A fast two-grid and finite section method for a class of integral equations on the real line with application to an acoustic scattering problem in the half-plane

We consider the numerical treatment of second kind integral equations on the real line of the form ∅(s) = ∫_(-∞)^(+∞)▒〖κ(s-t)z(t)ϕ(t)dt,s=R〗 (abbreviated ϕ= ψ+K_z ϕ) in which K ϵ L_1 (R), z ϵ L_∞ (R) and ψ ϵ BC(R), the space of bounded continuous functions on R, are assumed known and ϕ ϵ BC(R) is to be determined. We first derive sharp error estimates for the finite section approximation (reducing the range of integration to [-A, A]) via bounds on (1-K_z )^(-1)as an operator on spaces of weighted continuous functions. Numerical solution by a simple discrete collocation method on a uniform grid on R is then analysed: in the case when z is compactly supported this leads to a coefficient matrix which allows a rapid matrix-vector multiply via the FFT. To utilise this possibility we propose a modified two-grid iteration, a feature of which is that the coarse grid matrix is approximated by a banded matrix, and analyse convergence and computational cost. In cases where z is not compactly supported a combined finite section and two-grid algorithm can be applied and we extend the analysis to this case. As an application we consider acoustic scattering in the half-plane with a Robin or impedance boundary condition which we formulate as a boundary integral equation of the class studied. Our final result is that if z (related to the boundary impedance in the application) takes values in an appropriate compact subset Q of the complex plane, then the difference between ϕ(s)and its finite section approximation computed numerically using the iterative scheme proposed is ≤C_1 [kh log⁡〖(1⁄kh)+(1-Θ)^((-1)⁄2) (kA)^((-1)⁄2) 〗 ] in the interval [-ΘA,ΘA](Θ<1) for kh sufficiently small, where k is the wavenumber and h the grid spacing. Moreover this numerical approximation can be computed in ≤C_2 N log⁡N operations, where N = 2A/h is the number of degrees of freedom. The values of the constants C1 and C2 depend only on the set Q and not on the wavenumber k or the support of z.

Noise propagation from a cutting of arbitrary cross-section and impedance

A boundary integral equation is described for the prediction of acoustic propagation from a monofrequency coherent line source in a cutting with impedance boundary conditions onto surrounding flat impedance ground. The problem is stated as a boundary value problem for the Helmholtz equation and is subsequently reformulated as a system of boundary integral equations via Green's theorem. It is shown that the integral equation formulation has a unique solution at all wavenumbers. The numerical solution of the coupled boundary integral equations by a simple boundary element method is then described. The convergence of the numerical scheme is demonstrated experimentally. Predictions of A-weighted excess attenuation for a traffic noise spectrum are made illustrating the effects of varying the depth of the cutting and the absorbency of the surrounding ground surface.

The impedance boundary value problem for the Helmholtz equation in a half-plane

We prove unique existence of solution for the impedance (or third) boundary value problem for the Helmholtz equation in a half-plane with arbitrary L∞ boundary data. This problem is of interest as a model of outdoor sound propagation over inhomogeneous flat terrain and as a model of rough surface scattering. To formulate the problem and prove uniqueness of solution we introduce a novel radiation condition, a generalization of that used in plane wave scattering by one-dimensional diffraction gratings. To prove existence of solution and a limiting absorption principle we first reformulate the problem as an equivalent second kind boundary integral equation to which we apply a form of Fredholm alternative, utilizing recent results on the solvability of integral equations on the real line in [5].

A uniformly valid far field asymptotic expansion of the green function for two-dimensional propagation above a homogeneous impedance plane

A generalized asymptotic expansion in the far field for the problem of cylindrical wave reflection at a homogeneous impedance plane is derived. The expansion is shown to be uniformly valid over all angles of incidence and values of surface impedance, including the limiting cases of zero and infinite impedance. The technique used is a rigorous application of the modified steepest descent method of Ot

Efficient calculation of the green function for acoustic propagation above a homogeneous impedance plane

This paper is concerned with the problem of propagation from a monofrequency coherent line source above a plane of homogeneous surface impedance. The solution of this problem occurs in the kernel of certain boundary integral equation formulations of acoustic propagation above an impedance boundary, and the discussion of the paper is motivated by this application. The paper starts by deriving representations, as Laplace-type integrals, of the solution and its first partial derivatives. The evaluation of these integral representations by Gauss-Laguerre quadrature is discussed, and theoretical bounds on the truncation error are obtained. Specific approximations are proposed which are shown to be accurate except in the very near field, for all angles of incidence and a wide range of values of surface impedance. The paper finishes with derivations of partial results and analogous Laplace-type integral representations for the case of a point source.

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.

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.

A new governance perspective on port–hinterland relationships: the Port Hinterland Impact (PHI) matrix

We develop a new governance perspective on port–hinterland linkages and related port impacts. Many stakeholders in a port’s hinterland now demand tangible economic benefits from port activities, as a precondition for supporting port expansion and infrastructural investments. We use a governance lens to assess this farsighted contracting challenge. We find that most contemporary economic impact assessments of port investment projects pay scant attention to the contractual relationship challenges in port-hinterland relationships. In contrast, we focus explicitly on the spatial distribution of such impacts and the related contractual relationship issues facing port authorities or port users and their stakeholders in the port hinterland. We introduce a new concept, the Port Hinterland Impact (PHI) matrix, which focuses explicitly on the spatial distribution of port impacts and related contractual relationship challenges. The PHI matrix offers insight into port impacts using two dimensions: logistics dedicatedness, as an expression of Williamsonian asset specificity in the sphere of logistics contractual relationships, and geographic reach, with a longer reach typically reflecting the need for more complex contacting to overcome ‘distance’ challenges with external stakeholders. We use the PHI matrix in our empirical, governance-based analysis of contractual relationships between the port authorities in Antwerp and Zeebrugge, and their respective stakeholders.

Regulation of cell migration in cancer: investigation into the regulation of cancer cell blebbing in the extracellular matrix

Cell migration is a highly coordinated process and any aberration in the regulatory mechanisms could result in pathological conditions such as cancer. The ability of cancer cells to disseminate to distant sites within the body has made it difficult to treat. Cancer cells also exhibit plasticity that makes them able to interconvert from an elongated, mesenchymal morphology to an amoeboid blebbing form under different physiological conditions. Blebs are spherical membrane protrusions formed by actomyosin-mediated contractility of cortical actin resulting in increased hydrostatic pressure and subsequent detachment of the membrane from the cortex. Tumour cells use blebbing as an alternative mode of migration by squeezing through preexisting gaps in the ECM, and bleb formation is believed to be mediated by the Rho-ROCK signaling pathway. However, the involvement of transmembrane water and ion channels in cell blebbing has not been examined. In the present study, the role of the transmembrane water channels, aquaporins, transmembrane ion transporters and lipid signaling enzymes in the regulation of blebbing was investigated. Using 3D matrigel matrix as an in vitro model to mimic normal extracellular matrix, and a combination of confocal and time-lapse microscopy, it was found that AQP1 knockdown by siRNA ablated blebbing of HT1080 and ACHN cells, and overexpression of AQP1-GFP not only significantly increased bleb size with a corresponding decrease in bleb numbers, but also induced bleb formation in non-blebbing cell lines. Importantly, AQP1 overexpression reduces bleb lifespan due to faster bleb retraction. This novel finding of AQP1-facilitated bleb retraction requires the activity of the Na+/H+ pump as inhibition of the ion transporter, which was found localized to intracellular vesicles, blocked bleb retraction in both cell lines. This study also demonstrated that a differential regulation of cell blebbing by AQP isoforms exists as knockdown of AQP5 had no effect on bleb formation. Data from this study also demonstrates that the lipid signaling PLD2 signals through PA in the LPA-LPAR-Rho-ROCK axis to positively regulate bleb formation in both cell lines. Taken together, this work provides a novel role of AQP1 and Na+/H+ pump in regulation of cell blebbing, and this could be exploited in the development of new therapy to treat cancer.

The compositional and configurational heterogeneity of matrix habitats shape woodland carabid communities in wooded-agricultural landscapes

Landscape heterogeneity (the composition and configuration of matrix habitats) plays a major role in shaping species communities in wooded-agricultural landscapes. However, few studies consider the influence of different types of semi-natural and linear habitats in the matrix, despite their known ecological value for biodiversity. Objective To investigate the importance of the composition and configuration of matrix habitats for woodland carabid communities and identify whether specific landscape features can help to maintain long-term populations in wooded-agricultural environments. Methods Carabids were sampled from woodlands in 36 tetrads of 4 km2 across southern Britain. Landscape heterogeneity including an innovative representation of linear habitats was quantified for each tetrad. Carabid community response was analysed using ordination methods combined with variation partitioning and additional response trait analyses. Results Woodland carabid community response was trait-specific and better explained by simultaneously considering the composition and configuration of matrix habitats. Semi-natural and linear features provided significant refuge habitat and functional connectivity. Mature hedgerows were essential for slow-dispersing carabids in fragmented landscapes. Species commonly associated with heathland were correlated with inland water and woodland patches despite widespread heathland conversion to agricultural land, suggesting that species may persist for some decades when elements representative of the original habitat are retained following landscape modification. Conclusions Semi-natural and linear habitats have high biodiversity value. Landowners should identify features that can provide additional resources or functional connectivity for species relative to other habitat types in the landscape matrix. Agri-environment options should consider landscape heterogeneity to identify the most efficacious changes for biodiversity.

On mathematical and physical principles of transformations of the coherent radar backscatter matrix

The congruential rule advanced by Graves for polarization basis transformation of the radar backscatter matrix is now often misinterpreted as an example of consimilarity transformation. However, consimilarity transformations imply a physically unrealistic antilinear time-reversal operation. This is just one of the approaches found in literature to the description of transformations where the role of conjugation has been misunderstood. In this paper, the different approaches are examined in particular in respect to the role of conjugation. In order to justify and correctly derive the congruential rule for polarization basis transformation and properly place the role of conjugation, the origin of the problem is traced back to the derivation of the antenna height from the transmitted field. In fact, careful consideration of the role played by the Green’s dyadic operator relating the antenna height to the transmitted field shows that, under general unitary basis transformation, it is not justified to assume a scalar relationship between them. Invariance of the voltage equation shows that antenna states and wave states must in fact lie in dual spaces, a distinction not captured in conventional Jones vector formalism. Introducing spinor formalism, and with the use of an alternate spin frame for the transmitted field a mathematically consistent implementation of the directional wave formalism is obtained. Examples are given comparing the wider generality of the congruential rule in both active and passive transformations with the consimilarity rule.

The “pain matrix” in pain-free individuals

Human functional imaging provides a correlative picture of brain activity during pain. A particular set of central nervous system structures (eg, the anterior cingulate cortex, thalamus, and insula) consistently respond to transient nociceptive stimuli causing pain. Activation of this so-called pain matrix or pain signature has been related to perceived pain intensity, both within and between individuals,1,2 and is now considered a candidate biomarker for pain in medicolegal settings and a tool for drug discovery. The pain-specific interpretation of such functional magnetic resonance imaging (fMRI) responses, although logically flawed,3,4 remains pervasive. For example, a 2015 review states that “the most likely interpretation of activity in the pain matrix seems to be pain.”4 Demonstrating the nonspecificity of the pain matrix requires ruling out the presence of pain when highly salient sensory stimuli are presented. In this study, we administered noxious mechanical stimuli to individuals with congenital insensitivity to pain and sampled their brain activity with fMRI. Loss-of-function SCN9A mutations in these individuals abolishes sensory neuron sodium channel Nav1.7 activity, resulting in pain insensitivity through an impaired peripheral drive that leaves tactile percepts fully intact.5 This allows complete experimental disambiguation of sensory responses and painful sensations