Steiner’s formula in the Heisenberg group

Steiner’s tube formula states that the volume of an ϵ-neighborhood of a smooth regular domain in Rn is a polynomial of degree n in the variable ϵ whose coefficients are curvature integrals (also called quermassintegrals). We prove a similar result in the sub-Riemannian setting of the first Heisenberg group. In contrast to the Euclidean setting, we find that the volume of an ϵ-neighborhood with respect to the Heisenberg metric is an analytic function of ϵ that is generally not a polynomial. The coefficients of the series expansion can be explicitly written in terms of integrals of iteratively defined canonical polynomials of just five curvature terms.

Theoretical models of planetary system formation II. Post-formation evolution

Aims. We extend the results of planetary formation synthesis by computing the long-term evolution of synthetic systems from the clearing of the gas disk into the dynamical evolution phase. Methods. We use the symplectic integrator SyMBA to numerically integrate the orbits of planets for 100 Myr, using populations from previous studies as initial conditions. Results. We show that within the populations studied, mass and semimajor axis distributions experience only minor changes from post-formation evolution. We also show that, depending upon their initial distribution, planetary eccentricities can statistically increase or decrease as a result of gravitational interactions. We find that planetary masses and orbital spacings provided by planet formation models do not result in eccentricity distributions comparable to observed exoplanet eccentricities, requiring other phenomena, such as stellar fly-bys, to account for observed eccentricities.

Relative Distribution Methods in Stata

The concept of the relative density seems like a fruitful nonparametric approach to studying distributional differences between groups (Handcock and Morris 1999), yet it appears that the technique has gone more or less unnoticed in applied social science research. A scarcity of canned software might be one of the reasons the method is underutilized. Therefore, I present a new Stata command called reldist to plot the relative density, decompose distributional differences into location and shape effects, and compute relative distribution summary measures. The command is illustrated by an application comparing earnings by sex.

Relational Memory Is Evident in Eye Movement Behavior despite the Use of Subliminal Testing Methods

While it is generally agreed that perception can occur without awareness, there continues to be debate about the type of representational content that is accessible when awareness is minimized or eliminated. Most investigations that have addressed this issue evaluate access to well-learned representations. Far fewer studies have evaluated whether or not associations encountered just once prior to testing might also be accessed and influence behavior. Here, eye movements were used to examine whether or not memory for studied relationships is evident following the presentation of subliminal cues. Participants (assigned to experimental or control groups) studied scene-face pairs and test trials evaluated implicit and explicit memory for these pairs. Each test trial began with a subliminal scene cue, followed by three visible studied faces. For experimental group participants, one face was the studied associate of the scene (implicit test); for controls none were a match. Subsequently, the Display containing a match was presented to both groups, but now it was preceded by a visible scene cue (explicit test). Eye movements were recorded and recognition Memory responses were made. Participants in the experimental group looked disproportionately at matching faces on implicit test trials and participants from both groups looked disproportionately at matching faces on explicit test trials, even when that face had not been successfully identified as the associate. Critically, implicit memory-based viewing effects seemed not to depend on residual awareness of subliminal scenes cues, as subjective and objective measures indicated that scenes were successfully masked from view. The reported outcomes indicate that memory for studied relationships can be expressed in eye movement behavior without awareness.

Time-differentiated target temperature management after out-of-hospital cardiac arrest: a multicentre, randomised, parallel-group, assessor-blinded clinical trial (the TTH48 trial): study protocol for a randomised controlled trial

BACKGROUND The application of therapeutic hypothermia (TH) for 12 to 24 hours following out-of-hospital cardiac arrest (OHCA) has been associated with decreased mortality and improved neurological function. However, the optimal duration of cooling is not known. We aimed to investigate whether targeted temperature management (TTM) at 33 ± 1 °C for 48 hours compared to 24 hours results in a better long-term neurological outcome. METHODS The TTH48 trial is an investigator-initiated pragmatic international trial in which patients resuscitated from OHCA are randomised to TTM at 33 ± 1 °C for either 24 or 48 hours. Inclusion criteria are: age older than 17 and below 80 years; presumed cardiac origin of arrest; and Glasgow Coma Score (GCS) <8, on admission. The primary outcome is neurological outcome at 6 months using the Cerebral Performance Category score (CPC) by an assessor blinded to treatment allocation and dichotomised to good (CPC 1-2) or poor (CPC 3-5) outcome. Secondary outcomes are: 6-month mortality, incidence of infection, bleeding and organ failure and CPC at hospital discharge, at day 28 and at day 90 following OHCA. Assuming that 50 % of the patients treated for 24 hours will have a poor outcome at 6 months, a study including 350 patients (175/arm) will have 80 % power (with a significance level of 5 %) to detect an absolute 15 % difference in primary outcome between treatment groups. A safety interim analysis was performed after the inclusion of 175 patients. DISCUSSION This is the first randomised trial to investigate the effect of the duration of TTM at 33 ± 1 °C in adult OHCA patients. We anticipate that the results of this trial will add significant knowledge regarding the management of cooling procedures in OHCA patients. TRIAL REGISTRATION NCT01689077.