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.

A Nyström method for a class of integral equations on the real line with applications to scattering by diffraction gratings and rough surfaces

We propose a Nystr¨om/product integration method for a class of second kind integral equations on the real line which arise in problems of two-dimensional scalar and elastic wave scattering by unbounded surfaces. Stability and convergence of the method is established with convergence rates dependent on the smoothness of components of the kernel. The method is applied to the problem of acoustic scattering by a sound soft one-dimensional surface which is the graph of a function f, and superalgebraic convergence is established in the case when f is infinitely smooth. Numerical results are presented illustrating this behavior for the case when f is periodic (the diffraction grating case). The Nystr¨om method for this problem is stable and convergent uniformly with respect to the period of the grating, in contrast to standard integral equation methods for diffraction gratings which fail at a countable set of grating periods.

Examination of wind storms over Central Europe with respect to circulation weather types and NAO phases

The occurrence of wind storms in Central Europe is investigated with respect to large-scale atmospheric flow and local wind speeds in the investigation area. Two different methods of storm identification are applied for Central Europe as the target region: one based on characteristics of large-scale flow (circulation weather types, CWT) and the other on the occurrence of extreme wind speeds. The identified events are examined with respect to the NAO phases and CWTs under which they occur. Pressure patterns, wind speeds and cyclone tracks are investigated for storms assigned to different CWTs. Investigations are based on ERA40 reanalysis data. It is shown that about 80% of the storm days in Central Europe are connected with westerly flow and that Central European storm events primarily occur during a moderately positive NAO phase, while strongly positive NAO phases (6.4% of all days) account for more than 20% of the storms. A storm occurs over Central Europe during about 10% of the days with a strong positive NAO index. The most frequent pathway of cyclone systems associated with storms over Central Europe leads from the North Atlantic over the British Isles, North Sea and southern Scandinavia into the Baltic Sea. The mean intensity of the systems typically reaches its maximum near the British Isles. Differences between the characteristics for storms identified from the CWT identification procedure (gale days, based on MSLP fields) and those from extreme winds at Central European grid points are small, even though only 70% of the storm days agree. While most storms occur during westerly flow situations, specific characteristics of storms during the other CWTs are also considered. Copyright © 2009 Royal Meteorological Society

The European storm Kyrill in January 2007: synoptic evolution, meteorological impacts and some considerations with respect to climate change

The synoptic evolution and some meteorological impacts of the European winter storm Kyrill that swept across Western, Central, and Eastern Europe between 17 and 19 January 2007 are investigated. The intensity and large storm damage associated with Kyrill is explained based on synoptic and mesoscale environmental storm features, as well as on comparisons to previous storms. Kyrill appeared on weather maps over the US state of Arkansas about four days before it hit Europe. It underwent an explosive intensification over the Western North Atlantic Ocean while crossing a very intense zonal polar jet stream. A superposition of several favourable meteorological conditions west of the British Isles caused a further deepening of the storm when it started to affect Western Europe. Evidence is provided that a favourable alignment of three polar jet streaks and a dry air intrusion over the occlusion and cold fronts were causal factors in maintaining Kyrill's low pressure very far into Eastern Europe. Kyrill, like many other strong European winter storms, was embedded in a pre-existing, anomalously wide, north-south mean sea-level pressure (MSLP) gradient field. In addition to the range of gusts that might be expected from the synoptic-scale pressure field, mesoscale features associated with convective overturning at the cold front are suggested as the likely causes for the extremely damaging peak gusts observed at many lowland stations during the passage of Kyrill's cold front. Compared to other storms, Kyrill was by far not the most intense system in terms of core pressure and circulation anomaly. However, the system moved into a pre-existing strong MSLP gradient located over Central Europe which extended into Eastern Europe. This fact is considered determinant for the anomalously large area affected by Kyrill. Additionally, considerations of windiness in climate change simulations using two state-of-the-art regional climate models driven by ECHAM5 indicate that not only Central, but also Eastern Central Europe may be affected by higher surface wind speeds at the end of the 21st century. These changes are partially associated with the increased pressure gradient over Europe which is identified in the ECHAM5 simulations. Thus, with respect to the area affected, as well as to the synoptic and mesoscale storm features, it is proposed that Kyrill may serve as an interesting study case to assess future storm impacts.

The central European floods of August 2002: Part 2 - Synoptic causes and considerations with respect to climatic change

In the first part of this paper (Ulbrich et al. 2003), we gave a description of the August 2002 rainfall events and the resultant floods, in particular of the flood wave of the River Elbe. The extreme precipitation sums observed in the first half of the month were primarily associated with two rainfall episodes. The first episode occurred on 6/7 August 2002. The main rainfall area was situated over Lower Austria, the south-western part of the Czech Republic and south-eastern Germany. A severe flash flood was produced in the Lower Austrian Waldviertel (`forest quarter’ ). The second episode on 11± 13 August 2002 most severely affected the Erz Mountains and western parts of the Czech Republic. During this second episode 312mm of rain was recorded between 0600GMT on 12 August and 0600GMT on 13 August at the Zinnwald weather station in the ErzMountains, which is a new 24-hour record for Germany. The flash floods resulting from this rainfall episode and the subsequent Elbe flood produced the most expensive weatherrelated catastrophe in Europe in recent decades. In this part of the paper we discuss the meteorological conditions and physical mechanisms leading to the two main events. Similarities to the conditions that led to the recent summer floods of the River Oder in 1997 and the River Vistula in 2001 will be shown. This will lead us to a consideration of trends in extreme rainfall over Europe which are found in numerical simulations of anthropogenic climate change.

Utilizing electronic effects in the modulation of BTPhen ligands with respect to the partitioning of minor actinides from lanthanides

Effects of bromine substitution at the 5 and 5,6-positions of the 1,10-phenanthroline nucleus of BTPhen ligand on their extraction properties for Ln(III) andAn(III) cations have been studied. Compared to C5-BTPhen, electronic modulation in BrC5-BTPhen and Br2C5-BTPhen enabled these ligands to be fine-tuned in order to enhance the separation selectivity of Am(III) from Eu(III)

Magnetic resonance imaging of a randomized controlled trial investigating predictors of recovery following psychological treatment in adolescents with moderate to severe unipolar depression: study protocol for Magnetic Resonance - Improving Mood with Psychoanalytic and Cognitive Therapies (MR-IMPACT)

Background Major depressive disorders (MDD) are a debilitating and pervasive group of mental illnesses afflicting many millions of people resulting in the loss of 110 million working days and more than 2,500 suicides per annum. Adolescent MDD patients attending NHS clinics show high rates of recurrence into adult life. A meta-analysis of recent research shows that psychological treatments are not as efficacious as previously thought. Modest treatment outcomes of approximately 65% of cases responding suggest that aetiological and clinical heterogeneity may hamper the better use of existing therapies and discovery of more effective treatments. Information with respect to optimal treatment choice for individuals is lacking, with no validated biomarkers to aid therapeutic decision-making. Methods/Design Magnetic resonance-Improving Mood with Psychoanalytic and Cognitive Therapies, the MR-IMPACT study, plans to identify brain regions implicated in the pathophysiology of depressions and examine whether there are specific behavioural or neural markers predicting remission and/or subsequent relapse in a subsample of depressed adolescents recruited to the IMPACT randomised controlled trial (Registration # ISRCTN83033550). Discussion MR-IMPACT is an investigative biomarker component of the IMPACT pragmatic effectiveness trial. The aim of this investigation is to identify neural markers and regional indicators of the pathophysiology of and treatment response for MDD in adolescents. We anticipate that these data may enable more targeted treatment delivery by identifying those patients who may be optimal candidates for therapeutic response.

[3 + 2] Cycloaddition of acetylenes with azides to give 1,4-disubstituted 1,2,3-triazoles in a modular flow reactor

The cycloaddition of acetylenes with azides to give the corresponding 1,4-disubstituted 1,2,3-triazoles is reported using immobilised reagents and scavengers in pre-packed glass tubes in a modular flow reactor.

Parabens can enable hallmarks and characteristics of cancer in human breast epithelial cells: a review of the literature with reference to new exposure data and regulatory status

A framework for understanding the complexity of cancer development was established by Hanahan and Weinberg in their definition of the hallmarks of cancer. In this review, we consider the evidence that parabens can enable development in human breast epithelial cells of 4/6 of the basic hallmarks, 1/2 of the emerging hallmarks and 1/2 of the enabling characteristics. Hallmark 1: parabens have been measured as present in 99% of human breast tissue samples, possess oestrogenic activity and can stimulate sustained proliferation of human breast cancer cells at concentrations measurable in the breast. Hallmark 2: parabens can inhibit the suppression of breast cancer cell growth by hydroxytamoxifen, and through binding to the oestrogen-related receptor gamma (ERR) may prevent its deactivation by growth inhibitors. Hallmark 3: in the 10nM to 1M range, parabens give a dose-dependent evasion of apoptosis in high-risk donor breast epithelial cells. Hallmark 4: long-term exposure (>20weeks) to parabens leads to increased migratory and invasive activity in human breast cancer cells, properties which are linked to the metastatic process. Emerging hallmark: methylparaben has been shown in human breast epithelial cells to increase mTOR, a key regulator of energy metabolism. Enabling characteristic: parabens can cause DNA damage at high concentrations in the short term but more work is needed to investigate long-term low-doses of mixtures. The ability of parabens to enable multiple cancer hallmarks in human breast epithelial cells provides grounds for regulatory review of the implications of the presence of parabens in human breast tissue.

Trans/national dis/connections: silenced networks and strained belongings with reference to Albinia Catherine MacKay and Una Marson

This paper seeks to examine the particular operations of gender and cultural politics that both shaped and restrained possible 'networked' interactions between Jamaican women and their British 'motherlands' during the first forty years of the twentieth century. Paying particular attention to the poetry of Albinia Catherine MacKay (a Scots Creole) and the political journalism of Una Marson (a black Jamaica), I shall seek to examine why both writers speak in and of voices out of place. MacKay's poems work against the critical pull of transnational modernism to reveal aesthetic and cultural isolation through a model of strained belonging in relation to both her Jamaica home and an ancestral Scotland. A small number of poems from her 1912 collection that are dedicated to the historical struggle between the English and Scots for the rule of Scotland and cultural self-determination, some of which are written in a Scottish idiom, may help us to read the complex cultural negotiations that silently inform the seemingly in commensurability of location and locution revealed in these works. In contrast, Marson's journalism, although less known even than her creative writings, is both politically and intellectually radical in its arguments concerning the mutual articulation of race and gender empowerment. However, Marson remains aware of her inability to articulate these convictions with force in a British context and thereby of the way in which speaking out of place also silences her.

Improving mood with psychoanalytic and cognitive therapies (IMPACT): a pragmatic effectiveness superiority trial to investigate whether specialised psychological treatment reduces the risk for relapse in adolescents with moderate to severe unipolar depression: study protocol for a randomised controlled trial

Background Up to 70% of adolescents with moderate to severe unipolar major depression respond to psychological treatment plus Fluoxetine (20-50 mg) with symptom reduction and improved social function reported by 24 weeks after beginning treatment. Around 20% of non responders appear treatment resistant and 30% of responders relapse within 2 years. The specific efficacy of different psychological therapies and the moderators and mediators that influence risk for relapse are unclear. The cost-effectiveness and safety of psychological treatments remain poorly evaluated. Methods/Design Improving Mood with Psychoanalytic and Cognitive Therapies, the IMPACT Study, will determine whether Cognitive Behavioural Therapy or Short Term Psychoanalytic Therapy is superior in reducing relapse compared with Specialist Clinical Care. The study is a multicentre pragmatic effectiveness superiority randomised clinical trial: Cognitive Behavioural Therapy consists of 20 sessions over 30 weeks, Short Term Psychoanalytic Psychotherapy 30 sessions over 30 weeks and Specialist Clinical Care 12 sessions over 20 weeks. We will recruit 540 patients with 180 randomised to each arm. Patients will be reassessed at 6, 12, 36, 52 and 86 weeks. Methodological aspects of the study are systematic recruitment, explicit inclusion criteria, reliability checks of assessments with control for rater shift, research assessors independent of treatment team and blind to randomization, analysis by intention to treat, data management using remote data entry, measures of quality assurance, advanced statistical analysis, manualised treatment protocols, checks of adherence and competence of therapists and assessment of cost-effectiveness. We will also determine whether time to recovery and/or relapse are moderated by variations in brain structure and function and selected genetic and hormone biomarkers taken at entry. Discussion The objective of this clinical trial is to determine whether there are specific effects of specialist psychotherapy that reduce relapse in unipolar major depression in adolescents and thereby costs of treatment to society. We also anticipate being able to utilise psychotherapy experience, neuroimaging, genetic and hormone measures to reveal what techniques and their protocols may work best for which patients.

The uniqueness of signature problem in the non-Markov setting

We establish a general framework for a class of multidimensional stochastic processes over [0,1] under which with probability one, the signature (the collection of iterated path integrals in the sense of rough paths) is well-defined and determines the sample paths of the process up to reparametrization. In particular, by using the Malliavin calculus we show that our method applies to a class of Gaussian processes including fractional Brownian motion with Hurst parameter H>1/4, the Ornstein–Uhlenbeck process and the Brownian bridge.