Retracts of vertex sets of trees and the almost stability theorem

Let G be a group, let T be an (oriented) G-tree with finite edge stabilizers, and let VT denote the vertex set of T. We show that, for each G-retract V' of the G-set VT, there exists a G-tree whose edge stabilizers are finite and whose vertex set is V'. This fact leads to various new consequences of the almost stability theorem. We also give an example of a group G, a G-tree T and a G-retract V' of VT such that no G-tree has vertex set V'.Comment: 15 pages, 0 figures. Formerly titled "Some refinements of the almost stability theorem". Version

Chair Support, Faculty Entrepreneurship, and the Teaching of Statistical Reasoning to Journalism Undergraduates in the United States

Statistical reasoning is not the same as doing calculations. Instead, it involves cognitive skills such as the ability to think critically and systematically with data, skills important for everyday news work and essential for the era of data journalism. Twin surveys of the chairs of undergraduate journalism programs in the United States, conducted 11 years apart, revealed that those who perceived benefits from statistical reasoning instruction were more likely to reward entrepreneurship (faculty attempts to integrate this instruction into their classes), but with slow gains over time in the fairly small number of such faculty. Being consistent with university goals in statistical reasoning instruction appeared to motivate chairs’ reward decisions in both waves. Increasingly, they took into account what they saw as the general value of statistical reasoning for their students and the competitive edge it could give them in the journalism job market. Perceived constraints to teaching this content had no apparent overall impact on reward decisions