Complex problems often require coordinated group effort and can consume significant resources, yet our understanding of how teams form and succeed has been limited by a lack of large-scale, quantitative data. We analyse activity traces and success levels for approximately 150 000 self-organized, online team projects. While larger teams tend to be more successful, workload is highly focused across the team, with only a few members performing most work. We find that highly successful teams are significantly more focused than average teams of the same size, that their members have worked on more diverse sets of projects, and the members of highly successful teams are more likely to be core members or ‘leads’ of other teams. The relations between team success and size, focus and especially team experience cannot be explained by confounding factors such as team age, external contributions from non-team members, nor by group mechanisms such as social loafing. Taken together, these features point to organizational principles that may maximize the success of collaborative endeavours.

We exhibit a numerical method to compute three-point branched covers of the complex projective line. We develop algorithms for working explicitly with Fuchsian triangle groups and their finite-index subgroups, and we use these algorithms to compute power series expansions of modular forms on these groups.

Given a diagram for a trisection of a 4-manifold X, we describe the homology and the intersection form of X in terms of the three subgroups of H1(Σ; Z) generated by the three sets of curves and the intersection pairing on the diagram surface Σ. This includes explicit formulas for the second and third homology groups of X as well an algorithm to compute the intersection form. Moreover, we show that all (g; k, 0, 0)-trisections admit "algebraically trivial" diagrams.

PurposeThe purpose of this paper is to evaluate the effectiveness of negotiation training delivered to senior clinicians, managers and executives, by exploring whether staff members implemented negotiation skills in their workplace following the training, and if so, how and when.Design/methodology/approachThis is a qualitative study involving face-to-face interviews with 18 senior clinicians, managers and executives who completed a two-day intensive negotiation skills training course. Interviews were transcribed verbatim, and inductive interpretive analysis techniques were used to identify common themes. Research setting was a large tertiary care hospital and health service in regional Australia.FindingsParticipants generally reported positive affective and utility reactions to the training, and attempted to implement at least some of the skills in the workplace. The main enabler was provision of a Negotiation Toolkit to assist in preparing and conducting negotiations. The main barrier was lack of time to reflect on the principles and prepare for upcoming negotiations. Participants reported that ongoing skill development and retention were not adequately addressed; suggestions for improving sustainability included provision of refresher training and mentoring.Research limitations/implicationsLimitations include self-reported data, and interview questions positively elicited examples of training translation.Practical implicationsThe training was well matched to participant needs, with negotiation a common and daily activity for most healthcare professionals. Implementation of the skills showed potential for improving collaboration and problem solving in the workplace. Practical examples of how the skills were used in the workplace are provided.Originality/valueTo the authors’ knowledge, this is the first international study aimed at evaluating the effectiveness of an integrative bargaining negotiation training program targeting executives, senior clinicians and management staff in a large healthcare organization.

We compare two naturally arising notions of ‘unknotting number’ for 2‐spheres in the 4‐sphere: namely, the minimal number of 1‐handle stabilizations needed to obtain an unknotted surface, and the minimal number of Whitney moves required in a regular homotopy to the unknotted 2‐sphere. We refer to these invariants as the stabilization number and the Casson–Whitney number of the sphere, respectively. Using both algebraic and geometric techniques, we show that the stabilization number is bounded above by one more than the Casson–Whitney number. We also provide explicit families of spheres for which these invariants are equal, as well as families for which they are distinct. Furthermore, we give additional bounds for both invariants, concrete examples of their non‐additivity, and applications to classical unknotting number of 1‐knots.