Combined joint fusion for index and middle carpometacarpal instability in elite boxers

Isolated instability of the index and middle finger carpometacarpal joints is uncommon. An unpublished injury pattern in a consecutive series of 13 elite boxers is described, with mid-term radiological and functional results of two novel surgical treatments. All the boxers (from Australia and the UK) were unable to compete owing to pain and weakness. Four boxers were managed initially by open reduction and temporary K-wire fixation. Nine boxers underwent primary carpometacarpal arthrodesis. All were able to return to their previous level of competition. One boxer who had undergone a soft tissue reconstruction competed at international level but required an arthrodesis because of recurrent symptoms. In elite boxers, simple reduction and wiring may be appropriate for an acute injury causing index or middle finger carpometacarpal joint instability, however, arthrodesis is the treatment of choice when instability and degenerative changes are present.

Challenging the traditional sequence of teaching introductory calculus

Despite considerable research with students of calculus, rate, and hence derivative, remain difficult concepts to teach and learn. The demonstrated lack of conceptual understanding of introductory calculus limits its usefulness in related areas. Since rate is such a troublesome concept, this study piloted reversing the usual presentation of introductory calculus to begin with area and integration, rather than rate and derivative. Two classes of first-year university students taking introductory calculus were selected to pilot the effect of changing the sequence; one class was a control group and the other class followed the reversed sequence. Advances in technology, especially computer algebra systems (CASs) may facilitate new ways of studying mathematics. In this study, handheld CASs were used to support students’ thinking as they grappled with the concepts of introductory calculus. The use of CASs enabled consideration of symbolic patterns and numerical integration leading to a deeper conceptual understanding of integration. The easy access to the multiple representations of functions provided by CASs facilitated an exploration of rate where each representation highlighted different aspects of rate resulting in deeper conceptual understanding of differentiation.

Quantifying heteroskedasticity using slope of local variances index

In econometrics, heteroskedasticity refers to the case when the variances of the error terms of the data in hand are not equal. Heteroskedastic time series are challenging to different forecasting models. However, all available solutions adopt the strategy of accommodating heteroskedasticity in the time series and consider it as a type of noise. Some statistical tests were developed over the past three decades to determine whether a time series features heteroskedastic behaviour. This paper presents a novel strategy to handle this problem by deriving a quantifying measure for heteroskedasticity. The proposed measure relies on the definition of heteroskedasticity as a time-variant variance in the time series. In this work, heteroskedasticity is measured by calculating local variances using linear filters, estimating variance trends, calculating changes in variance slopes, and finally obtaining the average slope angle. The results confirm that the proposed index complies with the widely popular heteroskedasticity tests.