Buffon's needle problem with a twist

Some simple variations of Buffon's well-known needle problem in probability are discussed, and an interesting observation connecting the corresponding results is then made

Overseas trained teachers: part of a problem or part of a solution?

Overseas trained teachers (OTTs) have grown in numbers during the past decade, particularly in London and the South East of England. In this recruitment explosion many OTTs have experienced difficulties. In professional literature as well as press coverage OTTs often become part of a deficit discourse. A small-scale pilot investigation of OTT experience has begun to suggest why OTTs have been successful as well as the principal challenges they have faced. An important factor in their success was felt to be the quality of support in school from others on the staff. Major challenges included the complexity of the primary curriculum. The argument that globalisation leads to brain-drain may be exaggerated. Suggestions for further research are made, which might indicate the positive benefits OTTs can bring to a school.

Integrable quadratic Hamiltonians on the Euclidean group of motions

In this paper, we discuss the problem of globally computing sub-Riemannian curves on the Euclidean group of motions SE(3). In particular, we derive a global result for special sub-Riemannian curves whose Hamiltonian satisfies a particular condition. In this paper, sub-Riemannian curves are defined in the context of a constrained optimal control problem. The maximum principle is then applied to this problem to yield an appropriate left-invariant quadratic Hamiltonian. A number of integrable quadratic Hamiltonians are identified. We then proceed to derive convenient expressions for sub-Riemannian curves in SE(3) that correspond to particular extremal curves. These equations are then used to compute sub-Riemannian curves that could potentially be used for motion planning of underwater vehicles.

Long-lived halocarbon trends and budgets from atmospheric chemistry modelling constrained with measurements in polar firn

The budgets of seven halogenated gases (CFC-11, CFC-12, CFC-113, CFC-114, CFC-115, CCl4 and SF6) are studied by comparing measurements in polar firn air from two Arctic and three Antarctic sites, and simulation results of two numerical models: a 2-D atmospheric chemistry model and a 1-D firn diffusion model. The first one is used to calculate atmospheric concentrations from emission trends based on industrial inventories; the calculated concentration trends are used by the second one to produce depth concentration profiles in the firn. The 2-D atmospheric model is validated in the boundary layer by comparison with atmospheric station measurements, and vertically for CFC-12 by comparison with balloon and FTIR measurements. Firn air measurements provide constraints on historical atmospheric concentrations over the last century. Age distributions in the firn are discussed using a Green function approach. Finally, our results are used as input to a radiative model in order to evaluate the radiative forcing of our target gases. Multi-species and multi-site firn air studies allow to better constrain atmospheric trends. The low concentrations of all studied gases at the bottom of the firn, and their consistency with our model results confirm that their natural sources are small. Our results indicate that the emissions, sinks and trends of CFC-11, CFC-12, CFC-113, CFC-115 and SF6 are well constrained, whereas it is not the case for CFC-114 and CCl4. Significant emission-dependent changes in the lifetimes of halocarbons destroyed in the stratosphere were obtained. Those result from the time needed for their transport from the surface where they are emitted to the stratosphere where they are destroyed. Efforts should be made to update and reduce the large uncertainties on CFC lifetimes.

Worry and problem-solving skills and beliefs in primary school children

Objective. To examine the association between worry and problem-solving skills and beliefs (confidence and perceived control) in primary school children. Method. Children (8–11 years) were screened using the Penn State Worry Questionnaire for Children. High (N ¼ 27) and low (N ¼ 30) scorers completed measures of anxiety, problem-solving skills (generating alternative solutions to problems, planfulness, and effectiveness of solutions) and problem-solving beliefs(confidence and perceived control). Results. High and low worry groups differed significantly on measures of anxiety and problem-solving beliefs (confidence and control) but not on problem-solving skills. Conclusions. Consistent with findings with adults, worry in children was associated with cognitive distortions, not skills deficits. Interventions for worried children may benefit froma focus on increasing positive problem-solving beliefs.

A model for self-directed problem-based learning for renal therapeutics

Objective To introduce a new approach to problem-based learning (PBL) for self-directed learning in renal therapeutics. Design This 5-week course, designed for large student cohorts using minimal teaching resources, was based on a series of case studies and subsequent pharmaceutical care plans, followed by intensive and regular feedback from the instructor. Assessment Assessment of achievement of the learning outcomes was based on weekly-graded care plans and peer review assessment, allowing each student to judge the contributions of each group member and their own, along with a written case-study based examination. The pharmaceutical care plan template, designed using a “tick-box” system, significantly reduced staff time for feedback and scoring. Conclusion The proposed instructional model achieved the desired learning outcomes with appropriate student feedback, while promoting skills that are essential for the students' future careers as health care professionals.

Flexible rules cum constrained discretion: a new consensus in monetary policy

This paper demonstrates that recent influential contributions to monetary policy imply an emerging consensus whereby neither rigid rules nor complete discretion are found optimal. Instead, middle-ground monetary regimes based on rules (operative under 'normal' circumstances) to anchor inflation expectations over the long run, but designed with enough flexibility to mitigate the short-run effect of shocks (with communicated discretion in 'exceptional' circumstances temporarily overriding these rules), are gaining support in theoretical models and policy formulation and implementation. The opposition of 'rules versus discretion' has, thus, reappeared as the synthesis of 'rules cum discretion', in essence as inflation-forecast targeting. But such synthesis is not without major theoretical problems, as we argue in this contribution. Furthermore, the very recent real-world events have made it obvious that the inflation targeting strategy of monetary policy, which rests upon the new consensus paradigm in modern macroeconomics is at best a 'fair weather' model. In the turbulent economic climate of highly unstable inflation, deep financial crisis and world-wide, abrupt economic slowdown nowadays this approach needs serious rethinking to say the least, if not abandoning it altogether

On the principal eigenvalue of a Robin problem with a large parameter

We study the asymptotic behaviour of the principal eigenvalue of a Robin (or generalised Neumann) problem with a large parameter in the boundary condition for the Laplacian in a piecewise smooth domain. We show that the leading asymptotic term depends only on the singularities of the boundary of the domain, and give either explicit expressions or two-sided estimates for this term in a variety of situations.

Data based constructive identification - overcoming the curse of dimensionality

The modelling of a nonlinear stochastic dynamical processes from data involves solving the problems of data gathering, preprocessing, model architecture selection, learning or adaptation, parametric evaluation and model validation. For a given model architecture such as associative memory networks, a common problem in non-linear modelling is the problem of "the curse of dimensionality". A series of complementary data based constructive identification schemes, mainly based on but not limited to an operating point dependent fuzzy models, are introduced in this paper with the aim to overcome the curse of dimensionality. These include (i) a mixture of experts algorithm based on a forward constrained regression algorithm; (ii) an inherent parsimonious delaunay input space partition based piecewise local lineal modelling concept; (iii) a neurofuzzy model constructive approach based on forward orthogonal least squares and optimal experimental design and finally (iv) the neurofuzzy model construction algorithm based on basis functions that are Bézier Bernstein polynomial functions and the additive decomposition. Illustrative examples demonstrate their applicability, showing that the final major hurdle in data based modelling has almost been removed.

The Prony fitting method for digital deconvolution problem

The Prony fitting theory is applied in this paper to solve the deconvolution problem. There are two cases in deconvolution in which unstable solution is easy to appear. They are: (1)the frequency band of known kernel is more narraw than that of the unknown kernel; (2) there exists noise. These two cases are studied thoroughly and the effectiveness of Prony fitting method is showed. Finally, this method is simulated in computer. The simulation results are compared with those obtained by using FFT method directly.

On-line handwritten segmentation in linear drawings

This paper addresses the problem of tracking line segments corresponding to on-line handwritten obtained through a digitizer tablet. The approach is based on Kalman filtering to model linear portions of on-line handwritten, particularly, handwritten numerals, and to detect abrupt changes in handwritten direction underlying a model change. This approach uses a Kalman filter framework constrained by a normalized line equation, where quadratic terms are linearized through a first-order Taylor expansion. The modeling is then carried out under the assumption that the state is deterministic and time-invariant, while the detection relies on double thresholding mechanism which tests for a violation of this assumption. The first threshold is based on an approach of layout kinetics. The second one takes into account the jump in angle between the past observed direction of layout and its current direction. The method proposed enables real-time processing. To illustrate the methodology proposed, some results obtained from handwritten numerals are presented.