A criterion for quadraticity of a representation of the fundamental group of an algebraic variety

13 pagesInternational audienceLet $\Gamma$ be a finitely presented group and $G$ a linear algebraic group over $\mathbb{R}$. A representation $\rho:\Gamma\rightarrow G(\mathbb{R})$ can be seen as an $\mathbb{R}$-point of the representation variety $\mathfrak{R}(\Gamma, G)$. It is known from the work of Goldman and Millson that if $\Gamma$ is the fundamental group of a compact Kähler manifold and $\rho$ has image contained in a compact subgroup then $\rho$ is analytically defined by homogeneous quadratic equations in $\mathfrak{R}(\Gamma, G)$. When $X$ is a smooth complex algebraic variety, we study a certain criterion under which this same conclusion holds

Beer Consumption Increases Human Attractiveness to Malaria Mosquitoes

Background: Malaria and alcohol consumption both represent major public health problems. Alcohol consumption is rising in developing countries and, as efforts to manage malaria are expanded, understanding the links between malaria and alcohol consumption becomes crucial. Our aim was to ascertain the effect of beer consumption on human attractiveness to malaria mosquitoes in semi field conditions in Burkina Faso. Methodology/Principal Findings: We used a Y tube-olfactometer designed to take advantage of the whole body odour (breath and skin emanations) as a stimulus to gauge human attractiveness to Anopheles gambiae (the primary African malaria vector) before and after volunteers consumed either beer (n = 25 volunteers and a total of 2500 mosquitoes tested) or water (n = 18 volunteers and a total of 1800 mosquitoes). Water consumption had no effect on human attractiveness to An. gambiae mosquitoes, but beer consumption increased volunteer attractiveness. Body odours of volunteers who consumed beer increased mosquito activation (proportion of mosquitoes engaging in take-off and up-wind flight) and orientation (proportion of mosquitoes flying towards volunteers' odours). The level of exhaled carbon dioxide and body temperature had no effect on human attractiveness to mosquitoes. Despite individual volunteer variation, beer consumption consistently increased attractiveness to mosquitoes. Conclusions/Significance: These results suggest that beer consumption is a risk factor for malaria and needs to be integrated into public health policies for the design of control measures

Post-trauma scoliosis after conservative treatment of thoracolumbar spinal fracture in children and adolescents: results in 48 patients.

PURPOSE: Authors examined a case series of patients younger than 18 years old who had sustained a traumatic thoracolumbar spine fracture to evaluate radiological and clinical findings of coronal spinal balance, after conservative treatment. METHODS: From 1996 to 2014, a tricentric cohort of 48 patients with an average age of 12 years was radiographically reviewed at 50 months. Cobb angle of fractured vertebra and regional Cobb angle were measured both at baseline and follow-up. Analyses were done according to initial Risser grade, number of fractures and level of injury. RESULTS: There was a total of 11 scoliosis. In group with Risser grade 3 or above, with a single vertebral fracture and lumbar fracture, final regional Cobb angle was statistically higher than initial regional Cobb angle. CONCLUSIONS: The prevalence of scoliosis in our population is higher than those of idiopathic scoliosis; Risser grade 3 or above, lumbar fracture and a single fracture seem to account for more severe coronal deformatio

Conservative treatment of pediatric thoracic and lumbar spinal fractures

To assess sagittal plane spinopelvic balance and functional outcomes in a pediatric cohort of patients with a thoracic and/or a lumbar fracture treated conservatively. A multicentric study retrospectively reviewed radiological and functional outcomes (mean follow-up 49 months) of 48 patients (mean age 12 years) with thoracic and/or lumbar spinal fractures that occurred between 1996 and 2014. Demographic data and radiological spinopelvic parameters were analyzed. Functional outcome was evaluated by a telephone interview. First, a comparison between the initial and the last follow-up full-spine radiographs was performed for the assessment of bone remodeling and sagittal plane balance. Then, patients were classified into two groups (group 1: Risser≤2 and group 2, Risser>2) to assess the influence of skeletal maturity on the restoration of a correct sagittal balance. A total of 62% of the patients were at skeletal maturity at the final follow-up (Risser 4 and 5). Patients with a Risser grade of 2 or less had a higher remodeling potential. The mean residual local kyphosis in thoracic and lumbar fractures was, respectively, 8.2° and 8.7°. The mean thoracic global kyphosis remains stable at the last follow-up, in contrast to lumbar lordosis, which increased significantly. Sagittal plane global measurements on the basis of the C7-plumbline remained unchanged at the last follow-up. There was no change in the pelvic parameters, except for the sacral slope in the group 1 for patients with a lumbar fracture. The current study confirms a greater correction in younger patients (Risser≤2) in spinal fractures and reported that thoracic fractures have a higher remodeling potential than lumbar fracture. A local kyphosis of almost 10° remained at the last follow-up. However, no deterioration in the sagittal plane balance was found. This suggests compensatory mechanisms in adjacent structures for children and adolescents and excludes the only hypothesis of bone remodeling

Plant-mediated effects on mosquito capacity to transmit human malaria

The ecological context in which mosquitoes and malaria parasites interact has received little attention, compared to the genetic and molecular aspects of malaria transmission. Plant nectar and fruits are important for the nutritional ecology of malaria vectors, but how the natural diversity of plant-derived sugar sources affects mosquito competence for malaria parasites is unclear. To test this, we infected Anopheles coluzzi, an important African malaria vector, with sympatric field isolates of Plasmodium falciparum, using direct membrane feeding assays. Through a series of experiments, we then examined the effects of sugar meals from Thevetia neriifolia and Barleria lupilina cuttings that included flowers, and fruit from Lannea microcarpa and Mangifera indica on parasite and mosquito traits that are key for determining the intensity of malaria transmission. We found that the source of plant sugar meal differentially affected infection prevalence and intensity, the development duration of the parasites, as well as the survival and fecundity of the vector. These effects are likely the result of complex interactions between toxic secondary metabolites and the nutritional quality of the plant sugar source, as well as of host resource availability and parasite growth. Using an epidemiological model, we show that plant sugar source can be a significant driver of malaria transmission dynamics, with some plant species exhibiting either transmission-reducing or -enhancing activities

Théorie de Hodge mixte et variétés des représentations des groupes fondamentaux des variétés algébriques complexes

The mixed Hodge theory of Deligne provides additional structures on the cohomology groups of complex algebraic varieties. Since then, mixed Hodge structures have been constructed on the rational homotopy groups of such varieties by Morgan and Hain. In this vein, we construct mixed Hodge structures on invariants associated to linear representations of fundamental groups of smooth complex algebraic varieties. The starting point is the theory of Goldman and Millson that relates the deformation theory of such representations to the deformation theory via differential graded Lie algebras. This was reviewed by P. Eyssidieux and C. Simpson in the case of compact Kähler manifolds. In the non-compact case, and for representations with finite image, Kapovich and Millson constructed only non-canonical gradings. In order to construct mixed Hodge structures in the non-compact case and unify it with the compact case treated by Eyssidieux-Simpson, we re-write the classical Goldman-Millson theory using more modern ideas from derived deformation theory and a construction of L-infinity algebras due to Fiorenza and Manetti. Our mixed Hodge structure comes then directly from the H^0 of an explicit mixed Hodge complex, in a similar way as the method of Hain for the fundamental group, and whose functoriality appears clearly.La théorie de Hodge mixte de Deligne fournit des structures supplémentaires sur les groupes de cohomologie des variétés algébriques complexes. Depuis, des structures de Hodge mixtes ont été construites sur les groupes d'homotopie rationnels de telles variétés par Morgan et Hain. Dans cette lignée, nous construisons des structures de Hodge mixtes sur des invariants associés aux représentations linéaires des groupes fondamentaux des variétés algébriques complexes lisses. Le point de départ est la théorie de Goldman et Millson qui relie la théorie des déformations de telles représentations à la théorie des déformations via les algèbres de Lie différentielles graduées. Ceci a été relu par P. Eyssidieux et C. Simpson dans le cas des variétés kählériennes compactes. Dans le cas non compact, et pour des représentations d'image finie, Kapovich et Millson ont construit seulement des graduations non canoniques. Pour construire des structures de Hodge mixtes dans le cas non compact et l'unifier avec le cas compact traité par Eyssidieux-Simpson, nous ré-écrivons la théorie de Goldman-Millson classique en utilisant des idées plus modernes de la théorie des déformations dérivée et une construction d'algèbres L-infini due à Fiorenza et Manetti. Notre structure de Hodge mixte provient alors directement du H^0 d'un complexe de Hodge mixte explicite, de façon similaire à la méthode de Hain pour le groupe fondamental, et dont la fonctorialité apparaît clairement

Mixed Hodge structures and representations of fundamental groups of algebraic varieties

34 pagesInternational audienceGiven a complex variety $X$, a linear algebraic group $G$ and a representation $\rho$ of the fundamental group $\pi_1(X,x)$ into $G$, we develop a framework for constructing a functorial mixed Hodge structure on the formal local ring of the representation variety of $\pi_1(X,x)$ into $G$ at $\rho$ using mixed Hodge diagrams and methods of $L_\infty$ algebras. We apply it in two geometric situations: either when $X$ is compact Kähler and $\rho$ is the monodromy of a variation of Hodge structure, or when $X$ is smooth quasi-projective and $\rho$ has finite image