No abstract

In a previous paper Sharkey et al. [14] proved the exactness of closures at the level of triples for Markovian SIR (susceptible-infected-removed) dynamics on tree-like networks. This resulted in a deterministic representation of the epidemic dynamics on the network that can be numerically evaluated. In this paper, we extend this modelling framework to certain classes of networks exhibiting loops. We show that closures where the loops are kept intact are exact, and lead to a simplified and numerically solvable system of ODEs (ordinary-differential-equations). The findings of the paper lead us to a generalisation of closures that are based on partitioning the network around nodes that are cut-vertices (i.e. the removal of such a node leads to the network breaking down into at least two disjointed components or subnetworks). Exploiting this structural property of the network yields some natural closures, where the evolution of a particular state can typically be exactly given in terms of the corresponding or projected states on the subnetworks and the cut-vertex. A byproduct of this analysis is an alternative probabilistic proof of the exactness of the closures for tree-like networks presented in Sharkey et al. [14]. In this paper we also elaborate on how the main result can be applied to more realistic networks, for which we write down the ODEs explicitly and compare output from these to results from simulation. Furthermore, we give a general, recipe-like method of how to apply the reduction by closures technique for arbitrary networks, and give an upper bound on the maximum number of equations needed for an exact representation.

In analyses of transcripts from 108 3-man groups, perceived leaders participated significantly more than nonleaders in production, discussion, and problem solving tasks. With the effect of overall participation partialed out, very few behavioral differences between leaders and nonleaders remained. However, high participation was neither a sufficient nor necessary condition for perceived leadership. High participators, not perceived as leaders, emphasized activities detrimental to group creativity and deemphasized facilitative activities. Although it was not possible to account for the leadership ratings of most low participators, for some it appeared that nominal leadership assignments made by E were not altered by an appointed leader's relative lack of participation in his group. (17 ref.)

A SYSTEMATIC INVESTIGATION OF THE EFFECTS ON GROUP INTERACTION OF 2 TASK CHARACTERISTICS: TASK TYPE (PRODUCTION, DISCUSSION, PROBLEM SOLVING), AND LEVEL OF DIFFICULTY (HIGH, MEDIUM, LOW). EVIDENCE WAS ALSO GATHERED ON THE EFFECTS OF ORDINAL POSITION. ANALYSIS OF TRANSCRIPTS FROM 108 3-MAN GROUPS INDICATED THAT TASK TYPE SIGNIFICANTLY AFFECTED THE DISTRIBUTION OF MORE THAN 60% OF THE GROUP ACTIVITY, WITH PRODUCTION (CREATIVITY) AND DISCUSSION TASKS BEING LEAST ALIKE. TASK DIFFICULTY HAD LESS EFFECT ON GROUP ACTIVITY. SIGNIFICANT CHANGES WERE FOUND IN GROUP ACTIVITY FROM THE 1ST TO THE 4TH TASK SESSIONS. THE DATA WERE INTERPRETED IN TERMS OF METHODOLOGICAL IMPLICATIONS FOR SMALL-GROUP RESEARCH, AND SEVERAL RESEARCH STRATEGIES WERE PROPOSED TO MINIMIZE THESE METHODOLOGICAL PROBLEMS. (36 REF.)