Variational approach in weighted Sobolev spaces to scattering by unbounded rough surfaces

We consider the problem of scattering of time harmonic acoustic waves by an unbounded sound soft surface which is assumed to lie within a finite distance of some plane. The paper is concerned with the study of an equivalent variational formulation of this problem set in a scale of weighted Sobolev spaces. We prove well-posedness of this variational formulation in an energy space with weights which extends previous results in the unweighted setting [S. Chandler-Wilde and P. Monk, SIAM J. Math. Anal., 37 (2005), pp. 598–618] to more general inhomogeneous terms in the Helmholtz equation. In particular, in the two-dimensional case, our approach covers the problem of plane wave incidence, whereas in the three-dimensional case, incident spherical and cylindrical waves can be treated. As a further application of our results, we analyze a finite section type approximation, whereby the variational problem posed on an infinite layer is approximated by a variational problem on a bounded region.

A moving-mesh finite element method and its application to the numerical solution of phase-change problems

A distributed Lagrangian moving-mesh finite element method is applied to problems involving changes of phase. The algorithm uses a distributed conservation principle to determine nodal mesh velocities, which are then used to move the nodes. The nodal values are obtained from an ALE (Arbitrary Lagrangian-Eulerian) equation, which represents a generalization of the original algorithm presented in Applied Numerical Mathematics, 54:450--469 (2005). Having described the details of the generalized algorithm it is validated on two test cases from the original paper and is then applied to one-phase and, for the first time, two-phase Stefan problems in one and two space dimensions, paying particular attention to the implementation of the interface boundary conditions. Results are presented to demonstrate the accuracy and the effectiveness of the method, including comparisons against analytical solutions where available.

Visual surveillance for moving vehicles

An overview is given of a vision system for locating, recognising and tracking multiple vehicles, using an image sequence taken by a single camera mounted on a moving vehicle. The camera motion is estimated by matching features on the ground plane from one image to the next. Vehicle detection and hypothesis generation are performed using template correlation and a 3D wire frame model of the vehicle is fitted to the image. Once detected and identified, vehicles are tracked using dynamic filtering. A separate batch mode filter obtains the 3D trajectories of nearby vehicles over an extended time. Results are shown for a motorway image sequence.

Visual surveillance for moving vehicles

An overview is given of a novel vision system for locating, recognising and tracking multiple vehicles.

Velocity-based moving mesh methods for nonlinear partial differential equations

This article describes a number of velocity-based moving mesh numerical methods formultidimensional nonlinear time-dependent partial differential equations (PDEs). It consists of a short historical review followed by a detailed description of a recently developed multidimensional moving mesh finite element method based on conservation. Finite element algorithms are derived for both mass-conserving and non mass-conserving problems, and results shown for a number of multidimensional nonlinear test problems, including the second order porous medium equation and the fourth order thin film equation as well as a two-phase problem. Further applications and extensions are referenced.

Moving feedback forward: theory to practice

There is substantial research interest in tutor feedback and students’ perception and use of such feedback. This paper considers some of the major issues raised in relation to tutor feedback and student learning. We explore some of the current feedback drivers, most notably the need for feedback to move away from simply a monologue from a tutor to a student to a valuable tutor–student dialogue. In relation to moving feedback forward the notions of self regulation, dialogue and social learning are explored and then considered in relation to how such theory can translate into practice. The paper proposes a framework (GOALS) as a tool through which tutors can move theory into practice with the aim of improving student learning from feedback.

Citation and peer review of data: moving towards formal data publication

This paper discusses many of the issues associated with formally publishing data in academia, focusing primarily on the structures that need to be put in place for peer review and formal citation of datasets. Data publication is becoming increasingly important to the scientific community, as it will provide a mechanism for those who create data to receive academic credit for their work and will allow the conclusions arising from an analysis to be more readily verifiable, thus promoting transparency in the scientific process. Peer review of data will also provide a mechanism for ensuring the quality of datasets, and we provide suggestions on the types of activities one expects to see in the peer review of data. A simple taxonomy of data publication methodologies is presented and evaluated, and the paper concludes with a discussion of dataset granularity, transience and semantics, along with a recommended human-readable citation syntax.

ASSET: moving forward through feedback

Providing high quality and timely feedback to students is often a challenge for many staff in higher education as it can be both time-consuming and frustratingly repetitive. From the student perspective, feedback may sometimes be considered unhelpful, confusing and inconsistent and may not always be provided within a timeframe that is considered to be ‘useful’. The ASSET project, based at the University of Reading, addresses many of these inherent challenges by encouraging the provision of feedback that supports learning, i.e. feedback that contains elements of ‘feed-forward’, is of a high quality and is delivered in a timely manner. In particular, the project exploits the pedagogic benefits of video/audio media within a Web 2.0 context to provide a new, interactive resource, ‘ASSET’, to enhance the feedback experience for both students and staff. A preliminary analysis of both our quantitative and qualitative pedagogic data demonstrate that the ASSET project has instigated change in the ways in which both staff and students think about, deliver, and engage with feedback. For example, data from our online questionnaires and focus groups with staff and students indicate a positive response to the use of video as a medium for delivering feedback to students. In particular, the academic staff engaged in piloting the ASSET resource indicated that i) using video has made them think more, and in some cases differently, about the ways in which they deliver feedback to students and ii) they now see video as an effective means of making feedback more useful and engaging for students. Moreover, the majority of academic staff involved in the project have said they will continue to use video feedback. From the student perspective, 60% of those students whose lecturers used ASSET to provide video feedback said that “receiving video feedback encouraged me to take more notice of the feedback compared with normal methods” and 80% would like their lecturer to continue to use video as a method for providing feedback. An important aim of the project was for it to complement existing University-wide initiatives on feedback and for ASSET to become a ‘model’ resource for staff and students wishing to explore video as a medium for feedback provision. An institutional approach was therefore adopted and key members of Senior Management, academics, T&L support staff, IT support and Student Representatives were embedded within the project from the start. As with all initiatives of this kind, a major issue is the future sustainability of the ASSET resource and to have had both ‘top-down’ and ‘bottom-up’ support for the project has been extremely beneficial. In association with the project team the University is currently exploring the creation of an open-source, two-tiered video supply solution and a ‘framework’ (that other HEIs can adopt and/or adapt) to support staff in using video for feedback provision. In this way students and staff will have new opportunities to explore video and to exploit the benefits of this medium for supporting learning.

Time weighted portfolio optimisation

In estimating the inputs into the Modern Portfolio Theory (MPT) portfolio optimisation problem, it is usual to use equal weighted historic data. Equal weighting of the data, however, does not take account of the current state of the market. Consequently this approach is unlikely to perform well in any subsequent period as the data is still reflecting market conditions that are no longer valid. The need for some return-weighting scheme that gives greater weight to the most recent data would seem desirable. Therefore, this study uses returns data which are weighted to give greater weight to the most recent observations to see if such a weighting scheme can offer improved ex-ante performance over that based on un-weighted data.

Collision prediction of a moving object within a virtual world

This paper provides a solution for predicting moving/moving and moving/static collisions of objects within a virtual environment. Feasible prediction in real-time virtual worlds can be obtained by encompassing moving objects within a sphere and static objects within a convex polygon. Fast solutions are then attainable by describing the movement of objects parametrically in time as a polynomial.

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,