A technique for delivering individualised formative problems and examples

Active learning plays a strong role in mathematics and statistics, and formative problems are vital for developing key problem-solving skills. To keep students engaged and help them master the fundamentals before challenging themselves further, we have developed a system for delivering problems tailored to a student‟s current level of understanding. Specifically, by adapting simple methodology from clinical trials, a framework for delivering existing problems and other illustrative material has been developed, making use of macros in Excel. The problems are assigned a level of difficulty (a „dose‟), and problems are presented to the student in an order depending on their ability, i.e. based on their performance so far on other problems. We demonstrate and discuss the application of the approach with formative examples developed for a first year course on plane coordinate geometry, and also for problems centred on the topic of chi-square tests.

Solar influence on global and regional climates

The literature relevant to how solar variability influences climate is vast—but much has been based on inadequate statistics and non-robust procedures. The common pitfalls are outlined in this review. The best estimates of the solar influence on the global mean air surface temperature show relatively small effects, compared with the response to anthropogenic changes (and broadly in line with their respective radiative forcings). However, the situation is more interesting when one looks at regional and season variations around the global means. In particular, recent research indicates that winters in Eurasia may have some dependence on the Sun, with more cold winters occurring when the solar activity is low. Advances in modelling ‘‘top-down’’ mechanisms, whereby stratospheric changes influence the underlying troposphere, offer promising explanations of the observed phenomena. In contrast, the suggested modulation of low-altitude clouds by galactic cosmic rays provides an increasingly inadequate explanation of observations.

Law and the power of feminism: how marriage lost its power to oppress women

In Feminism and the Power of Law Carol Smart argued that feminists should use non-legal strategies rather than looking to law to bring about women’s liberation. This article seeks to demonstrate that, as far as marriage is concerned, she was right. Statistics and contemporary commentary show how marriage, once the ultimate and only acceptable status for women, has declined in social significance to such an extent that today it is a mere lifestyle choice. This is due to many factors, including the ‘sexual revolution’ of the 1960s, improved education and job opportunities for women, and divorce law reform, but the catalyst for change was the feminist critique that called for the abandonment (rather than the reform) of the institution and made the unmarried state possible for women. I conclude that this loss of significance has been more beneficial to British women in terms of the possibility of ‘liberation’ than appeals for legal change and recognition, and that we should continue to be wary of looking to law to solve women’s problems.

Probability of survival in a random exchange economy with dependent agents

In this paper I analyze the general equilibrium in a random Walrasian economy. Dependence among agents is introduced in the form of dependency neighborhoods. Under the uncertainty, an agent may fail to survive due to a meager endowment in a particular state (direct effect), as well as due to unfavorable equilibrium price system at which the value of the endowment falls short of the minimum needed for survival (indirect terms-of-trade effect). To illustrate the main result I compute the stochastic limit of equilibrium price and probability of survival of an agent in a large Cobb-Douglas economy.

Integrating science into humanitarian and development planning and practice to enhance community resilience

There has been an increased emphasis upon the application of science for humanitarian and development planning, decision-making and practice; particularly in the context of understanding, assessing and anticipating risk (e.g. HERR, 2011). However, there remains very little guidance for practitioners on how to integrate sciences they may have had little contact with in the past (e.g. climate). This has led to confusion as to which ‘science’ might be of use and how it would be best utilised. Furthermore, since this integration has stemmed from a need to be more predictive, agencies are struggling with the problems associated with uncertainty and probability. Whilst a range of expertise is required to build resilience, these guidelines focus solely upon the relevant data, information, knowledge, methods, principles and perspective which scientists can provide, that typically lie outside of current humanitarian and development approaches. Using checklists, real-life case studies and scenarios the full guidelines take practitioners through a five step approach to finding, understanding and applying science. This document provides a short summary of the five steps and some key lessons for integrating science.

Real-time factor model forecasting and the effects of instability

Factor forecasting models are shown to deliver real-time gains over autoregressive models for US real activity variables during the recent period, but are less successful for nominal variables. The gains are largely due to the Financial Crisis period, and are primarily at the shortest (one quarter ahead) horizon. Excluding the pre-Great Moderation years from the factor forecasting model estimation period (but not from the data used to extract factors) results in a marked fillip in factor model forecast accuracy, but does the same for the AR model forecasts. The relative performance of the factor models compared to the AR models is largely unaffected by whether the exercise is in real time or is pseudo out-of-sample.

Turbulent structure and scaling of the inertial subrange in a stratocumulus-topped boundary layer observed by a Doppler lidar

The turbulent structure of a stratocumulus-topped marine boundary layer over a 2-day period is observed with a Doppler lidar at Mace Head in Ireland. Using profiles of vertical velocity statistics, the bulk of the mixing is identified as cloud driven. This is supported by the pertinent feature of negative vertical velocity skewness in the sub-cloud layer which extends, on occasion, almost to the surface. Both coupled and decoupled turbulence characteristics are observed. The length and timescales related to the cloud-driven mixing are investigated and shown to provide additional information about the structure and the source of the mixing inside the boundary layer. They are also shown to place constraints on the length of the sampling periods used to derive products, such as the turbulent dissipation rate, from lidar measurements. For this, the maximum wavelengths that belong to the inertial subrange are studied through spectral analysis of the vertical velocity. The maximum wavelength of the inertial subrange in the cloud-driven layer scales relatively well with the corresponding layer depth during pronounced decoupled structure identified from the vertical velocity skewness. However, on many occasions, combining the analysis of the inertial subrange and vertical velocity statistics suggests higher decoupling height than expected from the skewness profiles. Our results show that investigation of the length scales related to the inertial subrange significantly complements the analysis of the vertical velocity statistics and enables a more confident interpretation of complex boundary layer structures using measurements from a Doppler lidar.

Uniform factorial decay estimate for the remainder of rough Taylor expansion

We establish an uniform factorial decay estimate for the Taylor approximation of solutions to controlled differential equations. Its proof requires a factorial decay estimate for controlled paths which is interesting in its own right.

University teaching: recognition and reward

Teaching in universities has increased in importance in recent years which, in part, is a consequence of the change in funding of universities from block grants to student tuition fees. Various initiatives have been made which serve to raise the profile of teaching and give it greater recognition. It is also important that teaching is recognised even more fully and widely, and crucially that it is rewarded accordingly. We propose a mechanism for recognising and rewarding university teaching that is based on a review process that is supported by documented evidence whose outcomes can be fed into performance and development reviews, and used to inform decisions about reward and promotion, as well as the review of probationary status where appropriate.