Censoring Outdegree Compromises Inferences of Social Network Peer Effects and Autocorrelation

I examine the consequences of modelling contagious influence in a social network with incomplete edge information, namely in the situation where each individual may name a limited number of friends, so that extra outbound ties are censored. In particular, I consider a prototypical time series configuration where a property of the "ego" is affected in a causal fashion by the properties of their "alters" at a previous time point, both in the total number of alters as well as the deviation from a central value. This is considered with three potential methods for naming one's friends: a strict upper limit on the number of declarations, a flexible limit, and an instruction where a person names a prespecified fraction of their friends. I find that one of two effects is present in the estimation of these effects: either that the size of the effect is inflated in magnitude, or that the estimators instead are centered about zero rather than related to the true effect. The degree of heterogeneity in friend count is one of the major factors into whether such an analysis can be salvaged by post-hoc adjustments.Comment: 22 pages, 8 figure

The Effect of Secret Clock Manipulation on 10 km Cycle Time Trial Performance.

The anticipatory RPE feedback model (Tucker 2009) proposes that during self paced exercise tasks, muscular work is continually regulated through comparison of a subconscious ‘template’ Rating of Perceived Exertion (RPE) that serves to protect against the development of catastrophic physiological failure, and a ‘conscious’ RPE that is generated through afferent feedback with regards to peripheral physiological status and through psychological inputs. The aim of this study was to investigate the effect of altering psychological inputs via incorrect time feedback on both RPE and performance during a series of maximal effort 10km cycle time trials. After task familiarisation, eight participants performed three separate time trials using their own cycle mounted onto the Kingcycle ergometer rig. Distance covered was available via large visual display along with elapsed time. On one occasion the display clock ran at the correct speed, but on two other occasions the clock manipulation was altered so that it ran either 10% too fast or 10% too slow. The order of the interventions was randomised. Although no significant differences were observed in total performance time, the magnitude of the endspurt participants were able to generate in the final 10% of the trial was significantly (P<0.01) greater during the slow clock trials than during the fast clock trials. Despite differences in pace distribution under each clock condition, a similar generally linear increase in RPE was observed throughout trials in all conditions. It is proposed that these findings lend support to the anticipatory RPE feedback model, and that altered psychological inputs probably act by influencing the fraction of metabolic reserve capacity that can be accessed during such trials

Generating the Johnson filtration

For k >= 1, let Torelli_g^1(k) be the k-th term in the Johnson filtration of the mapping class group of a genus g surface with one boundary component. We prove that for all k, there exists some G_k >= 0 such that Torelli_g^1(k) is generated by elements which are supported on subsurfaces whose genus is at most G_k. We also prove similar theorems for the Johnson filtration of Aut(F_n) and for certain mod-p analogues of the Johnson filtrations of both the mapping class group and of Aut(F_n). The main tools used in the proofs are the related theories of FI-modules (due to the first author together with Ellenberg and Farb) and central stability (due to the second author), both of which concern the representation theory of the symmetric groups over Z.Comment: 32 pages; v2: paper reorganized. Final version, to appear in Geometry and Topolog