near-field dispersion are documented by analysing data from direct numerical simulations in arrays of building-like obstacles and are related to the underlying flow structure. The mean flow structure around the buildings is found to exert a strong influence over the dispersion of material in the near field. Diverging streamlines around buildings enhance lateral dispersion. Entrainment of material into building wakes in the very near field gives rise to secondary sources, which then affect the subsequent dispersion pattern. High levels of concentration fluctuations are also found in this very near field; the fluctuation intensity is of order 2 to 5.

A compact low-cost electronic hardware design for actuating soft robots

A low cost, compact embedded design approach for actuating soft robots is presented. The complete fabrication procedure and mode of operation was demonstrated, and the performance of the complete system was also demonstrated by building a microcontroller based hardware system which was used to actuate a soft robot for bending motion. The actuation system including the electronic circuit board and actuation components was embedded in a 3D-printed casing to ensure a compact approach for actuating soft robots. Results show the viability of the system in actuating and controlling siliconebased soft robots to achieve bending motions. Qualitative measurements of uniaxial tensile test, bending distance and pressure were obtained. This electronic design is easy to reproduce and integrate into any specified soft robotic device requiring pneumatic actuation.

Root elongation rate is correlated with the length of the bare root apex of maize and lupin roots despite contrasting responses of root growth to compact and dry soils

Background We investigated interacting effects of matric potential and soil strength on root elongation of maize and lupin, and relations between root elongation rates and the length of bare (hairless) root apex. Methods Root elongation rates and the length of bare root apexwere determined formaize and lupin seedlings in sandy loam soil of various matric potentials (−0.01 to −1.6 MPa) and bulk densities (0.9 to 1.5 Mg m−3). Results Root elongation rates slowed with both decreasing matric potential and increasing penetrometer resistance. Root elongation of maize slowed to 10 % of the unimpeded rate when penetrometer resistance increased to 2 MPa, whereas lupin elongated at about 40 % of the unimpeded rate. Maize root elongation rate was more sensitive to changes in matric potential in loosely packed soil (penetrometer resistances <1 MPa) than lupin. Despite these differing responses, root elongation rate of both species was linearly correlated with length of the bare root apex (r2 0.69 to 0.97). Conclusion Maize root elongation was more sensitive to changes in matric potential and mechanical impedance than lupin. Robust linear relationships between elongation rate and length of bare apex suggest good potential for estimating root elongation rates for excavated roots.