A Robust and Efficient Method for Solving Point Distance Problems by Homotopy

The goal of Point Distance Solving Problems is to find 2D or 3D placements of points knowing distances between some pairs of points. The common guideline is to solve them by a numerical iterative method (\emph{e.g.} Newton-Raphson method). A sole solution is obtained whereas many exist. However the number of solutions can be exponential and methods should provide solutions close to a sketch drawn by the user.Geometric reasoning can help to simplify the underlying system of equations by changing a few equations and triangularizing it.This triangularization is a geometric construction of solutions, called construction plan. We aim at finding several solutions close to the sketch on a one-dimensional path defined by a global parameter-homotopy using a construction plan. Some numerical instabilities may be encountered due to specific geometric configurations. We address this problem by changing on-the-fly the construction plan.Numerical results show that this hybrid method is efficient and robust

Parkinson's disease and iatrogenic impulsive-compulsive behaviors: A case/non-case study to build a complete model of individual vulnerability

Background and aims: Parkinson’s disease (PD) is one of the most prevalent neurodegenerative diseases. First-line medications consist of drugs that act by counteracting dopamine deficiency in the basal ganglia. Unfortunately, iatrogenic impulsive-compulsive behaviors (ICBs) can occur in up to 20% of PD patients over the course of their illness. ICBs must be considered multifactorial disorders that reflect the interactions of the medication with an individual’s vulnerability and the underlying neurobiology of PD. We aimed to explore the predictive genetic, psychopathological and neurological factors involved in the development of ICBs in PD patients by building a complete model of individual vulnerability. Methods: The PARKADD study was a case/non-case study. A total of 225 patients were enrolled (“ICB” group, N 5 75; “no ICB” group, N 5 150), and 163 agreed to provide saliva samples for genetic analysis. Sociodemographic, neurological and psychiatric characteristics were assessed, and genotyping for the characterization of polymorphisms related to dopaminergic and opioid systems was performed. Results: Factors associated with “ICBs” were younger age of PD onset, personal history of ICB prior to PD onset and higher scores on the urgency and sensation seeking facets of impulsivity. No gene variant was significantly associated, but the association with the opioid receptor mu 1 (OPRM1) rs1799971 polymorphism was close to significance. Discussion and conclusions: The influence of gene-environment interactions probably exists, and additional studies are needed to decipher the possible role of the opioid system in the development of ICBs in PD patients

Changes in temperature and precipitation extremes over the Greater Horn of Africa region from 1961 to 2010

Recent special reports on climate extremes have shown evidences of changes in the patterns of climate extremes at global, regional and local scales. Understanding the characteristics of climate extremes at regional and local levels is critical not only for the development of preparedness and early warning systems, but is also fundamental in the development of any adaptation strategies. There is still very limited knowledge regarding the past, present and future patterns of climate extremes in the Greater Horn of Africa (GHA). This study, which was supported by the World Bank Global Facility for Disaster Reduction and Recovery (WB-GFDRR) and implemented by the World Meteorological Organization, was organized in terms of three workshops with three main objectives; (1) analysis of daily rainfall and temperature extremes for ten countries in the GHA region using observed in situ data running from 1971 to 2006, (2) assessing whether the United Kingdom Met-office and Hadley centre Providing REgional Climates for Impact Studies (UK-PRECIS) modelling system can provide realistic representation of the past and present climate extremes as observed by available in situ data, and (3) studying the future regional climate extremes under different scenarios to further assess the expected changes in climate extremes.This paper, therefore, uses the outputs of these workshops and also includes post-workshop analyses to assess the changes of climate extremes within the GHA. The results showed a significant decrease in total precipitation in wet days greater than 1mm and increasing warm extremes, particularly at night, while cold extremes are decreasing. Considering a combination of geophysical models and satellite gravimetry observations from the Gravity Recovery and Climate Experiment (GRACE) mission in the frame of GRACE daily Kalman-smoothing models, for the years 2002 to 2010, we explored a decline in total water storage variations over the GHA

On the Mechanization of Straightedge and Compass Constructions

International audienceThe geometric constructions obtained with only straightedge and compass are famous and play a special role in the development of geometry. On the one hand, the constructibility of figures is a key ingredient in Euclid geometry and, on the other hand, unconstructibility gave birth to famous open problems of the ancient Greece which were unlocked only in the nineteenth century using discoveries in algebra. This paper discusses the mechanization of straightedge and compass constructions. It focuses on the algebraic approaches and presents two methods which are implemented; one is due to Lebesgue and the other one was jointly designed by Gao and Chou. Some links between the algebraic approach of constructions and synthetic geometry are described

Using jointly geometry and algebra to determine RC-constructibility

International audienceIn most cases in geometry, applying analytic or algebraic tools on coordinates helps to solve some difficult problems. For instance, proving that a geometrical construction problem is solvable using ruler and compass is often impossible within a synthetic geometry framework. But in an analytic geometry framework, it is a direct application of Galois theory after performing triangularizations. However, these algebraic tools lead to a large amount of computation. Their implementation in modern Computer Algebra Systems (CAS) are still too time consuming to provide an answer in a reasonable time. In addition, they require a lot of memory space which can grow exponentially with the size of the problem. Fortunately, some geometrical properties can be used to setup the algebraic systems so that they can be more efficiently computed. These properties turn polynomials into new ones so as to reduce both the degrees and the number of monomials. The present paper promotes this approach by considering two corpora of geometric construction problems, namely Wernick's and Connely's lists. These lists contain about 280 problems. The purpose is to determine their status i.e. whether they are constructible or not with ruler and compass. Some of these problems had unknown status that will be settled in this paper. More generally, the status of all problems of these corpora are fully automatically given by an approach combining geometry and algebra

Résolution de contraintes géométriques : des systèmes experts aux méthodes numériques

Exposé invitéLa résolution de contraintes géométriques s'inscrit dans le contexte plus général de la satisfaction de contraintes (CSP), dans un domaine connu depuis l'antiquité et dont la spécificité a conduit à la mise en oeuvre de méthodes particulières. Le but de l'exposé dont je donne ici le résumé consiste à mettre en évidence les particularités des approches classiques et, dans un deuxième temps, à montrer qu'on peut marier des approches reposant sur des systèmes à base de connaissances avec des méthodes numériques traditionnelles

Why are under-constrained systems not that bad

International audienceUnder-constrained geometric constraint systems are often considered as mis-constrained systems which have to be corrected by a completion mechanism. We expose here some works performed in our team and where under-constrained systems are considered as a wish of the designer or a step in order to solve a well-constrained system

Geometric Construction Problem Solving in Computer-Aided Learning

International audienceConstraint satisfaction problems related to geometry mostly arise in CAD. But even though they are designed for geometry, none of the methods proposed to solve these problems fully meets the requirements needed by the educational domain. In this paper, we adapt CAD methods to education and show that results must be construction programs in order to take into account particular cases. We present then a framework implemented in Prolog as a knowledge-based system called Progé

Leading a continuation method by geometry for solving geometric constraints

International audienceGeometric constraint problems arise in domains such as CAD, Robotics, Molecular Chemistry, whenever one expects 2D or 3D configurations of some geometric primitives fulfilling some geometric constraints. Most well-constrained 3D problems are resistant to geometric knowledge based systems. They are often solved by purely numerical methods that are efficient but provide only one solution. Finding all the solutions can be achieved by using, among others, generic homotopy methods, that become costly when the number of constraints grows. This paper focuses on using geometric knowledges to specialize a so-called coefficient parameter continuation to 3D geometric constraint systems. Even if the proposed method does not ensure obtaining all the solutions, it provides several real ones. Geometric knowledges are used to justify it and lead the search of new solutions

Decomposition of geometrical constraint systems with reparameterization

International audienceDecomposition of constraint systems is a key component of geometric constraint solving in CAD. On the other hand, some authors have introduced the notion of reparameterization which aims at helping the solving of indecomposable systems by replacing some geometric constraints by other ones. In previous works, the minimal change of the initial system is a main criterion. We propose to marry these two ingredients, decomposition and reparameterization, in a method able to reparameterize and to decompose a constraint system according to this reparameterization. As a result, we do not aim at minimizing the number of added constraints during the reparameterization, but we want to decompose the system such that each component owns a minimal number of such added constraints