Numerical computation of an analytic singular value decomposition of a matrix valued function

This paper extends the singular value decomposition to a path of matricesE(t). An analytic singular value decomposition of a path of matricesE(t) is an analytic path of factorizationsE(t)=X(t)S(t)Y(t) T whereX(t) andY(t) are orthogonal andS(t) is diagonal. To maintain differentiability the diagonal entries ofS(t) are allowed to be either positive or negative and to appear in any order. This paper investigates existence and uniqueness of analytic SVD's and develops an algorithm for computing them. We show that a real analytic pathE(t) always admits a real analytic SVD, a full-rank, smooth pathE(t) with distinct singular values admits a smooth SVD. We derive a differential equation for the left factor, develop Euler-like and extrapolated Euler-like numerical methods for approximating an analytic SVD and prove that the Euler-like method converges.

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.

Self-assembly of a peptide amphiphile containing l-carnosine and its mixtures with a multilamellar vesicle forming lipid

The self-assembly of the peptide amphiphile (PA) hexadecyl-(β-alaninehistidine) is examined in aqueous solution, along with its mixtures with multilamellar vesicles formed by DPPC (dipalmitoyl phosphatidylcholine). This PA, denoted C16-βAH, contains a dipeptide headgroup corresponding to the bioactive molecule L-carnosine. It is found to selfassemble into nanotapes based on stacked layers of molecules. Bilayers are found to coexist with monolayers in which the PA molecules pack with alternating up−down arrangement so that the headgroups decorate both surfaces. The bilayers become dehydrated as PA concentration increases and the number of layers in the stack decreases to produce ultrathin nanotapes comprised of 2−3 bilayers. Addition of the PA to DPPC multilamellar vesicles leads to a transition to well-defined unilamellar vesicles. The unique ability to modulate the stacking of this PA as a function of concentration, combined with its ability to induce a multilamellar to unilamellar thinning of DPPC vesicles, may be useful in biomaterials applications where the presentation of the peptide function at the surface of self-assembled nanostructures is crucial.

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.

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.

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.

Synaptic vesicle glycoprotein 2A modulates vesicular release and calcium channel function at peripheral sympathetic synapses

Synaptic vesicle glycoprotein (SV)2A is a transmembrane protein found in secretory vesicles and is critical for Ca2+-dependent exocytosis in central neurons, although its mechanism of action remains uncertain. Previous studies have proposed, variously, a role of SV2 in the maintenance and formation of the readily releasable pool (RRP) or in the regulation of Ca2+ responsiveness of primed vesicles. Such previous studies have typically used genetic approaches to ablate SV2 levels; here, we used a strategy involving small interference RNA (siRNA) injection to knockdown solely presynaptic SV2A levels in rat superior cervical ganglion (SCG) neuron synapses. Moreover, we investigated the effects of SV2A knockdown on voltage-dependent Ca2+ channel (VDCC) function in SCG neurons. Thus, we extended the studies of SV2A mechanisms by investigating the effects on vesicular transmitter release and VDCC function in peripheral sympathetic neurons. We first demonstrated an siRNA-mediated SV2A knockdown. We showed that this SV2A knockdown markedly affected presynaptic function, causing an attenuated RRP size, increased paired-pulse depression and delayed RRP recovery after stimulus-dependent depletion. We further demonstrated that the SV2A–siRNA-mediated effects on vesicular release were accompanied by a reduction in VDCC current density in isolated SCG neurons. Together, our data showed that SV2A is required for correct transmitter release at sympathetic neurons. Mechanistically, we demonstrated that presynaptic SV2A: (i) acted to direct normal synaptic transmission by maintaining RRP size, (ii) had a facilitatory role in recovery from synaptic depression, and that (iii) SV2A deficits were associated with aberrant Ca2+ current density, which may contribute to the secretory phenotype in sympathetic peripheral neurons.

Culture bag systems for clinical applications of adult human neural crest-derived stem cells

Introduction Facing the challenging treatment of neurodegenerative diseases as well as complex craniofacial injuries such as those common after cancer therapy, the field of regenerative medicine increasingly relies on stem cell transplantation strategies. Here, neural crest-derived stem cells (NCSCs) offer many promising applications, although scale up of clinical-grade processes prior to potential transplantations is currently limiting. In this study, we aimed to establish a clinical-grade, cost-reducing cultivation system for NCSCs isolated from the adult human nose using cGMP-grade Afc-FEP bags. Methods We cultivated human neural crest-derived stem cells from inferior turbinate (ITSCs) in a cell culture bag system using Afc-FEP bags in human blood plasma-supplemented medium. Investigations of viability, proliferation and expression profile of bag-cultured ITSCs were followed by DNA-content and telomerase activity determination. Cultivated ITSCs were introduced to directed in vitro differentiation assays to assess their potential for mesodermal and ectodermal differentiation. Mesodermal differentiation was determined using an enzyme activity assay (alkaline phosphatase, ALP), respective stainings (Alizarin Red S, Von Kossa and Oil Red O), and RT-PCR, while immunocytochemistry and synaptic vesicle recycling were applied to assay neuroectodermal differentiation of ITSCs. Results When cultivated within Afc-FEP bags, ITSCs grew three-dimensionally in a human blood plasma-derived matrix, thereby showing unchanged morphology, proliferation capability, viability and expression profile in comparison to three dimensionally-cultured ITSCs growing in standard cell culture plastics. Genetic stability of bag-cultured ITSCs was further accompanied by unchanged telomerase activity. Importantly, ITSCs retained their potential to differentiate into mesodermal cell types, particularly including ALP-active, Alizarin Red S-, and Von Kossa-positive osteogenic cell types, as well as adipocytes positive in Oil Red O assays. Bag culture further did not affect the potential of ITSCs to undergo differentiation into neuroectodermal cell types coexpressing β-III-tubulin and MAP2 and exhibiting the capability for synaptic vesicle recycling. Conclusions Here, we report for the first time the successful cultivation of human NCSCs within cGMP-grade Afc-FEP bags using a human blood plasma-supplemented medium. Our findings particularly demonstrate the unchanged differentiation capability and genetic stability of the cultivated NCSCs, suggesting the great potential of this culture system for future medical applications in the field of regenerative medicine.

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.

Investigating the influence of extracellular matrix and glycolytic metabolism on muscle stem cell migration on their native fibre environment

The composition of the extracellular matrix (ECM) of skeletal muscle fibres is a unique environment that supports the regenerative capacity of satellite cells; the resident stem cell population. The impact of environment has great bearing on key properties permitting satellite cells to carry out tissue repair. In this study, we have investigated the influence of the ECM and glycolytic metabolism on satellite cell emergence and migration- two early processes required for muscle repair. Our results show that both influence the rate at which satellite cells emerge from the sub-basal lamina position and their rate of migration. These studies highlight the necessity of performing analysis of satellite behaviour on their native substrate and will inform on the production of artificial scaffolds intended for medical uses.