Robust eigenstructure assignment in quadratic matrix polynomials: nonsingular case

Feedback design for a second-order control system leads to an eigenstructure assignment problem for a quadratic matrix polynomial. It is desirable that the feedback controller not only assigns specified eigenvalues to the second-order closed loop system but also that the system is robust, or insensitive to perturbations. We derive here new sensitivity measures, or condition numbers, for the eigenvalues of the quadratic matrix polynomial and define a measure of the robustness of the corresponding system. We then show that the robustness of the quadratic inverse eigenvalue problem can be achieved by solving a generalized linear eigenvalue assignment problem subject to structured perturbations. Numerically reliable methods for solving the structured generalized linear problem are developed that take advantage of the special properties of the system in order to minimize the computational work required. In this part of the work we treat the case where the leading coefficient matrix in the quadratic polynomial is nonsingular, which ensures that the polynomial is regular. In a second part, we will examine the case where the open loop matrix polynomial is not necessarily regular.

A matrix iteration for dynamic network summaries

We propose a new algorithm for summarizing properties of large-scale time-evolving networks. This type of data, recording connections that come and go over time, is being generated in many modern applications, including telecommunications and on-line human social behavior. The algorithm computes a dynamic measure of how well pairs of nodes can communicate by taking account of routes through the network that respect the arrow of time. We take the conventional approach of downweighting for length (messages become corrupted as they are passed along) and add the novel feature of downweighting for age (messages go out of date). This allows us to generalize widely used Katz-style centrality measures that have proved popular in network science to the case of dynamic networks sampled at non-uniform points in time. We illustrate the new approach on synthetic and real data.

A note on the Fredholm properties of Toeplitz operators on weighted Bergman spaces with matrix-valued symbols

We characterize the essential spectra of Toeplitz operators Ta on weighted Bergman spaces with matrix-valued symbols; in particular we deal with two classes of symbols, the Douglas algebra C+H∞ and the Zhu class Q := L∞ ∩VMO∂ . In addition, for symbols in C+H∞ , we derive a formula for the index of Ta in terms of its symbol a in the scalar-valued case, while in the matrix-valued case we indicate that the standard reduction to the scalar-valued case fails to work analogously to the Hardy space case. Mathematics subject classification (2010): 47B35,

Importance of oceanic resolution and mean state on the extra-tropical response to El Niño in a matrix of coupled models

The extra-tropical response to El Niño in configurations of a coupled model with increased horizontal resolution in the oceanic component is shown to be more realistic than in configurations with a low resolution oceanic component. This general conclusion is independent of the atmospheric resolution. Resolving small-scale processes in the ocean produces a more realistic oceanic mean state, with a reduced cold tongue bias, which in turn allows the atmospheric model component to be forced more realistically. A realistic atmospheric basic state is critical in order to represent Rossby wave propagation in response to El Niño, and hence the extra-tropical response to El Niño. Through the use of high and low resolution configurations of the forced atmospheric-only model component we show that, in isolation, atmospheric resolution does not significantly affect the simulation of the extra-tropical response to El Niño. It is demonstrated, through perturbations to the SST forcing of the atmospheric model component, that biases in the climatological SST field typical of coupled model configurations with low oceanic resolution can account for the erroneous atmospheric basic state seen in these coupled model configurations. These results highlight the importance of resolving small-scale oceanic processes in producing a realistic large-scale mean climate in coupled models, and suggest that it might may be possible to “squeeze out” valuable extra performance from coupled models through increases to oceanic resolution alone.

Direct observation of membrane insertion by enveloped virus matrix proteins by phosphate displacement

Enveloped virus release is driven by poorly understood proteins that are functional analogs of the coat protein assemblies that mediate intracellular vesicle trafficking. We used differential electron density mapping to detect membrane integration by membrane-bending proteins from five virus families. This demonstrates that virus matrix proteins replace an unexpectedly large portion of the lipid content of the inner membrane face, a generalized feature likely to play a role in reshaping cellular membranes.

Daidzein, R-(+)equol and S-(-)equol inhibit the invasion of MDA-MB-231 breast cancer cells potentially via the down-regulation of matrix metalloproteinase-2

PURPOSE: Soy isoflavones may inhibit tumor cell invasion and metastasis via their effects on matrix metalloproteinases (MMPs) and their tissue inhibitors (TIMPs). The current study investigates the effects of daidzein, R- and S-equol on the invasion of MDA-MB-231 human breast cancer cells and the effects of these compounds on MMP/TIMP expression at the mRNA level. METHODS: The anti-invasive effects of daidzein, R- and S-equol (0, 2.5, 10, 50 μM) on MDA-MB-231 cells were determined using the Matrigel invasion assay following 48-h exposure. Effects on MMP-2, MMP-9, TIMP-1 and TIMP-2 expression were assessed using real-time PCR. Chiral HPLC analysis was used to determine intracellular concentrations of R- and S-equol. RESULTS: The invasive capacity of MDA-MB-231 cells was significantly reduced (by approximately 50-60 %) following treatment with 50 μM daidzein, R- or S-equol. Anti-invasive effects were also observed with R-equol at 2.5 and 10 μM though overall equipotent effects were induced by all compounds. Inhibition of invasion induced by all three compounds at 50 μM was associated with the down-regulation of MMP-2, while none of the compounds tested significantly affected the expression levels of MMP-9, TIMP-1 or TIMP-2 at this concentration. Following exposure to media containing 50 μM R- or S-equol for 48-h intracellular concentrations of R- and S-equol were 4.38 ± 1.17 and 3.22 ± 0.47 nM, respectively. CONCLUSION: Daidzein, R- and S-equol inhibit the invasion of MDA-MB-231 human breast cancer cells in part via the down-regulation of MMP-2 expression, with equipotent effects observed for the parent isoflavone daidzein and the equol enantiomers.

A refined sampling strategy for intra-tooth stable isotope analysis of mammalian enamel

Serial sampling and stable isotope analysis performed along the growth axis of vertebrate tooth enamel records differences attributed to seasonal variation in diet, climate or animal movement. Because several months are required to obtain mature enamel in large mammals, modifications in the isotopic composition of environmental parameters are not instantaneously recorded, and stable isotope analysis of tooth enamel returns a time-averaged signal attenuated in its amplitude relative to the input signal. For convenience, stable isotope profiles are usually determined on the side of the tooth where enamel is thickest. Here we investigate the possibility of improving the time resolution by targeting the side of the tooth where enamel is thinnest. Observation of developing third molars (M3) in sheep shows that the tooth growth rate is not constant but decreases exponentially, while the angle between the first layer of enamel deposited and the enamel–dentine junction increases as a tooth approaches its maximal length. We also noted differences in thickness and geometry of enamel growth between the mesial side (i.e., the side facing the M2) and the buccal side (i.e., the side facing the cheek) of the M3. Carbon and oxygen isotope variations were measured along the M3 teeth from eight sheep raised under controlled conditions. Intra-tooth variability was systematically larger along the mesial side and the difference in amplitude between the two sides was proportional to the time of exposure to the input signal. Although attenuated, the mesial side records variations in the environmental signal more faithfully than the buccal side. This approach can be adapted to other mammals whose teeth show lateral variation in enamel thickness and could potentially be used as an internal check for diagenesis.

Introducing matrix management within a children's services setting - personal reflections

This article reflects on the introduction of ‘matrix management’ arrangements for an Educational Psychology Service (EPS) within a Children’s Service Directorate of a Local Authority (LA). It seeks to demonstrate critical self-awareness, consider relevant literature with a view to bringing insights to processes and outcomes, and offers recommendations regarding the use of matrix management. The report arises from an East Midland’s LA initiative: ALICSE − Advanced Leadership in an Integrated Children’s Service Environment. Through a literature review and personal reflection, the authors consider the following: possible tensions within the development of matrix management arrangements; whether matrix management is a prerequisite within complex organizational systems; and whether competing professional cultures may contribute barriers to creating complementary and collegiate working. The authors briefly consider some research paradigms, notably ethnographic approaches, soft systems methodology, activity theory and appreciative inquiry. These provide an analytic framework for the project and inform this iterative process of collaborative inquiry. Whilst these models help illuminate otherwise hidden processes, none have been implemented following full research methodologies, reflecting the messy reality of local authority working within dynamic organizational structures and shrinking budgets. Nevertheless, this article offers an honest reflection of organizational change within a children’s services environment.

Season of birth and sheep husbandry in late Roman and Medieval coastal Flanders: a pilot study using tooth enamel d18O analysis

From the early Roman period, there is archaeological evidence for the exploitation of the Flemish coastal plain (Belgium) for a range of activities, such as sheep herding on the then developing salt-marshes and salt-meadows for the production of wool. During the early Middle Ages, this culminated in the establishment of dedicated ‘sheep estates’. This phase of exploitation was followed by extensive drainage and land reclamation measures in the high Medieval period, transforming areas into grassland, suited for cattle breeding. As part of a larger project investigating the onset, intensification and final decline of sheep management in coastal Flanders in the historical period, this pilot study presents the results of sequential sampling and oxygen isotope analysis of a number of sheep teeth (M2, n = 8) from four late Roman and Medieval sites (dating from 4th to 15th century AD), in order to assess potential variations in season of birth between the different sites and through time. In comparison with published data from herds of known birth season, incremental enamel data from the Flemish sites are consistent with late winter/spring births, with the possibility of some instances of slightly earlier parturition. These findings suggest that manipulation of season of birth was not a feature of the sheep husbandry-based economies of early historic Flanders, further evidencing that wool production was the main purpose of contemporary sheep rearing in the region. Manipulation of season of birth is not likely to have afforded economic advantage in wool-centred economies, unlike in some milk- or meat-based regimes.

Self-assembly of a dual functional bioactive peptide amphiphile incorporating both matrix metalloprotease substrate and cell adhesion motifs

We describe a bioactive lipopeptide that combines the capacity to promote the adhesion and subsequent self-detachment of live cells, using template-cell-environment feedback interactions. This self-assembling peptide amphiphile comprises a diene-containing hexadecyl lipid chain (C16e) linked to a matrix metalloprotease-cleavable sequence, Thr-Pro-Gly-Pro-Gln-Gly-Ile-Ala-Gly-Gln, and contiguous with a cell-attachment and signalling motif, Arg-Gly-Asp-Ser. Biophysical characterisation revealed that the PA self-assembles into 3 nm diameter spherical micelles above a critical aggregation concentration (cac). In addition, when used in solution at 5–150 nM (well below the cac), the PA is capable of forming film coatings that provide a stable surface for human corneal fibroblasts to attach and grow. Furthermore, these coatings were demonstrated to be sensitive to metalloproteases expressed endogenously by the attached cells, and consequently to elicit the controlled detachment of cells without compromising their viability. As such, this material constitutes a novel class of multi-functional coating for both fundamental and clinical applications in tissue engineering.

Comparative in situ analyses of cell wall matrix polysaccharide dynamics in developing rice and wheat grain

Cell wall polysaccharides of wheat and rice endosperm are an important source of dietary fibre. Monoclonal antibodies specific to cell wall polysaccharides were used to determine polysaccharide dynamics during the development of both wheat and rice grain. Wheat and rice grain present near synchronous developmental processes and significantly different endosperm cell wall compositions, allowing the localisation of these polysaccharides to be related to developmental changes. Arabinoxylan (AX) and mixed-linkage glucan (MLG) have analogous cellular locations in both species, with deposition of AX and MLG coinciding with the start of grain filling. A glucuronoxylan (GUX) epitope was detected in rice, but not wheat endosperm cell walls. Callose has been reported to be associated with the formation of cell wall outgrowths during endosperm cellularisation and xyloglucan is here shown to be a component of these anticlinal extensions, occurring transiently in both species. Pectic homogalacturonan (HG) was abundant in cell walls of maternal tissues of wheat and rice grain, but only detected in endosperm cell walls of rice in an unesterified HG form. A rhamnogalacturonan-I (RG-I) backbone epitope was observed to be temporally regulated in both species, detected in endosperm cell walls from 12 DAA in rice and 20 DAA in wheat grain. Detection of the LM5 galactan epitope showed a clear distinction between wheat and rice, being detected at the earliest stages of development in rice endosperm cell walls, but not detected in wheat endosperm cell walls, only in maternal tissues. In contrast, the LM6 arabinan epitope was detected in both species around 8 DAA and was transient in wheat grain, but persisted in rice until maturity.