Combinatorics of tight geodesics and stable lengths

We give an algorithm to compute the stable lengths of pseudo-Anosovs on the curve graph, answering a question of Bowditch. We also give a procedure to compute all invariant tight geodesic axes of pseudo-Anosovs. Along the way we show that there are constants $1<a_1<a_2$ such that the minimal upper bound on `slices' of tight geodesics is bounded below and above by $a_1^{\xi(S)}$ and $a_2^{\xi(S)}$, where $\xi(S)$ is the complexity of the surface. As a consequence, we give the first computable bounds on the asymptotic dimension of curve graphs and mapping class groups. Our techniques involve a generalization of Masur--Minsky's tight geodesics and a new class of paths on which their tightening procedure works.Comment: 19 pages, 2 figure

Principal agent problems under loss aversion: an application to executive stock options

Executive stock options reward success but do not penalise failure. In contrast, the standard principalagent model implies that pay is normally monotonically increasing in performance. This paper shows that, under loss aversion, the use of carrots but not sticks is a feature of an optimal compensation contract. Low risk aversion and high loss aversion is particularly propitious to the use of options. Moreover, loss aversion on the part of executives explains the award of at the money options rather than discounted stock or bonus related pay. Other features of stock option grants are also explained, such as resetting or reloading with an exercise price equal to the current stock price

A Narrative Structure for Teacher Educator Team Analysis and Development

United Kingdom (UK) teacher educators in the midst of professional practice changes have been reported to find benefit in being exposed to different theories with a view to resolving conflicting demands and developing new perspectives. This paper provides a synthesis of theories that can help teacher educator teams in universities to make sense of changes in practice together. The theoretical synthesis presented includes models of stages of team development, sense-making, experiential learning and complexity science principles. It is here argued that such a deftly applied synthesis can then facilitate higher education institution (HEI) education department teams to create individual narratives with a view to then sharing them with each other to develop a group narrative. The purpose and benefits of this would immediately be sought in improving team functioning and performance in order to create a more solid foundation from which individuals might even begin to engage in career development along the fellowship trajectory assumed by the UK Higher Education Academy (HEA). A key assumption this paper rests on therefore is that team functioning is a positive asset that is pivotal to individual career development and prerequisite impacts on teaching and learning, and leadership and management of coaching and mentoring with respect to these in a department or team. The contribution this paper makes therefore is a practical approach for analysing and further developing academic teams of teacher educators in a landscape of continual professional change, with a greater theoretical toolkit to draw from to achieve this

Information literacy and the secondary school

Maximising student attainment is a key issue for every secondary school. Student attainment can be improved by raising their information literacy levels. It is part of a school librarian’s role to promote these skills. This is complicated by the absence of information literacy in secondary school curricula, teachers’ low awareness of the concept and the lack of teacher training in the professional education of librarians. There are a range of definitions and different approaches to teaching information literacy published leading to conflict over choices. Overall there is a lack of empirically tested pedagogy, particularly for synthesis and assessment. This research explores what it means to be information literate and addresses the fundamental question of ‘How can we raise information literacy levels in a secondary school? The research strategy explored the teachers’ perspectives to ascertain their perceptions of information literacy, how it is currently taught by them and their understanding of the librarian’s role. The research was conducted in a secondary school where semi-structured interviews were used with a sample of twelve teachers selected by age, experience and subject. The analysis examined three diverse teacher voices and compared these with insights from the remaining nine teachers’ perspectives. The research findings show that teachers view information literacy differently. This is shaped by the role of information in their subject’s approach to learning. Student progress to higher information literacy levels requires a pedagogy that is situated in subject teaching, rather than generic sessions, with clarity of how skills are deployed in different subject contexts to support learning transfer and work that is differentiated to meet different learning needs. Conceptually it was found that information literacy is contingent upon the context in which it is being used. A new instrument has been designed depicting progress in information literacy to stimulate thinking about possible pedagogy and assessment

Neotropical Bird Migration During The Ice Ages: Orientation And Ecology

Reconstruction of breeding habitat of North American Neotropical migrants 18,000 years ago and 9,000 years ago indicated major shifts in both location and composition of plant communities relative to present conditions. Increased vegetation in xeric areas may have compensated, at least in part, for the reduction in breeding habitat due to glaciation. Autumnal flights of Neotropical passerine migrants flying on constant headings from North America to Central and South America were simulated under present wind conditions and for winds during periods of glaciation at 18,000 and 9,000 years ago. The 155 degrees average headings currently observed for Atlantic migrants were found to function well during periods of glaciation and may have been more generally useful during those times than at present