K-independent percolation on trees

Consider the class of k-independent bond, respectively site, percolations with parameter p on an infinite tree T. We derive tight bounds on p for both a.s. percolation and a.s. nonpercolation. The bounds are continuous functions of k and the branching number of T. This extends previous results by Lyons for the independent case (k=0) and by Bollob\`as & Balister for 1-independent bond percolations. Central to our argumentation are moment method bounds \`a la Lyons supplemented by explicit percolation models \`a la Bollob\`as & Balister. An indispensable tool is the minimality and explicit construction of Shearer's measure on the k-fuzz of Z.Comment: 28 pages, 4 figure

Attachment‑based parent–adolescent interaction linked to visual attention and autonomic arousal to distress and comfort stimuli

In infancy and in the early years of life, emotion regulation and attachment relationships with parents are tightly intertwined. However, whether this link persists into adolescence has not yet been established and requires exploration. This pilot study utilizes an experimental design to assess the patterns of parent–adolescent interactions that are hypothesised to be related to two specific aspects of adolescents’ emotion regulation, namely: visual attention and autonomic arousal to distress and comfort stimuli. Two innovative and ecologically valid methodologies were utilized to assess (a) patterns of attachment-based parent–adolescent interactions among 39 adolescent–parent dyads from the general population, using the Goal-corrected Partnership in Adolescence Coding System (Lyons-Ruth et al. Goal corrected partnership in adolescence coding system (GPACS), 2005) applied to a conflict discussion task; (b) the two aspects of adolescent emotion regulation were assessed with the Visual/Autonomic Regulation of Emotions Assessment (VAREA) (Vulliez-Coady et al. Visual/Autonomic Regulation of Emotions Assessment, VAREA) paradigm, an attachment-related, emotionally arousing experimental procedure, using a distress-then-comfort paradigm, in conjunction to an eye-tracker synchronized with a physiological device that measured gaze and skin conductance response, (SCR), or emotional reactivity. In line with research in infancy, as predicted, markers of secure parent–adolescent interaction were linked to higher amplitude of SCR for distress and comfort pictures, and with longer attention to comfort pictures. On the other hand, parental role-confusion was associated with less time spent on comfort pictures by the adolescent. Overall, this pilot study suggests that interventions supporting collaborative communication between adolescents and their parents, as well as working to reduce parental role-confusion, may improve adaptive adolescent emotion regulation as assessed via physiological measures

Two Types of Burst Firing in Gonadotrophin‐Releasing Hormone Neurones

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/92106/1/j.1365-2826.2012.02313.x.pd

Hip fracture risk in relation to vitamin D supplementation and serum 25-hydroxyvitamin D levels: a systematic review and meta-analysis of randomised controlled trials and observational studies

<p>Abstract</p> <p>Background</p> <p>Vitamin D supplementation for fracture prevention is widespread despite conflicting interpretation of relevant randomised controlled trial (RCT) evidence. This study summarises quantitatively the current evidence from RCTs and observational studies regarding vitamin D, parathyroid hormone (PTH) and hip fracture risk.</p> <p>Methods</p> <p>We undertook separate meta-analyses of RCTs examining vitamin D supplementation and hip fracture, and observational studies of serum vitamin D status (25-hydroxyvitamin D (25(OH)D) level), PTH and hip fracture. Results from RCTs were combined using the reported hazard ratios/relative risks (RR). Results from case-control studies were combined using the ratio of 25(OH)D and PTH measurements of hip fracture cases compared with controls. Original published studies of vitamin D, PTH and hip fracture were identified through PubMed and Web of Science databases, searches of reference lists and forward citations of key papers.</p> <p>Results</p> <p>The seven eligible RCTs identified showed no significant difference in hip fracture risk in those randomised to cholecalciferol or ergocalciferol supplementation versus placebo/control (RR = 1.13[95%CI 0.98-1.29]; 801 cases), with no significant difference between trials of <800 IU/day and ≥800 IU/day. The 17 identified case-control studies found 33% lower serum 25(OH)D levels in cases compared to controls, based on 1903 cases. This difference was significantly greater in studies with population-based compared to hospital-based controls (χ²₁(heterogeneity) = 51.02, p < 0.001) and significant heterogeneity was present overall (χ²₁₆(heterogeneity) = 137.9, p < 0.001). Serum PTH levels in hip fracture cases did not differ significantly from controls, based on ten case-control studies with 905 cases (χ²₉(heterogeneity) = 149.68, p < 0.001).</p> <p>Conclusions</p> <p>Neither higher nor lower dose vitamin D supplementation prevented hip fracture. Randomised and observational data on vitamin D and hip fracture appear to differ. The reason for this is unclear; one possible explanation is uncontrolled confounding in observational studies. Post-fracture PTH levels are unrelated to hip fracture risk.</p