Obtaining presentations from group actions without making choices

Obtaining presentations from group actions without making choices

Consider a group G acting nicely on a simply-connected simplicial complex X . Numerous classical methods exist for using this group action to produce a presentation for G. For the case that X/G is 2-connected, we give a new method that has the novelty that one does not have to identify a fundamental domain for the action. Indeed, the resulting presentation is canonical in the sense that no arbi...

Making Choices between Rules or between Actions

A new study by Klaes et al. in this issue of Neuron shows that the brain can simultaneously apply two rules to the same sensory information in order to specify two parallel potential action goals, which then compete for execution in the sensorimotor system.

The priority heuristic: making choices without trade-offs.

Bernoulli's framework of expected utility serves as a model for various psychological processes, including motivation, moral sense, attitudes, and decision making. To account for evidence at variance with expected utility, the authors generalize the framework of fast and frugal heuristics from inferences to preferences. The priority heuristic predicts (a) the Allais paradox, (b) risk aversion f...

Making safer treatment choices

Some Challenging Group Presentations

We study some challenging presentations which arise as groups of deeciency zero. In four cases we settle niteness: we show that two presentations are for nite groups while two are for innnite groups. Thus we answer three explicit questions in the literature and we provide the rst published deeciency zero presentation for a group with soluble length seven. The tools we use are coset enumeration ...