Height estimates for Killing graphs

The paper aims at proving global height estimates for Killing graphs defined over a complete manifold with nonempty boundary. To this end, we first point out how the geometric analysis on a Killing graph is naturally related to a weighted manifold structure, where the weight is defined in terms of the length of the Killing vector field. According to this viewpoint, we introduce some potential theory on weighted manifolds with boundary and we prove a weighted volume estimate for intrinsic balls on the Killing graph. Finally, using these tools, we provide the desired estimate for the weighted height in the assumption that the Killing graph has constant weighted mean curvature and the weighted geometry of the ambient space is suitably controlled.Comment: 26 pages. Final version. To appear on Journal of Geometric Analysi

The Impact of Acute Psychosocial Stress on Magnetoencephalographic Correlates of Emotional Attention and Exogenous Visual Attention

Stress-induced acute activation of the cerebral catecholaminergic systems has often been found in rodents. However, little is known regarding the consequences of this activation on higher cognitive functions in humans. Theoretical inferences would suggest increased distractibility in the sense of increased exogenous attention and emotional attention. The present study investigated the influence of acute stress responses on magnetoencephalographic (MEG) correlates of visual attention. Healthy male subjects were presented emotional and neutral pictures in three subsequent MEG recording sessions after being exposed to a TSST-like social stressor, intended to trigger a HPA-response. The subjects anticipation of another follow-up stressor was designed to sustain the short-lived central catecholaminergic stress reactions throughout the ongoing MEG recordings. The heart rate indicates a stable level of anticipatory stress during this time span, subsequent cortisol concentrations and self-report measures of stress were increased. With regard to the MEG correlates of attentional functions, we found that the N1m amplitude remained constantly elevated during stressor anticipation. The magnetic early posterior negativity (EPNm) was present but, surprisingly, was not at all modulated during stressor anticipation. This suggests that a general increase of the influence of exogenous attention but no specific effect regarding emotional attention in this time interval. Regarding the time course of the effects, an influence of the HPA on these MEG correlates of attention seems less likely. An influence of cerebral catecholaminergic systems is plausible, but not definite

MRI in active surveillance: a critical review

INTRODUCTION: Recent technological advancements and the introduction of modern anatomical and functional sequences have led to a growing role for multiparametric magnetic resonance imaging (mpMRI) in the detection, risk assessment and monitoring of early prostate cancer. This includes men who have been diagnosed with lower-risk prostate cancer and are looking at the option of active surveillance (AS). The purpose of this paper is to review the recent evidence supporting the use of mpMRI at different time points in AS, as well as to discuss some of its potential pitfalls. METHODS: A combination of electronic and manual searching methods were used to identify recent, important papers investigating the role of mpMRI in AS. RESULTS: The high negative predictive value of mpMRI can be exploited for the selection of AS candidates. In addition, mpMRI can be efficiently used to detect higher risk disease in patients already on surveillance. CONCLUSION: Although there is an ongoing debate regarding the precise nature of its optimal implementation, mpMRI is a promising risk stratification tool and should be considered for men on AS