Modélisation de terrains par primitives

National audienceNous proposons un modèle de terrain hiérarchique et compact permettant de représenter des scènes complexes. Ce modèle de représentation s'inspire des surfaces implicites à squelettes et définit une fonction d'élévation sous la forme d'un arbre de construction. Les feuilles sont des primitives décrivant des morceaux de terrains à différentes échelles (montagnes, fleuves, ...) et les noeuds internes sont des opérateurs de combinaison. L'élévation d'un point est calculée en traversant la structure d'arbre et en combinant les contributions de chaque primitive. La définition des feuilles et des opérateurs garantit que la fonction d'élévation résultante est Lipschitzienne, ce qui permet d'accélérer les calculs de visualisation en utilisant un algorithme de sphere tracing. Mots Clés : modélisation de terrains, phénomènes naturels, modélisation procédurale, surface implicite We propose a compact hierarchical procedural model that combines feature-based primitives to create complex continuous terrains. Our model is inspired by skeletal implicit surfaces and defines the terrain elevation by using a construction tree whose leaves are primitives describing terrain fragments, and whose inner nodes include operations that combine its sub-trees. The elevation of a point is evaluated by traversing the tree and by combining the contributions of each primitive. The definition of both leaves and operators guarantees that the resulting elevation function is Lipschitz which enables us to speed up sphere tracing and surface adaptive tesselation algorithms

Normal random matrix ensemble as a growth problem

In general or normal random matrix ensembles, the support of eigenvalues of large size matrices is a planar domain (or several domains) with a sharp boundary. This domain evolves under a change of parameters of the potential and of the size of matrices. The boundary of the support of eigenvalues is a real section of a complex curve. Algebro-geometrical properties of this curve encode physical properties of random matrix ensembles. This curve can be treated as a limit of a spectral curve which is canonically defined for models of finite matrices. We interpret the evolution of the eigenvalue distribution as a growth problem, and describe the growth in terms of evolution of the spectral curve. We discuss algebro-geometrical properties of the spectral curve and describe the wave functions (normalized characteristic polynomials) in terms of differentials on the curve. General formulae and emergence of the spectral curve are illustrated by three meaningful examples.Comment: 44 pages, 14 figures; contains the first part of the original file. The second part will be submitted separatel

Viscous shocks in Hele-Shaw flow and Stokes phenomena of the Painleve I transcendent

In Hele-Shaw flows at vanishing surface tension, the boundary of a viscous fluid develops cusp-like singularities. In recent papers [1, 2] we have showed that singularities trigger viscous shocks propagating through the viscous fluid. Here we show that the weak solution of the Hele-Shaw problem describing viscous shocks is equivalent to a semiclassical approximation of a special real solution of the Painleve I equation. We argue that the Painleve I equation provides an integrable deformation of the Hele-Shaw problem which describes flow passing through singularities. In this interpretation shocks appear as Stokes level-lines of the Painleve linear problem.Comment: A more detailed derivation is include

Exploring the Variable Sky with LINEAR. III. Classification of Periodic Light Curves

We describe the construction of a highly reliable sample of ~7000 optically faint periodic variable stars with light curves obtained by the asteroid survey LINEAR across 10,000 deg^2 of the northern sky. The majority of these variables have not been cataloged yet. The sample flux limit is several magnitudes fainter than most other wide-angle surveys; the photometric errors range from ~0.03 mag at r = 15 to ~0.20 mag at r = 18. Light curves include on average 250 data points, collected over about a decade. Using Sloan Digital Sky Survey (SDSS) based photometric recalibration of the LINEAR data for about 25 million objects, we selected ~200,000 most probable candidate variables with r < 17 and visually confirmed and classified ~7000 periodic variables using phased light curves. The reliability and uniformity of visual classification across eight human classifiers was calibrated and tested using a catalog of variable stars from the SDSS Stripe 82 region and verified using an unsupervised machine learning approach. The resulting sample of periodic LINEAR variables is dominated by 3900 RR Lyrae stars and 2700 eclipsing binary stars of all subtypes and includes small fractions of relatively rare populations such as asymptotic giant branch stars and SX Phoenicis stars. We discuss the distribution of these mostly uncataloged variables in various diagrams constructed with optical-to-infrared SDSS, Two Micron All Sky Survey, and Wide-field Infrared Survey Explorer photometry, and with LINEAR light-curve features. We find that the combination of light-curve features and colors enables classification schemes much more powerful than when colors or light curves are each used separately. An interesting side result is a robust and precise quantitative description of a strong correlation between the light-curve period and color/spectral type for close and contact eclipsing binary stars (β Lyrae and W UMa): as the color-based spectral type varies from K4 to F5, the median period increases from 5.9 hr to 8.8 hr. These large samples of robustly classified variable stars will enable detailed statistical studies of the Galactic structure and physics of binary and other stars and we make these samples publicly available

Generic critical points of normal matrix ensembles

The evolution of the degenerate complex curve associated with the ensemble at a generic critical point is related to the finite time singularities of Laplacian Growth. It is shown that the scaling behavior at a critical point of singular geometry $x^3 \sim y^2$ is described by the first Painlev\'e transcendent. The regularization of the curve resulting from discretization is discussed.Comment: Based on a talk given at the conference on Random Matrices, Random Processes and Integrable Systems, CRM Montreal, June 200

A Reconciled Estimate of Ice-Sheet Mass Balance

We combined an ensemble of satellite altimetry, interferometry, and gravimetry data sets using common geographical regions, time intervals, and models of surface mass balance and glacial isostatic adjustment to estimate the mass balance of Earth's polar ice sheets. We find that there is good agreement between different satellite methods-especially in Greenland and West Antarctica-and that combining satellite data sets leads to greater certainty. Between 1992 and 2011, the ice sheets of Greenland, East Antarctica, West Antarctica, and the Antarctic Peninsula changed in mass by -142 plus or minus 49, +14 plus or minus 43, -65 plus or minus 26, and -20 plus or minus 14 gigatonnes year(sup 1), respectively. Since 1992, the polar ice sheets have contributed, on average, 0.59 plus or minus 0.20 millimeter year(sup 1) to the rate of global sea-level rise

Functional illness in primary care: dysfunction versus disease

<p>Abstract</p> <p>Background</p> <p>The Biopsychosocial Model aims to integrate the biological, psychological and social components of illness, but integration is difficult in practice, particularly when patients consult with medically unexplained physical symptoms or functional illness.</p> <p>Discussion</p> <p>This Biopsychosocial Model was developed from General Systems Theory, which describes nature as a dynamic order of interacting parts and processes, from molecular to societal. Despite such conceptual progress, the biological, psychological, social and spiritual components of illness are seldom managed as an integrated whole in conventional medical practice. This is because the biomedical model can be easier to use, clinicians often have difficulty relinquishing a disease-centred approach to diagnosis, and either dismiss illness when pathology has been excluded, or explain all undifferentiated illness in terms of psychosocial factors. By contrast, traditional and complementary treatment systems describe reversible functional disturbances, and appear better at integrating the different components of illness. Conventional medicine retains the advantage of scientific method and an expanding evidence base, but needs to more effectively integrate psychosocial factors into assessment and management, notably of 'functional' illness. As an aid to integration, pathology characterised by structural change in tissues and organs is contrasted with dysfunction arising from disordered physiology or psychology that may occur independent of pathological change.</p> <p>Summary</p> <p>We propose a classification of illness that includes orthogonal dimensions of pathology and dysfunction to support a broadly based clinical approach to patients; adoption of which may lead to fewer inappropriate investigations and secondary care referrals and greater use of cognitive behavioural techniques, particularly when managing functional illness.</p

The Changing Landscape for Stroke\ua0Prevention in AF: Findings From the GLORIA-AF Registry Phase 2

Background GLORIA-AF (Global Registry on Long-Term Oral Antithrombotic Treatment in Patients with Atrial Fibrillation) is a prospective, global registry program describing antithrombotic treatment patterns in patients with newly diagnosed nonvalvular atrial fibrillation at risk of stroke. Phase 2 began when dabigatran, the first non\u2013vitamin K antagonist oral anticoagulant (NOAC), became available. Objectives This study sought to describe phase 2 baseline data and compare these with the pre-NOAC era collected during phase&nbsp;1. Methods During phase 2, 15,641 consenting patients were enrolled (November 2011 to December 2014); 15,092 were eligible. This pre-specified cross-sectional analysis describes eligible patients\u2019 baseline characteristics. Atrial fibrillation&nbsp;disease characteristics, medical outcomes, and concomitant diseases and medications were collected. Data were analyzed using descriptive statistics. Results Of the total patients, 45.5% were female; median age was 71 (interquartile range: 64, 78) years. Patients were from Europe (47.1%), North America (22.5%), Asia (20.3%), Latin America (6.0%), and the Middle East/Africa (4.0%). Most had high stroke risk (CHA2DS2-VASc [Congestive heart failure, Hypertension, Age&nbsp; 6575 years, Diabetes mellitus, previous Stroke, Vascular disease, Age 65 to 74 years, Sex category] score&nbsp; 652; 86.1%); 13.9% had moderate risk (CHA2DS2-VASc&nbsp;= 1). Overall, 79.9% received oral anticoagulants, of whom 47.6% received NOAC and 32.3% vitamin K antagonists (VKA); 12.1% received antiplatelet agents; 7.8% received no antithrombotic treatment. For comparison, the proportion of phase 1 patients (of N&nbsp;= 1,063 all eligible) prescribed VKA was 32.8%, acetylsalicylic acid 41.7%, and no therapy 20.2%. In Europe in phase 2, treatment with NOAC was more common than VKA (52.3% and 37.8%, respectively); 6.0% of patients received antiplatelet treatment; and 3.8% received no antithrombotic treatment. In North America, 52.1%, 26.2%, and 14.0% of patients received NOAC, VKA, and antiplatelet drugs, respectively; 7.5% received no antithrombotic treatment. NOAC use was less common in Asia (27.7%), where 27.5% of patients received VKA, 25.0% antiplatelet drugs, and 19.8% no antithrombotic treatment. Conclusions The baseline data from GLORIA-AF phase 2 demonstrate that in newly diagnosed nonvalvular atrial fibrillation patients, NOAC have been highly adopted into practice, becoming more frequently prescribed than VKA in&nbsp;Europe and North America. Worldwide, however, a large proportion of patients remain undertreated, particularly in&nbsp;Asia&nbsp;and North America. (Global Registry on Long-Term Oral Antithrombotic Treatment in Patients With Atrial Fibrillation [GLORIA-AF]; NCT01468701

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