Let $\eta (G)$ be the number of conjugacy classes of maximal cyclic subgroups of G. We prove that if G is a p-group of order $p^n$ and nilpotence class l, then $\eta (G)$ is bounded below by a linear function in $n/l$ .

Morgan and Parker proved that if G is a group with ${\textbf{Z}(G)} = 1$ , then the connected components of the commuting graph of G have diameter at most $10$ . Parker proved that if, in addition, G is solvable, then the commuting graph of G is disconnected if and only if G is a Frobenius group or a $2$ -Frobenius group, and if the commuting graph of G is connected, then its diameter is at most $8$ . We prove that the hypothesis $Z (G) = 1$ in these results can be replaced with $G' \cap {\textbf{Z}(G)} = 1$ . We also prove that if G is solvable and $G/{\textbf{Z}(G)}$ is either a Frobenius group or a $2$ -Frobenius group, then the commuting graph of G is disconnected.

Cognitive-behavioural therapy (CBT) is an effective treatment for depressed adults. CBT interventions are complex, as they include multiple content components and can be delivered in different ways. We compared the effectiveness of different types of therapy, different components and combinations of components and aspects of delivery used in CBT interventions for adult depression. We conducted a systematic review of randomised controlled trials in adults with a primary diagnosis of depression, which included a CBT intervention. Outcomes were pooled using a component-level network meta-analysis. Our primary analysis classified interventions according to the type of therapy and delivery mode. We also fitted more advanced models to examine the effectiveness of each content component or combination of components. We included 91 studies and found strong evidence that CBT interventions yielded a larger short-term decrease in depression scores compared to treatment-as-usual, with a standardised difference in mean change of −1.11 (95% credible interval −1.62 to −0.60) for face-to-face CBT, −1.06 (−2.05 to −0.08) for hybrid CBT, and −0.59 (−1.20 to 0.02) for multimedia CBT, whereas wait list control showed a detrimental effect of 0.72 (0.09 to 1.35). We found no evidence of specific effects of any content components or combinations of components. Technology is increasingly used in the context of CBT interventions for depression. Multimedia and hybrid CBT might be as effective as face-to-face CBT, although results need to be interpreted cautiously. The effectiveness of specific combinations of content components and delivery formats remain unclear. Wait list controls should be avoided if possible.

OBJECTIVES/SPECIFIC AIMS: To use a systematic and iterative process to develop and refine toolkits to support dissemination and implementation (D&I) research. METHODS/STUDY POPULATION: Participants included research staff from the Dissemination and Implementation Research Core (DIRC), a research methods core from the Institute of Clinical and Translational Science at Washington University in St. Louis, other D&I experts from the University, and national experts from the D&I field. This project used education design research methodology and a systematic and iterative process involving several phases. The first phase (preliminary research and initial development) consisted of analysis of the educational problem and its context, and led to the development of toolkit prototypes and plans for their implementation. In the second phase (development and formative evaluation), toolkits were iteratively evaluated with emphasis on content validity and consistency and effectiveness as perceived by the users. Finally, in the summative evaluation, the toolkits were evaluated based on their use as intended. RESULTS/ANTICIPATED RESULTS: Our team identified the target audience as DIRC customers and investigators from disciplines across the University, and found that resources for beginners to D&I were lacking. The team developed 8 toolkits: (1) Introduction to D&I; (2) How to develop D&I Aims; (3) D&I Designs; (4) Implementation Outcomes; (5) Implementation Organizational Measures; (6) Assessing Barriers and Facilitators; (7) D&I Designs; and (8) Guideline research. These prototypes were iteratively revised for content validity and consistency. Finally, each toolkit was evaluated by two national experts in D&I science, and further refined. DISCUSSION/SIGNIFICANCE OF IMPACT: This systematic and cyclical process led to the development of 8 toolkits to support researchers in D&I science, which are now available on the DIRC Web site. This set the stage for development of new toolkits as additional needs are identified.

In this study photo-identification data were used to better understand movements, population structure and abundance of common bottlenose dolphin (Tursiops truncatus) in south-west England and surrounding waters, to inform conservation efforts. A catalogue of 485 photographic sightings of 113 individuals was compiled from ~150 common bottlenose dolphin encounters made on 87 dates between March 2007 and January 2014. From these and other data, three likely sub-populations were identified in the western English Channel, demarcated by bathymetry and distance to land: (1) south-west England – inshore Cornwall to Devon, (2) offshore English/French waters and (3) inshore France from Brittany to Normandy. Maximum abundance estimates for south-west England coastal waters, using two methods, ranged between 102 and 113 (range 87–142, 95% CL) over the period 2008–2013, likely qualifying the region as nationally important, whilst the yearly maximum was 58 in 2013. The population was centred on Cornwall, where 19 well-marked animals were considered ‘probable’ residents. There were no ‘probable’ resident well-marked individuals found to be restricted to either Devon or Dorset, with animals moving freely within coastal areas across the three counties. Movements were also detected within offshore English waters and French waters (from other studies) of the western English Channel, but no interchange has as yet been detected between the three regions, highlighting the possible separation of the populations, though sample sizes are insufficient to confirm this. Given the findings, south-west England waters should be considered as a separate management unit requiring targeted conservation efforts.

We welcome Kline's attempt to develop an overarching framework to allow much needed collaboration between fields in the study of teaching. While we see much utility in this enterprise, we are concerned that there is too much focus on the behavior of the teacher, without examining results or costs, and the categories within the framework are not sufficiently distinct.