Sylvester's question and the Random Acceleration Process

Let n points be chosen randomly and independently in the unit disk. "Sylvester's question" concerns the probability p_n that they are the vertices of a convex n-sided polygon. Here we establish the link with another problem. We show that for large n this polygon, when suitably parametrized by a function r(phi) of the polar angle phi, satisfies the equation of the random acceleration process (RAP), d^2 r/d phi^2 = f(phi), where f is Gaussian noise. On the basis of this relation we derive the asymptotic expansion log p_n = -2n log n + n log(2 pi^2 e^2) - c_0 n^{1/5} + ..., of which the first two terms agree with a rigorous result due to Barany. The nonanalyticity in n of the third term is a new result. The value 1/5 of the exponent follows from recent work on the RAP due to Gyorgyi et al. [Phys. Rev. E 75, 021123 (2007)]. We show that the n-sided polygon is effectively contained in an annulus of width \sim n^{-4/5} along the edge of the disk. The distance delta_n of closest approach to the edge is exponentially distributed with average 1/(2n).Comment: 29 pages, 4 figures; references added and minor change

The exact hausdorff measure of the zero set of a stable process

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47654/1/440_2004_Article_BF00537139.pd

Acyclovir suppression to prevent recurrent genital herpes at delivery.

OBJECTIVE: To determine if suppressive acyclovir near term decreased the frequency of clinical recurrences at delivery in women with recurrent genital herpes simplex virus (HSV) infection. METHODS: We conducted a prospective, double-blind, randomized trial in 234 women with recurrent genital herpes. Women with genital infection of any frequency were enrolled. Patients received either suppressive oral acyclovir 400 mg three times daily or an identical placebo after 36 weeks' gestation. Clinical lesions were identified, and HSV cultures were obtained at delivery. The frequencies of clinical and subclinical HSV recurrences at delivery were evaluated. RESULTS: Six percent of patients treated with acyclovir, and 14% of patients treated with placebo had clinical HSV at delivery (p = 0.046). No patients in the acyclovir group had positive HSV cultures, compared with 6% of placebo-treated patients (p = 0.029). There was no significant difference in subclinical HSV shedding in the acyclovir group (0%) compared with the placebo-treated group (3%) (p = 0.102). CONCLUSIONS: Suppressive acyclovir therapy significantly decreased the incidence of clinical genital herpes and the overall incidence of HSV excretion at delivery in patients with previous herpes infection

TopiaryExplorer: visualizing large phylogenetic trees with environmental metadata

Motivation: Microbial community profiling is a highly active area of research, but tools that facilitate visualization of phylogenetic trees and associated environmental data have not kept up with the increasing quantity of data generated in these studies

Sitting Behaviors and Mental Health among Workers and Nonworkers: The Role of Weight Status

Objective. To explore the associations between sitting time in various domains and mental health for workers and nonworkers and the role of weight status. Design. Cross-sectional analyses were performed for 1064 respondents (47% men, mean age 59 years) from the Doetinchem Cohort Study 2008-2009. Sedentary behavior was measured by self-reported time spent sitting during transport, leisure time, and at work. Mental health was assessed by the Mental Health Inventory (MHI-5). BMI was calculated based on measured body height and weight. Results. Neither sitting time during transport nor at work was associated with mental health. In the working population, sitting during leisure time, and particularly TV viewing, was associated with poorer mental health. BMI was an effect modifier in this association with significant positive associations for healthy-weight non-workers and obese workers. Conclusion. Both BMI and working status were effect modifiers in the relation between TV viewing and mental health. More longitudinal research is needed to confirm the results and to gain insight into the causality and the underlying mechanisms for the complex relationships among sedentary behaviors, BMI, working status, and mental health

Liver Resection for Primary Hepatic Neoplasms.

Subtotal hepatic resection was performed in 356 patients; 87 had primary hepatic malignancies, 108 had metastatic tumors, and 161 had benign lesions including 8 traumatic injuries. The global mortality was 4.2%. The experience has elucidated the role of subtotal hepatic resection both for benign and malignant neoplasms

RELAP5 model for advanced neutron source reactor thermal-hydraulic transients, three-element-core design

In order to utilize reduced enrichment fuel, the three-element-core design has been proposed. The proposed core configuration consists of inner, middle, and outer elements, with the middle element offset axially beneath the inner and outer elements, which are axially aligned. The three-element-core RELAP5 model assumes that the reactor hardware is changed only within the core region, so that the loop piping, heat exchangers, and pumps remain as assumed for the two-element-core configuration. However, the total flow rate through the core is greater and the pressure drop across the core is less so that the primary coolant pumps and heat exchangers are operating at a different point in their performance curves. This report describes the new RELAP5 input for the core components

A method to assess the relevance of nanomaterial dissolution during reactivity testing

The reactivity of particle surfaces can be used as a criterion to group nanoforms (NFs) based on similar potential hazard. Since NFs may partially or completely dissolve over the duration of the assays, with the ions themselves inducing a response, reactivity assays commonly measure the additive reactivity of the particles and ions combined. Here, we determine the concentration of ions released over the course of particle testing, and determine the relative contributions of the released ions to the total reactivity measured. We differentiate three classes of reactivity, defined as being A) dominated by particles, B) additive of particles and ions, or C) dominated by ions. We provide examples for each class by analyzing the NF reactivity of Fe2O3, ZnO, CuO, Ag using the ferric reduction ability of serum (FRAS) assay. Furthermore, another two reactivity tests were performed: Dichlorodihydrofluorescin diacetate (DCFH2‑DA) assay and electron paramagnetic resonance (EPR) spectroscopy. We compare assays and demonstrate that the dose‑response may be almost entirely assigned to ions in one assay (CuO in DCFH2‑DA), but to particles in others (CuO in EPR and FRAS). When considering this data, we conclude that one cannot specify the contribution of ions to NF toxicity for a certain NF, but only for a certain NF in a specific assay, medium and dose. The extent of dissolution depends on the buffer used, particle concentration applied, and duration of exposure. This culminates in the DCFH2‑DA, EPR, FRAS assays being performed under different ion‑to‑particle ratios, and differing in their sensitivity towards reactions induced by either ions or particles. If applied for grouping, read‑across, or other concepts based on the similarity of partially soluble NFs, results on reactivity should only be compared if measured by the same assay, incubation time, and dose range