Collective communication and behaviour in response to uncertain ‘Danger’ in network experiments

In emergencies, social coordination is especially challenging. People connected with each other may respond better or worse to an uncertain danger than isolated individuals. We performed experiments involving a novel scenario simulating an unpredictable situation faced by a group in which 2480 subjects in 108 groups had to both communicate information and decide whether to ‘evacuate’. We manipulated the permissible sorts of interpersonal communication and varied group topology and size. Compared to groups of isolated individuals, we find that communication networks suppress necessary evacuations because of the spontaneous and diffuse emergence of false reassurance; yet, communication networks also restrain unnecessary evacuations in situations without disasters. At the individual level, subjects have thresholds for responding to social information that are sensitive to the negativity, but not the actual accuracy, of the signals being transmitted. Social networks can function poorly as pathways for inconvenient truths that people would rather ignore.

The geometry of k-free hyperbolic 3-manifolds

We investigate the geometry of closed, orientable, hyperbolic 3-manifolds whose fundamental groups are [Formula: see text]-free for a given integer [Formula: see text]. We show that any such manifold [Formula: see text] contains a point [Formula: see text] with the following property: If [Formula: see text] is the set of maximal cyclic subgroups of [Formula: see text] that contain non-trivial elements represented by loops of [Formula: see text], then for every subset [Formula: see text], we have rank [Formula: see text]. This generalizes to all [Formula: see text] results proved in [J. W. Anderson, R. D. Canary, M. Culler and P. B. Shalen, Free Kleinian groups and volumes of hyperbolic 3-manifolds, J. Differential Geom. 43 (1996) 738–782; M. Culler and P. B. Shalen, 4-free groups and hyperbolic geometry, J. Topol. 5 (2012) 81–136], which have been used to relate the volume of a hyperbolic manifold to its topological properties, and it strictly improves on the result obtained in [R. K. Guzman, Hyperbolic 3-manifolds with [Formula: see text]-free fundamental group, Topology Appl. 173 (2014) 142–156] for [Formula: see text]. The proof avoids the use of results about ranks of joins and intersections in free groups that were used in [M. Culler and P. B. Shalen, 4-free groups and hyperbolic geometry, J. Topol. 5 (2012) 81–136; R. K. Guzman, Hyperbolic 3-manifolds with [Formula: see text]-free fundamental group, Topology Appl. 173 (2014) 142–156].

Group, basic assumptions and complexity science

This article represents the first complete systematization of the basic assumptions as theorized by Wilfred R. Bion and post-Bionian authors. The authors reviewed, compared and systematized all the Bionian developments concerning the basic assumptions taking the prevailing anxieties, group topology, leader peculiarities, interactions with the work-group mentality into account. The analysis evinced five main ba(s) and five subsets (i.e. their features resemble one of the five main basic assumptions). Briefly, in the first paragraph the authors summarize Bionian thought and its underlying logical criteria while in the second they reviewed all the new proposals for basic assumptions emerging from the psychoanalytic literature (i.e. Lawrence, Bain and Gould, 1996; Romano, 1997; Sandler, 2002; Sarno, 1999; Turquet, 1974; Hopper, 2009). In conclusion the authors focus on the main strengths and critical points of the systematization. In the last section ‘Promising developments’ they address the methodology of the study of basic assumptions, its main features and potential developments. The article rounds off with a clinical appendix.

AUTOMATIC CONTINUITY FOR ISOMETRY GROUPS

We present a general framework for automatic continuity results for groups of isometries of metric spaces. In particular, we prove automatic continuity property for the groups of isometries of the Urysohn space and the Urysohn sphere, i.e. that any homomorphism from either of these groups into a separable group is continuous. This answers a question of Ben Yaacov, Berenstein and Melleray. As a consequence, we get that the group of isometries of the Urysohn space has unique Polish group topology and the group of isometries of the Urysohn sphere has unique separable group topology. Moreover, as an application of our framework we obtain new proofs of the automatic continuity property for the group $\text{Aut}([0,1],\unicode[STIX]{x1D706})$, due to Ben Yaacov, Berenstein and Melleray and for the unitary group of the infinite-dimensional separable Hilbert space, due to Tsankov.

Continuity properties of discontinuous homomorphisms and refinements of group topologies

We present several conditions on topological groups G and H under which every discontinuous homomorphism of G to H preserves accumulation points of open sets in G. It is also proved that every (locally) precompact abelian group admits a strictly finer zero-dimensional (locally) precompact topological group topology of the same weight as the original one.