Distance statistics in large toroidal maps

We compute a number of distance-dependent universal scaling functions characterizing the distance statistics of large maps of genus one. In particular, we obtain explicitly the probability distribution for the length of the shortest non-contractible loop passing via a random point in the map, and that for the distance between two random points. Our results are derived in the context of bipartite toroidal quadrangulations, using their coding by well-labeled 1-trees, which are maps of genus one with a single face and appropriate integer vertex labels. Within this framework, the distributions above are simply obtained as scaling limits of appropriate generating functions for well-labeled 1-trees, all expressible in terms of a small number of basic scaling functions for well-labeled plane trees.Comment: 24 pages, 9 figures, minor corrections, new added reference

Confluence of geodesic paths and separating loops in large planar quadrangulations

We consider planar quadrangulations with three marked vertices and discuss the geometry of triangles made of three geodesic paths joining them. We also study the geometry of minimal separating loops, i.e. paths of minimal length among all closed paths passing by one of the three vertices and separating the two others in the quadrangulation. We concentrate on the universal scaling limit of large quadrangulations, also known as the Brownian map, where pairs of geodesic paths or minimal separating loops have common parts of non-zero macroscopic length. This is the phenomenon of confluence, which distinguishes the geometry of random quadrangulations from that of smooth surfaces. We characterize the universal probability distribution for the lengths of these common parts.Comment: 48 pages, 33 color figures. Final version, with one concluding paragraph and one reference added, and several other small correction

Random Planar Lattices and Integrated SuperBrownian Excursion

In this paper, a surprising connection is described between a specific brand of random lattices, namely planar quadrangulations, and Aldous' Integrated SuperBrownian Excursion (ISE). As a consequence, the radius r_n of a random quadrangulation with n faces is shown to converge, up to scaling, to the width r=R-L of the support of the one-dimensional ISE. More generally the distribution of distances to a random vertex in a random quadrangulation is described in its scaled limit by the random measure ISE shifted to set the minimum of its support in zero. The first combinatorial ingredient is an encoding of quadrangulations by trees embedded in the positive half-line, reminiscent of Cori and Vauquelin's well labelled trees. The second step relates these trees to embedded (discrete) trees in the sense of Aldous, via the conjugation of tree principle, an analogue for trees of Vervaat's construction of the Brownian excursion from the bridge. From probability theory, we need a new result of independent interest: the weak convergence of the encoding of a random embedded plane tree by two contour walks to the Brownian snake description of ISE. Our results suggest the existence of a Continuum Random Map describing in term of ISE the scaled limit of the dynamical triangulations considered in two-dimensional pure quantum gravity.Comment: 44 pages, 22 figures. Slides and extended abstract version are available at http://www.loria.fr/~schaeffe/Pub/Diameter/ and http://www.iecn.u-nancy.fr/~chassain

Statistics of geodesics in large quadrangulations

We study the statistical properties of geodesics, i.e. paths of minimal length, in large random planar quadrangulations. We extend Schaeffer's well-labeled tree bijection to the case of quadrangulations with a marked geodesic, leading to the notion of "spine trees", amenable to a direct enumeration. We obtain the generating functions for quadrangulations with a marked geodesic of fixed length, as well as with a set of "confluent geodesics", i.e. a collection of non-intersecting minimal paths connecting two given points. In the limit of quadrangulations with a large area n, we find in particular an average number 3*2^i of geodesics between two fixed points at distance i>>1 from each other. We show that, for generic endpoints, two confluent geodesics remain close to each other and have an extensive number of contacts. This property fails for a few "exceptional" endpoints which can be linked by truly distinct geodesics. Results are presented both in the case of finite length i and in the scaling limit i ~ n^(1/4). In particular, we give the scaling distribution of the exceptional points.Comment: 37 pages, 18 color figures, improved version with several clarifications (mostly in sections 2.1 and 2.4) and one added section (3.1) on ensembles of random quadrangulation

The topological structure of scaling limits of large planar maps

We discuss scaling limits of large bipartite planar maps. If p is a fixed integer strictly greater than 1, we consider a random planar map M(n) which is uniformly distributed over the set of all 2p-angulations with n faces. Then, at least along a suitable subsequence, the metric space M(n) equipped with the graph distance rescaled by the factor n to the power -1/4 converges in distribution as n tends to infinity towards a limiting random compact metric space, in the sense of the Gromov-Hausdorff distance. We prove that the topology of the limiting space is uniquely determined independently of p, and that this space can be obtained as the quotient of the Continuum Random Tree for an equivalence relation which is defined from Brownian labels attached to the vertices. We also verify that the Hausdorff dimension of the limit is almost surely equal to 4.Comment: 45 pages Second version with minor modification

Randomized Controlled Trial of a Positive Affect Intervention to Reduce Stress in People Newly Diagnosed with HIV; Protocol and Design for the IRISS Study

Increasing evidence suggests that positive affect plays an important role in adaptation to chronic illness, independent of levels of negative affects like depression. Positive affect may be especially beneficial for people in the midst of severe stress, such as the diagnosis of human immunodeficiency virus (HIV). As medical treatments for HIV have improved, the number of people living with HIV has increased, and prevention strategies tailored specifically to people living with HIV have become a priority. There is a need for effective, creative, client-centered interventions that can be easily disseminated to community treatment settings, but there are currently few established interventions for people who are newly diagnosed with HIV. We present the design and methods for a randomized trial in which we test the efficacy of one such skills-based intervention that targets positive affect as a novel mechanism of change. The proposed research builds on observational findings of the important unique functions of positive affect. We aim to determine whether a five-session theory- and evidence-based intervention designed to teach skills for increasing the frequency and intensity of daily positive affect does so, and whether this intervention has beneficial effects on subsequent psychological well-being, health behaviors, and physical health up to 15 months after diagnosis with HIV. This is a randomized controlled trial in a sample of adults recruited within 12 weeks of testing positive for HIV. The control group is attention-matched, and follow up assessments will be conducted immediately post intervention (approximately 5 months post diagnosis) and at 10 and 15 months post diagnosis. This study is an important next step in research concerning the adaptive functions of positive affect for people coping with HIV or other health-related life stress

A guided tour of asynchronous cellular automata

Research on asynchronous cellular automata has received a great amount of attention these last years and has turned to a thriving field. We survey the recent research that has been carried out on this topic and present a wide state of the art where computing and modelling issues are both represented.Comment: To appear in the Journal of Cellular Automat

Severe Aortic Stenosis and Myocardial Function: Diagnostic and Prognostic Usefulness of Ultrasonic Integrated Backscatter Analysis

Background— The aim of this study was to assess the myocardial reflectivity pattern in severe aortic valve stenosis through the use of integrated backscatter (IBS) analysis. Patients with aortic stenosis (AS) were carefully selected in the Department of Cardiology. Methods and Results— Thirty-five subjects (AS: valve orifice ≤1 cm2; 12 female; mean age, 71.8±6.2 years) and 25 healthy subjects were studied. All subjects of the study had conventional 2D-Doppler echocardiography and IBS. Backscatter signal was sampled at the septum and posterior wall levels. Patients with AS were divided into 2 groups: 16 patients with initial signs of congestive heart failure and a depressed left ventricular systolic function (DSF) (ejection fraction [EF] range, 35% to 50%) and 19 asymptomatic patients with normal left ventricular systolic function (NSF) (EF >50%). Myocardial echo intensity (pericardium related) was significantly higher at the septum and posterior wall levels in DSF than in NSF and in control subjects. IBS variation, as an expression of variation of the signal, appeared to be significantly lower in AS with DSF than in NSF and in control subjects, at both the septum and posterior wall levels. Patients with DSF underwent aortic valve replacement, and, during surgical intervention, a septal myocardial biopsy was made for evaluation of myocardium/fibrosis ratio. Abnormally increased echo intensity was detected in left ventricular pressure overload by severe aortic stenosis and correlated with increase of myocardial collagen content (operating biopsy). Conclusions— One year after aortic valve replacement, we observed a significant reduction of left ventricular mass, and, only if pericardial indexed IBS value (reduction of interstitial fibrosis) decreased, it was possible to observe an improvement of EF and of IBS variation

Assessment of epidemic projections using recent HIV survey data in South Africa: a validation analysis of ten mathematical models of HIV epidemiology in the antiretroviral therapy era

Background Mathematical models are widely used to simulate the eff ects of interventions to control HIV and to project future epidemiological trends and resource needs. We aimed to validate past model projections against data from a large household survey done in South Africa in 2012. Methods We compared ten model projections of HIV prevalence, HIV incidence, and antiretroviral therapy (ART) coverage for South Africa with estimates from national household survey data from 2012. Model projections for 2012 were made before the publication of the 2012 household survey. We compared adult (age 15–49 years) HIV prevalence in 2012, the change in prevalence between 2008 and 2012, and prevalence, incidence, and ART coverage by sex and by age groups between model projections and the 2012 household survey. Findings All models projected lower prevalence estimates for 2012 than the survey estimate (18·8%), with eight models’ central projections being below the survey 95% CI (17·5–20·3). Eight models projected that HIV prevalence would remain unchanged (n=5) or decline (n=3) between 2008 and 2012, whereas prevalence estimates from the household surveys increased from 16·9% in 2008 to 18·8% in 2012 (diff erence 1·9, 95% CI –0·1 to 3·9). Model projections accurately predicted the 1·6 percentage point prevalence decline (95% CI –0·3 to 3·5) in young adults aged 15–24 years, and the 2·2 percentage point (0·5 to 3·9) increase in those aged 50 years and older. Models accurately represented the number of adults on ART in 2012; six of ten models were within the survey 95% CI of 1·54–2·12 million. However, the diff erential ART coverage between women and men was not fully captured; all model projections of the sex ratio of women to men on ART were lower than the survey estimate of 2·22 (95% CI 1·73–2·71). Interpretation Projections for overall declines in HIV epidemics during the ART era might have been optimistic. Future treatment and HIV prevention needs might be greater than previously forecasted. Additional data about service provision for HIV care could help inform more accurate projections

Aortic stiffness is associated with cardiac function and cerebral small vessel disease in patients with type 1 diabetes mellitus: assessment by magnetic resonance imaging

To evaluate, with the use of magnetic resonance imaging (MRI), whether aortic pulse wave velocity (PWV) is associated with cardiac left ventricular (LV) function and mass as well as with cerebral small vessel disease in patients with type 1 diabetes mellitus (DM). We included 86 consecutive type 1 DM patients (49 male, mean age 46.9 +/- 11.7 years) in a prospective, cross-sectional study. Exclusion criteria included aortic/heart disease and general MRI contra-indications. MRI of the aorta, heart and brain was performed for assessment of aortic PWV, as a marker of aortic stiffness, systolic LV function and mass, as well as for the presence of cerebral white matter hyperintensities (WMHs), microbleeds and lacunar infarcts. Multivariate linear or logistic regression was performed to analyse the association between aortic PWV and outcome parameters, with covariates defined as age, gender, mean arterial pressure, heart rate, BMI, smoking, DM duration and hypertension. Mean aortic PWV was 7.1 +/- 2.5 m/s. Aortic PWV was independently associated with LV ejection fraction ( = -0.406, P = 0.006), LV stroke volume ( = -0.407, P = 0.001), LV cardiac output ( = -0.458, P = 0.001), and with cerebral WMHs (P < 0.05). There were no independent associations between aortic stiffness and LV mass, cerebral microbleeds or lacunar infarcts. Aortic stiffness is independently associated with systolic LV function and cerebral WMHs in patients with type 1 DM.Neuro Imaging Researc