Studying advanced mathematics in England: findings from a survey of student choices and attitudes

The UK Government has set a goal that the “vast majority” of students in England will be studying mathematics to the age of 18 by the end of the decade. The policy levers for achieving this goal include new Core Maths qualifications, designed for over 200,000 students who have achieved good grades at the age of 16 but then opt out of advanced or A level mathematics. This article reports findings from a cluster-sampled survey of over 10,000 17-year-olds in England in 2015. Participants’ views on post-16 mathematics are presented and discussed. The main finding is that they are strongly opposed to the idea of compulsory mathematical study, but are less antithetical to being encouraged to study mathematics beyond 16. We consider how attitudes vary by gender, prior attainment, study patterns and future aspirations. The article considers the implications of these findings in the current policy landscape.     

Evaluation of Selected Binding Domains for the Analysis of Ubiquitinated Proteomes

Ubiquitination is an abundant post-translational modification that consists of covalent attachment of ubiquitin to lysine residues or the N-terminus of proteins. Mono- and polyubiquitination have been shown to be involved in many critical eukaryotic cellular functions and are often disrupted by intracellular bacterial pathogens. Affinity enrichment of ubiquitinated proteins enables global analysis of this key modification. In this context, the use of ubiquitin-binding domains is a promising but relatively unexplored alternative to more broadly used immunoaffinity or tagged affinity enrichment methods. In this study, we evaluated the application of eight ubiquitin-binding domains that have differing affinities for ubiquitination states. Small-scale proteomics analysis identified ~200 ubiquitinated protein candidates per ubiquitin-binding domain pull-down experiment. Results from subsequent Western blot analyses that employed anti-ubiquitin or monoclonal antibodies against polyubiquitination at lysine 48 and 63 suggest that ubiquitin-binding domains from Dsk2 and ubiquilin-1 have the broadest specificity in that they captured most types of ubiquitination, whereas the binding domain from NBR1 was more selective to polyubiquitination. These data demonstrate that with optimized purification conditions, ubiquitin-binding domains can be an alternative tool for proteomic applications. This approach is especially promising for the analysis of tissues or cells resistant to transfection, of which the overexpression of tagged ubiquitin is a major hurdle.

The fan-pall imbedding theorem over formally real fields

The converse of the Cauchy interlacing theorem, relating eigenvalues of a symmetric real matrix and eigenvalues of a principal submatrix, first proved by Fan and Pall, is extended to the case of symmetric matrices with entries in an arbitrary formally real field.     

The effect of tax depreciation on the stochastic replacement policy

The optimal replacement policy for an asset subject to a stochastic deteriorating operating cost is determined for three different tax depreciation schedules and a known re-investment cost, as the solution to a two-factor model using a quasi-analytical method. We find that tax depreciation exerts a critical influence over the replacement policy by lowering the operating cost thresholds. Although typically a decline in the corporate tax rate, increase in any initial capital allowance, or decrease in the depreciation lifetime (increase in depreciation rate) results in a lower operating cost threshold which justifies replacing older equipment, these results are not universal, and indeed for younger age assets the result may be the opposite. An accelerating depreciation schedule may incentivize early replacement in a deterministic context, but not necessarily for an environment of uncertainty.     

The Skyrme model with pion masses

We study the SU(2) × SU(2) Skyrme model with an explicit chiral breaking term. The new quantities that we evaluate are the pion-nucleon sigma term and the isovector charge radii, whose values come out in reasonable agreement with experiment. The other static properties of nucleons differ by a few percent from the corresponding values in the chiral limit.