Spectral theory of some non-selfadjoint linear differential operators

We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary conditions may be such that the resulting operator is not selfadjoint. We associate the spectral properties of such an operator $S$ with the properties of the solution of a corresponding boundary value problem for the partial differential equation $\partial_t q \pm iSq=0$. Namely, we are able to establish an explicit correspondence between the properties of the family of eigenfunctions of the operator, and in particular whether this family is a basis, and the existence and properties of the unique solution of the associated boundary value problem. When such a unique solution exists, we consider its representation as a complex contour integral that is obtained using a transform method recently proposed by Fokas and one of the authors. The analyticity properties of the integrand in this representation are crucial for studying the spectral theory of the associated operator.

Analysis of the variability of auditory brainstem response components through linear regression

(ABR) is of fundamental importance to the investiga- tion of the auditory system behavior, though its in- terpretation has a subjective nature because of the manual process employed in its study and the clinical experience required for its analysis. When analyzing the ABR, clinicians are often interested in the identi- fication of ABR signal components referred to as Jewett waves. In particular, the detection and study of the time when these waves occur (i.e., the wave la- tency) is a practical tool for the diagnosis of disorders affecting the auditory system. In this context, the aim of this research is to compare ABR manual/visual analysis provided by different examiners. Methods: The ABR data were collected from 10 normal-hearing subjects (5 men and 5 women, from 20 to 52 years). A total of 160 data samples were analyzed and a pair- wise comparison between four distinct examiners was executed. We carried out a statistical study aiming to identify significant differences between assessments provided by the examiners. For this, we used Linear Regression in conjunction with Bootstrap, as a me- thod for evaluating the relation between the responses given by the examiners. Results: The analysis sug- gests agreement among examiners however reveals differences between assessments of the variability of the waves. We quantified the magnitude of the ob- tained wave latency differences and 18% of the inves- tigated waves presented substantial differences (large and moderate) and of these 3.79% were considered not acceptable for the clinical practice. Conclusions: Our results characterize the variability of the manual analysis of ABR data and the necessity of establishing unified standards and protocols for the analysis of these data. These results may also contribute to the validation and development of automatic systems that are employed in the early diagnosis of hearing loss.

Classification of cortical microcircuits based on micro-electrode-array data from slices of rat barrel cortex

The bewildering complexity of cortical microcircuits at the single cell level gives rise to surprisingly robust emergent activity patterns at the level of laminar and columnar local field potentials (LFPs) in response to targeted local stimuli. Here we report the results of our multivariate data-analytic approach based on simultaneous multi-site recordings using micro-electrode-array chips for investigation of the microcircuitary of rat somatosensory (barrel) cortex. We find high repeatability of stimulus-induced responses, and typical spatial distributions of LFP responses to stimuli in supragranular, granular, and infragranular layers, where the last form a particularly distinct class. Population spikes appear to travel with about 33 cm/s from granular to infragranular layers. Responses within barrel related columns have different profiles than those in neighbouring columns to the left or interchangeably to the right. Variations between slices occur, but can be minimized by strictly obeying controlled experimental protocols. Cluster analysis on normalized recordings indicates specific spatial distributions of time series reflecting the location of sources and sinks independent of the stimulus layer. Although the precise correspondences between single cell activity and LFPs are still far from clear, a sophisticated neuroinformatics approach in combination with multi-site LFP recordings in the standardized slice preparation is suitable for comparing normal conditions to genetically or pharmacologically altered situations based on real cortical microcircuitry.

Fine-grained multi-phase array designs

Hybrid multiprocessor architectures which combine re-configurable computing and multiprocessors on a chip are being proposed to transcend the performance of standard multi-core parallel systems. Both fine-grained and coarse-grained parallel algorithm implementations are feasible in such hybrid frameworks. A compositional strategy for designing fine-grained multi-phase regular processor arrays to target hybrid architectures is presented in this paper. The method is based on deriving component designs using classical regular array techniques and composing the components into a unified global design. Effective designs with phase-changes and data routing at run-time are characteristics of these designs. In order to describe the data transfer between phases, the concept of communication domain is introduced so that the producer–consumer relationship arising from multi-phase computation can be treated in a unified way as a data routing phase. This technique is applied to derive new designs of multi-phase regular arrays with different dataflow between phases of computation.

Synthesis of novel hyperbranched polymers featuring oxazoline linear units and their application in fast-drying solvent-borne coating formulations

Novel acid-terminated hyperbranched polymers (HBPs) containing adipic acid and oxazoline monomers derived from oleic and linoleic acid have been synthesized via a bulk polymerization procedure. Branching was achieved as a consequence of an acid-catalyzed opening of the oxazoline ring to produce a trifunctional monomer in situ which delivered branching levels of >45% as determined by 1H and 13C NMR spectroscopy. The HBPs were soluble in common solvents, such as CHCl3, acetone, tetrahydrofuran, dimethylformamide, and dimethyl sulfoxide and were further functionalized by addition of citronellol to afford white-spirit soluble materials that could be used in coating formulations. During end group modification, a reduction in branching levels of the HBPs (down to 12–24%) was observed, predominantly on account of oxazoline ring reformation and trans-esterification processes under the reaction conditions used. In comparison to commercial alkyd resin paint coatings, formulations of the citronellol-functionalized hyperbranched materials blended with a commercial alkyd resin exhibited dramatic decreases of the blend viscosity when the HBP content was increased. The curing characteristics of the HBP/alkyd blend formulations were studied by dynamic mechanical analysis which revealed that the new coatings cured more quickly and produced tougher materials than otherwise identical coatings prepared from only the commercial alkyd resins.

Retrieval characteristics of non-linear sea surface temperature from the Advanced Very High Resolution Radiometer

Criteria are proposed for evaluating sea surface temperature (SST) retrieved from satellite infra-red imagery: bias should be small on regional scales; sensitivity to atmospheric humidity should be small; and sensitivity of retrieved SST to surface temperature should be close to 1 K K−1. Their application is illustrated for non-linear sea surface temperature (NLSST) estimates. 233929 observations from the Advanced Very High Resolution Radiometer (AVHRR) on Metop-A are matched with in situ data and numerical weather prediction (NWP) fields. NLSST coefficients derived from these matches have regional biases from −0.5 to +0.3 K. Using radiative transfer modelling we find that a 10% increase in humidity alone can change the retrieved NLSST by between −0.5 K and +0.1 K. A 1 K increase in SST changes NLSST by <0.5 K in extreme cases. The validity of estimates of sensitivity by radiative transfer modelling is confirmed empirically.

Genes driving potato tuber initiation and growth: identification based on transcriptional changes using the POCI array

The increasing amount of available expressed gene sequence data makes whole-transcriptome analysis of certain crop species possible. Potato currently has the second largest number of publicly available expressed sequence tag (EST) sequences among the Solanaceae. Most of these ESTs, plus other proprietary sequences, were combined and used to generate a unigene assembly. The set of 246,182 sequences produced 46,345 unigenes, which were used to design a 44K 60-mer oligo array (Potato Oligo Chip Initiative: POCI). In this study, we attempt to identify genes controlling and driving the process of tuber initiation and growth by implementing large-scale transcriptional changes using the newly developed POCI array. Major gene expression profiles could be identified exhibiting differential expression at key developmental stages. These profiles were associated with functional roles in cell division and growth. A subset of genes involved in the regulation of the cell cycle, based on their Gene Ontology classification, exhibit a clear transient upregulation at tuber onset indicating increased cell division during these stages. The POCI array allows the study of potato gene expression on a much broader level than previously possible and will greatly enhance analysis of transcriptional control mechanisms in a wide range of potato research areas. POCI sequence and annotation data are publicly available through the POCI database (http://pgrc.ipk-gatersleben.de/poci).

A Brassica exon array for whole-transcript gene expression profiling

Affymetrix GeneChip (R) arrays are used widely to study transcriptional changes in response to developmental and environmental stimuli. GeneChip (R) arrays comprise multiple 25-mer oligonucleotide probes per gene and retain certain advantages over direct sequencing. For plants, there are several public GeneChip (R) arrays whose probes are localised primarily in 39 exons. Plant whole-transcript (WT) GeneChip (R) arrays are not yet publicly available, although WT resolution is needed to study complex crop genomes such as Brassica, which are typified by segmental duplications containing paralogous genes and/or allopolyploidy. Available sequence data were sampled from the Brassica A and C genomes, and 142,997 gene models identified. The assembled gene models were then used to establish a comprehensive public WT exon array for transcriptomics studies. The Affymetrix GeneChip (R) Brassica Exon 1.0 ST Array is a 5 mu M feature size array, containing 2.4 million 25-base oligonucleotide probes representing 135,201 gene models, with 15 probes per gene distributed among exons. Discrimination of the gene models was based on an E-value cut-off of 1E(-5), with <= 98 sequence identity. The 135 k Brassica Exon Array was validated by quantifying transcriptome differences between leaf and root tissue from a reference Brassica rapa line (R-o-18), and categorisation by Gene Ontologies (GO) based on gene orthology with Arabidopsis thaliana. Technical validation involved comparison of the exon array with a 60-mer array platform using the same starting RNA samples. The 135 k Brassica Exon Array is a robust platform. All data relating to the array design and probe identities are available in the public domain and are curated within the BrassEnsembl genome viewer at http://www.brassica.info/BrassEnsembl/index.html.

Concurrent recordings of bladder afferents from multiple nerves using a microfabricated PDMS microchannel electrode array

In this paper we present a compliant neural interface designed to record bladder afferent activity. We developed the implant's microfabrication process using multiple layers of silicone rubber and thin metal so that a gold microelectrode array is embedded within four parallel polydimethylsiloxane (PDMS) microchannels (5 mm long, 100 μm wide, 100 μm deep). Electrode impedance at 1 kHz was optimized using a reactive ion etching (RIE) step, which increased the porosity of the electrode surface. The electrodes did not deteriorate after a 3 month immersion in phosphate buffered saline (PBS) at 37 °C. Due to the unique microscopic topography of the metal film on PDMS, the electrodes are extremely compliant and can withstand handling during implantation (twisting and bending) without electrical failure. The device was transplanted acutely to anaesthetized rats, and strands of the dorsal branch of roots L6 and S1 were surgically teased and inserted in three microchannels under saline immersion to allow for simultaneous in vivo recordings in an acute setting. We utilized a tripole electrode configuration to maintain background noise low and improve the signal to noise ratio. The device could distinguish two types of afferent nerve activity related to increasing bladder filling and contraction. To our knowledge, this is the first report of multichannel recordings of bladder afferent activity.

Evaluation of an elastomer based gold microelectrode array for neural recording applications

We are reporting on the fabrication and electrical characterization of a novel elastomer based micro-cuff neural interface. Electrodes are gold (Au) tracks of sub-100nm thickness and are thermally evaporated on a 0.5 mm thick polydimethylsiloxane (PDMS) substrate. We investigate how electrode area and immersion in phosphate buffered saline (PBS) at 37°C influence electrode impedance. A microfluidic channel is bonded to the electrode array to form the cuff. In an acute, in-vivo, proof-of-principle recording, the device is capable of detecting light stroking and pinch of a hind leg of an anaesthetized rat.

Compliant Multi-electrode Micro-channel Array for Recording Afferent Nerve Activity

We have fabricated a compliant neural interface to record afferent nerve activity. Stretchable gold electrodes were evaporated on a polydimethylsiloxane (PDMS) substrate and were encapsulated using photo-patternable PDMS. The built-in microstructure of the gold film on PDMS allows the electrodes to twist and flex repeatedly, without loss of electrical conductivity. PDMS microchannels (5mm long, 100μm wide, 100μm deep) were then plasma bonded irreversibly on top of the electrode array to define five parallel-conduit implants. The soft gold microelectrodes have a low impedance of ~200kΩ at the 1kHz frequency range. Teased nerves from the L6 dorsal root of an anaesthetized Sprague Dawley rat were threaded through the microchannels. Acute tripolar recordings of cutaneous activity are demonstrated, from multiple nerve rootlets simultaneously. Confinement of the axons within narrow microchannels allows for reliable recordings of low amplitude afferents. This electrode technology promises exciting applications in neuroprosthetic devices including bladder fullness monitors and peripheral nervous system implants.

Further investigations of the quartz optically stimulated luminescence components using linear modulation

The optically stimulated luminescence (OSL) from quartz is known to be the sum of several components with different rates of charge loss, originating from different trap types. The OSL components are clearly distinguished using the linear modulation (LM OSL) technique. A variety of pre-treatment and measurement conditions have been used on sedimentary samples in conjunction with linearly modulated optical stimulation to study in detail the behaviour of the OSL components of quartz. Single aliquots of different quartz samples have been found to contain typically five or six common LM OSL components when stimulated at View the MathML source. The components have been parameterised in terms of thermal stability (i.e. E and s), photoionisation cross-section energy dependence and dose response. The results of studies concerning applications of component-resolved LM OSL measurements on quartz are also presented. These include the detection of partial bleaching in young samples, use of ‘stepped wavelength’ stimulation to observe OSL from single components and attempts to extend the age range of quartz OSL dating.

Linear vs. log-linear unit-root specification: an application of mis-specification encompassing

The objective of this paper is to apply the mis-specification (M-S) encompassing perspective to the problem of choosing between linear and log-linear unit-root models. A simple M-S encompassing test, based on an auxiliary regression stemming from the conditional second moment, is proposed and its empirical size and power are investigated using Monte Carlo simulations. It is shown that by focusing on the conditional process the sampling distributions of the relevant statistics are well behaved under both the null and alternative hypotheses. The proposed M-S encompassing test is illustrated using US total disposable income quarterly data.

Conditional mean functions of non-linear models of US output

We compare a number of models of post War US output growth in terms of the degree and pattern of non-linearity they impart to the conditional mean, where we condition on either the previous period's growth rate, or the previous two periods' growth rates. The conditional means are estimated non-parametrically using a nearest-neighbour technique on data simulated from the models. In this way, we condense the complex, dynamic, responses that may be present in to graphical displays of the implied conditional mean.