Braid groups of imprimitive complex reflection groups

We obtain new presentations for the imprimitive complex reflection groups of type $(de,e,r)$ and their braid groups $B(de,e,r)$ for $d,r \ge 2$. Diagrams for these presentations are proposed. The presentations have much in common with Coxeter presentations of real reflection groups. They are positive and homogeneous, and give rise to quasi-Garside structures. Diagram automorphisms correspond to group automorphisms. The new presentation shows how the braid group $B(de,e,r)$ is a semidirect product of the braid group of affine type $\widetilde A_{r-1}$ and an infinite cyclic group. Elements of $B(de,e,r)$ are visualized as geometric braids on $r+1$ strings whose first string is pure and whose winding number is a multiple of $e$. We classify periodic elements, and show that the roots are unique up to conjugacy and that the braid group $B(de,e,r)$ is strongly translation discrete.Comment: published versio

Conjugacy in singular Artin monoids

We define a notion of conjugacy in singular Artin moniods, and solve the corresponding conjugacy problem for finite types. We sgiw that this definition is appropriate to describe type (1) singular Markov moves on singular braids. Parabolic submonoids of singular Artin monoids are defined and, in finite type, are shown to be singular Artin monoids. Solutions to conjugacy-type problems of parabolic submonoids are described. Geometric objects defined by Fenn, Rolfsen and Zhu, called (j, k)-bands, are algebraically characterised, and a procedure is given which determines when a word represents a (j, k)-ban

A SMASHing approach for developing staff and student digital capabilities within a community of practice

SMASH is a student-led partnership which considers how social media could be used to enhance learning and teaching. Mentored by their tutor, members of the team identified three key areas where social media may be utilised: within learning activities, as a means of organising learning and as a way of showcasing learning. The three strands of this framework have provided a focus to develop a range of resources and the foundation for a digital toolkit. This case study reflects upon not just the outputs developed thus far, but also on the experience, the learning gained and the sense of belonging and identify as a result of being part of this community of practice

Implementing a hybrid cognitive-behavioural therapy for pain-related insomnia in primary care : lessons learnt from a mixed-methods feasibility study

Objectives: To test the feasibility of implementing a brief but intensive hybrid cognitive behavioural therapy (Hybrid CBT) for pain-related insomnia. Design: Mixed-methods, with qualitative process evaluation on a two-arm randomised controlled feasibility trial. Setting: Primary care. Participants: Twenty-five adult patients with chronic pain and insomnia. Intervention: Hybrid CBT or self-help control intervention. Primary and secondary outcome measures: Primary outcomes measures were the Insomnia Severity Index and interference scale of the Brief Pain Inventory (BPI). Secondary outcomes measures were the present pain intensity rating from the BPI, Multidimensional Fatigue Inventory, Hospital Anxiety and Depression Scale and EQ-5D-5L. Results: Fourteen participants were randomised to receive Hybrid CBT, 11 to receive the self-help control treatment. Of the 14 in the Hybrid CBT group, 9 (64%) completed all four treatment sessions (4 discontinued due to poor health; 1 due to time constraints). Adherence to the self-help control treatment was not monitored. The total number of participants completing the 12-week and 24-week follow-ups were 12 (6 in each group; Hybrid CBT: 43%; self-help: 55%) and 10 (5 in each group; Hybrid CBT: 36%; self-help: 45%). Based on the data available, candidate outcome measures appeared to be sensitive to changes associated with interventions. Thematic analysis of pre-postintervention interview data revealed satisfaction with treatment content among those who completed the Hybrid CBT, whereas those in the self-help control treatment wanted more contact hours and therapist guidance. Other practical suggestions for improvement included shortening the duration of each treatment session, reducing the amount of assessment paperwork, and minimising the burden of sleep and pain monitoring. Conclusion: Important lessons were learnt with regard to the infrastructure required to achieve better patient adherence and retention. Based on the qualitative feedback provided by a subset of treatment completers, future trials should also consider lowering the intensity of treatment and streamlining the data collection procedure. Trial registration number: ISRCTN17294365