Rayleigh processes, real trees, and root growth with re-grafting

The real trees form a class of metric spaces that extends the class of trees with edge lengths by allowing behavior such as infinite total edge length and vertices with infinite branching degree. Aldous's Brownian continuum random tree, the random tree-like object naturally associated with a standard Brownian excursion, may be thought of as a random compact real tree. The continuum random tree is a scaling limit as N tends to infinity of both a critical Galton-Watson tree conditioned to have total population size N as well as a uniform random rooted combinatorial tree with N vertices. The Aldous--Broder algorithm is a Markov chain on the space of rooted combinatorial trees with N vertices that has the uniform tree as its stationary distribution. We construct and study a Markov process on the space of all rooted compact real trees that has the continuum random tree as its stationary distribution and arises as the scaling limit as N tends to infinity of the Aldous--Broder chain. A key technical ingredient in this work is the use of a pointed Gromov--Hausdorff distance to metrize the space of rooted compact real trees.Comment: 48 Pages. Minor revision of version of Feb 2004. To appear in Probability Theory and Related Field

The spans in Brownian motion

For $d \in \{1,2,3\}$, let $(B^d_t;~ t \geq 0)$ be a $d$-dimensional standard Brownian motion. We study the $d$-Brownian span set Span(d):=\{t-s;~ B^d_s=B^d_t~\mbox{for some}~0 \leq s \leq t\}. We prove that almost surely the random set $Span(d)$ is $\sigma$-compact and dense in $\mathbb{R}_{+}$. In addition, we show that $Span(1)=\mathbb{R}_{+}$ almost surely; the Lebesgue measure of $Span(2)$ is $0$ almost surely and its Hausdorff dimension is $1$ almost surely; and the Hausdorff dimension of $Span(3)$ is $\frac{1}{2}$ almost surely. We also list a number of conjectures and open problems.Comment: 33 pages, 4 figures. This paper is published by http://projecteuclid.org/euclid.aihp/150062403

Open versus blind peer review: is anonymity better than transparency?

Peer review is widely accepted as essential to ensuring scientific quality in academic journals, yet little training is provided in the specifics of how to conduct peer review. In this article we describe the different forms of peer review, with a particular focus on the differences between single-blind, double-blind and open peer review, and the advantages and disadvantages of each. These illustrate some of the challenges facing the community of authors, editors, reviewers and readers in relation to the process of peer review. We also describe other forms of peer review, such as post-publication review, transferable review and collaborative review, and encourage clinicians and academics at all training stages to engage in the practice of peer review as part of continuing professional development

Goethite on Mars - A laboratory study of physically and chemically bound water in ferric oxides

Thermogravimetric study of physically and chemically bound water in ferric oxides of limonite with application to goethite on Mar

Association between sensory impairment and suicidal ideation and attempt: a cross-sectional analysis of nationally representative English household data

OBJECTIVES: Sensory impairments are associated with worse mental health and poorer quality of life, but few studies have investigated whether sensory impairment is associated with suicidal behaviour in a population sample. We investigated whether visual and hearing impairments were associated with suicidal ideation and attempt. DESIGN: National cross-sectional study. SETTING: Households in England. PARTICIPANTS: We analysed data for 7546 household residents in England, aged 16 and over from the 2014 Adult Psychiatric Morbidity Survey. EXPOSURES: Sensory impairment (either visual or hearing), Dual sensory impairment (visual and hearing), visual impairment, hearing impairment. PRIMARY OUTCOME: Suicidal ideation and suicide attempt in the past year. RESULTS: People with visual or hearing sensory impairments had twice the odds of past-year suicidal ideation (OR 2.06; 95% CI 1.17 to 2.73; p<0.001), and over three times the odds of reporting past-year suicide attempt (OR 3.12; 95% CI 1.57 to 6.20; p=0.001) compared with people without these impairments. Similar results were found for hearing and visual impairments separately and co-occurring. CONCLUSIONS: We found evidence that individuals with sensory impairments are more likely to have thought about or attempted suicide in the past year than individuals without

Levy-Student Distributions for Halos in Accelerator Beams

We describe the transverse beam distribution in particle accelerators within the controlled, stochastic dynamical scheme of the Stochastic Mechanics (SM) which produces time reversal invariant diffusion processes. This leads to a linearized theory summarized in a Shchr\"odinger--like (\Sl) equation. The space charge effects have been introduced in a recent paper~\cite{prstab} by coupling this \Sl equation with the Maxwell equations. We analyze the space charge effects to understand how the dynamics produces the actual beam distributions, and in particular we show how the stationary, self--consistent solutions are related to the (external, and space--charge) potentials both when we suppose that the external field is harmonic (\emph{constant focusing}), and when we \emph{a priori} prescribe the shape of the stationary solution. We then proceed to discuss a few new ideas~\cite{epac04} by introducing the generalized Student distributions, namely non--Gaussian, L\'evy \emph{infinitely divisible} (but not \emph{stable}) distributions. We will discuss this idea from two different standpoints: (a) first by supposing that the stationary distribution of our (Wiener powered) SM model is a Student distribution; (b) by supposing that our model is based on a (non--Gaussian) L\'evy process whose increments are Student distributed. We show that in the case (a) the longer tails of the power decay of the Student laws, and in the case (b) the discontinuities of the L\'evy--Student process can well account for the rare escape of particles from the beam core, and hence for the formation of a halo in intense beams.Comment: revtex4, 18 pages, 12 figure

Individual and area-level risk factors for suicidal ideation and attempt in people with severe depression

INTRODUCTION: Previous research has identified several risk factors that are strongly associated with suicidal behavior in patients with severe depression. However, the effects of area-level characteristics on suicidal ideation and attempt in this population remain unclear. METHODS: The Clinical Record Interactive Search (CRIS) database was used to identify 2587 patients with severe depression who received secondary mental health services from the Camden & Islington NHS Foundation Trust. Stepwise multivariable logistic regression models were used to examine associations between socio-demographic characteristics, clinical variables, area-level measures, and suicidal ideation and attempt as separate outcomes. RESULTS: Both suicidal ideation and attempts were common among this cohort of severely depressed individuals (70.5% and 37.7%, respectively). While several individual socio-demographic and clinical characteristics were associated with both outcomes, particularly past psychiatric admission (suicidal ideation: adjusted OR=2.86, 95% CI: 2.26-3.62; suicide attempt: adjusted OR=4.00, 95% CI: 3.30-4.89), neither social deprivation nor ethnic density (measured at the area-level) was associated with risk for either outcome. LIMITATIONS: Data were not collected specifically for research purposes and hence information on some potential confounders was not available. Additionally, information was restricted to individuals who accessed secondary mental health services in a defined catchment area and period. The study therefore does not take into account individuals who did not access mental health services. CONCLUSIONS: The variation in risk for suicidal ideation and attempt among severely depressed individuals is explained by differences in individual socio-demographic and clinical characteristics, most notably past psychiatric admission and substance misuse, and not by area-level measures