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.

The dependent variable problem in quantitative studies of Active Labour Market Programmes: uncovering hidden dynamics?

The question of what explains variation in expenditures on Active Labour Market Programs (ALMPs) has attracted significant scholarship in recent years. Significant insights have been gained with respect to the role of employers, unions and dual labour markets, openness, and partisanship. However, there remain significant disagreements with respects to key explanatory variables such the role of unions or the impact of partisanship. Qualitative studies have shown that there are both good conceptual reasons as well as historical evidence that different ALMPs are driven by different dynamics. There is little reason to believe that vastly different programs such as training and employment subsidies are driven by similar structural, interest group or indeed partisan dynamics. The question is therefore whether different ALMPs have the same correlation with different key explanatory variables identified in the literature? Using regression analysis, this paper shows that the explanatory variables identified by the literature have different relation to distinct ALMPs. This refinement adds significant analytical value and shows that disagreements are at least partly due to a dependent variable problem of ‘over-aggregation’.

Reported assembly scenes in Greek Tragedy

This paper presents a detailed consideration of the three democratic assembly meetings that are reported in Greek tragedy. The three scenes in their different ways reveal a preoccupation with a tension between elite rhetoric and popular wisdom in a democracy. Behind this preoccupation lies a shared assumption: that many people attended assemblies expecting their minds to be made up; and that persuasive oratory and the popular judgment of persuasive oratory could have a decisive influence on a vote.

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.

Pronoun ambiguity resolution in Greek: evidence from monolingual adults and children

A large body of psycholinguistic research has revealed that during sentence interpretation adults coordinate multiple sources of information. Particularly, they draw both on linguistic properties of the message and on information from the context to constrain their interpretations. Relatively little however is known about how this integrative processor develops through language acquisition and about how children process language. In this study, two on-line picture verification tasks were used to examine how 1st, 2nd and 4th/5th grade monolingual Greek children resolve pronoun ambiguities during sentence interpretation and how their performance compares to that of adults on the same tasks. Specifically, we manipulated the type of subject pronoun, i.e. null or overt, and examined how this affected participants’ preferences for competing antecedents, i.e. in the subject or object position. The results revealed both similarities and differences in how adults and the various child groups comprehended ambiguous pronominal forms. Particularly, although adults and children alike showed sensitivity to the distribution of overt and null subject pronouns, this did not always lead to convergent interpretation preferences.

Financial protection in the UK building industry: a guide for clients and the construction supply chain.

There is a clear need for financial protection in the construction industry, both to guarantee satisfactory completion of construction projects and to guard against non-payment. However, the cost of financial protection is often felt to be disproportionately high, with unnecessary overlap between different measures. The Reading Construction Forum has commissioned and steered research which is published in this report in an effort to bring the problem out into the open and to clarify the various options open to the various parties and stakeholders in the construction process. "Financial Protection in the UK Building Industry" is the first definitive report on the subject, offering an accurate and simple guide that all levels within the construction industry can understand. This accessible new guide considers the problem of financial protection and clearly lays out the alternative solutions.It looks by turn at the client, the main contractor, and the sub-contractor, discussing which financial protection options are available to each of them, and considers the pros and cons of each option. The cost of each type of financial protection is weighed against the amount of protection provided and the risks involved. The book concludes with guidance for consultants, emphasising relevant points to consider when advising clients and contractors about which type of financial protection to choose. "Financial Protection in the UK Building Industry" was researched by a literature search, collection of statistical data, and financial data, as well as discussions with clients, contractors, sub-contractors and consultants. This investigation has shown that the direct costs of implementing financial protection measures are marginal, and that wider adoption of payment protection would create a more equitable situation between contracting parties.This guide will enable anyone in the construction industry to consider all the options, and determine what is the best solution for them. "Reading Construction Forum Financial Protection for the UK Building Industry" was complied by the University of Reading, funded by the Reading Construction Forum. The Forum has recently commissioned and steered a number of high-profile reports covering important aspects of the construction industry. Members of the Forum include major companies which are concerned with achieving high quality in the design, construction and use of commercial, retail and industrial buildings. All are committed to change and innovation in the British and European construction industries.

Switching on a two-dimensional time-harmonic scalar wave in the presence of a diffracting edge

This paper concerns the switching on of two-dimensional time-harmonic scalar waves. We first review the switch-on problem for a point source in free space, then proceed to analyse the analogous problem for the diffraction of a plane wave by a half-line (the ‘Sommerfeld problem’), determining in both cases the conditions under which the field is well-approximated by the solution of the corresponding frequency domain problem. In both cases the rate of convergence to the frequency domain solution is found to be dependent on the strength of the singularity on the leading wavefront. In the case of plane wave diffraction at grazing incidence the frequency domain solution is immediately attained along the shadow boundary after the arrival of the leading wavefront. The case of non-grazing incidence is also considered.

The acquisition of person and number morphology within the verbal domain in Early Greek

The aim of this paper is to examine the acquisition pattern of person and number verb morphology within the generative framework and to compare the results of the analyses with previous research in Greek and other European languages. The study considers previous data on the acquisition of subject-verb agreement, and thereafter, examines the acquisition of person and number morphology in a new dataset of two monolingual Greek-speaking children. The analyses present quantitative data of accuracy of person and number marking, error data, and qualitative analyses addressing the productivity of person and number marking. The results suggest that person and number morphology is used correctly and productively from a very early age in Greek speaking children. The findings provide new insight into early Greek language acquisition and are also relevant for research in early development of languages with rich inflectional morphology.

Processing coordinate subject-verb agreement in L1 and L2 Greek

The present study examines the processing of subject-verb (SV) number agreement with coordinate subjects in pre-verbal and post-verbal positions in Greek. Greek is a language with morphological number marked on nominal and verbal elements. Coordinate SV agreement, however, is special in Greek as it is sensitive to the coordinate subject's position: when pre-verbal, the verb is marked for plural while when post-verbal the verb can be in the singular. We conducted two experiments, an acceptability judgment task with adult monolinguals as a pre-study (Experiment 1) and a self-paced reading task as the main study (Experiment 2) in order to obtain acceptance as well as processing data. Forty adult monolingual speakers of Greek participated in Experiment 1 and a hundred and forty one in Experiment 2. Seventy one children participated in Experiment 2: 30 Albanian-Greek sequential bilingual children and 41 Greek monolingual children aged 10–12 years. The adult data in Experiment 1 establish the difference in acceptability between singular VPs in SV and VS constructions reaffirming our hypothesis. Meanwhile, the adult data in Experiment 2 show that plural verbs accelerate processing regardless of subject position. The child online data show that sequential bilingual children have longer reading times (RTs) compared to the age-matched monolingual control group. However, both child groups follow a similar processing pattern in both pre-verbal and post-verbal constructions showing longer RTs immediately after a singular verb when the subject was pre-verbal indicating a grammaticality effect. In the post-verbal coordinate subject sentences, both child groups showed longer RTs on the first subject following the plural verb due to the temporary number mismatch between the verb and the first subject. This effect was resolved in monolingual children but was still present at the end of the sentence for bilingual children indicating difficulties to reanalyze and integrate information. Taken together, these findings demonstrate that (a) 10–12 year-old sequential bilingual children are sensitive to number agreement in SV coordinate constructions parsing sentences in the same way as monolingual children even though their vocabulary abilities are lower than that of age-matched monolingual peers and (b) bilinguals are slower in processing overall.

The acquisition of verbal paradigms in Dutch and Greek L2 children: cross-linguistic differences and inflectional defaults

Previous research with children learning a second language (L2) has reported errors with verb inflection and cross-linguistic variation in accuracy and error patterns. However, owing to the cross-linguistic complexity and diversity of different verbal paradigms, the cross-linguistic effects on the nature of default forms has not been directly addressed in L2 acquisition studies. In the present study, we compared accuracy and error patterns in verbal agreement inflections in L2 children acquiring Dutch and Greek, keeping the children’s L1 constant (Turkish). Results showed that inflectional defaults in Greek follow universal predictions regarding the morphological underspecification of paradigms. However, the same universal predictions do not apply to the same extent to Dutch. It is argued that phonological properties of inflected forms should be taken into account to explain cross-linguistic differences in the acquisition of inflection. By systematically comparing patterns in child L2 Dutch and Greek, this study shows how universal mechanisms and target language properties work in tandem in the acquisition of inflectional paradigms.