Uniform ball property and existence of optimal shapes for a wide class of geometric functionals

In this paper, we are interested in shape optimization problems involving the ge ometry (normal, curvatures) of the surfaces. We consider a class of hypersurface s in $\mathbb{R}^{n}$ satisfying a uniform ball condition and we prove the exist ence of a $C^{1,1}$-regular minimizer for general geometric functionals and cons traints involving the first- and second-order properties of surfaces, such as in $\mathbb{R}^{3}$ problems of the form: $$\inf \int_{\partial \Omega} j_0 [ \mathbf{x},\mathbf{n}(\mathbf{x}) ] dA (\mathbf{x}) + \int_{\partial \Omega} j_1 [ \mathbf{x},\mathbf{n}(\mathbf{x}),H(\mathbf{x}) ] dA (\mathbf{x}) + \int_{\partial \Omega} j_2 [\mathbf{x},\mathbf{n}(\mathbf{x}),K(\mathbf{x})] dA (\mathbf{x}),$$ where $\mathbf{n}$, $H$, and $K$ respectively denotes the normal, the scalar mea n curvature and the Gaussian curvature. We gives some various applications in th e modelling of red blood cells such as the Canham-Helfrich energy and the Willmo re functional

Two-Photon Voltage Imaging of Supragranular Barrel Cortex in Mice: Oscillations and Responses

The supragranular layers of cortex are key information integration and computation areas with dominant cortico-cortical connections. While layers 2 and 3 are densely packed with somata, layer 1 is almost free of somata. The absence of somata makes the analysis of layer 1 difficult. Electrical recording from small processes within layer 1 are not possible and electric field recordings are difficult due to the low seal resistance. Imaging processes of layer 1 remains difficult as cells project into it from many distant areas and due to the dense and intermingled packing.Here, I record sensory signals in supragranular layers, including layer 1 through a combination of voltage sensitive dye imaging, and an intracellular calcium indicator. Optical sectioning with two-photon microscopy allowed resolution in depth, showing changes in the sensory signal within layer 1. Additionally, cortical oscillations were detected with the voltage-sensitive dye in the delta, theta, and beta bands, and, for the first time with voltage imaging, also in the slow-gamma (35 Hz) band, in vivo. Delta, theta, and gamma oscillations were modulated by sensory stimuli.As very little is known about membrane voltage oscillations in layer 1 and to optimize optical voltage recordings in layer 1, I developed a novel surgery to apply voltage dye primarily to layer 1, without removing the dura or injecting dye within the brain. I also applied a new voltage-sensitive dye optimized for tissue diffusion with this surgery. I imaged cortical membrane potential oscillations with two-photon microscopy depth-resolved (25 to 100 µm below dura) in anesthetized and awake mice. Again, I found delta (0.5-4 Hz), theta (4-10 Hz), low beta (10-20 Hz), and low gamma (30-40 Hz) oscillations. All oscillation bands were stronger in awake animals. While the power of delta, theta, and low beta oscillations increased with depth, the power of low gamma was more constant throughout layer 1. These findings identify layer 1 as an important coordination hub for the dynamic binding process of neurons mediated by oscillations.Okinawa Institute of Science and Technology Graduate Universit

On the minimization of total mean curvature

International audienceIn this paper we are interested in possible extensions of an inequality due to Minkowski: $\int_{\partial\Omega} H\,dA \geq \sqrt{4\pi A(\partial\Omega)}$ valid for any regular open set $\Omega\subset\mathbb{R}^3$, where $H$ denotes the scalar mean curvature and $A$ the area. We prove that this inequality holds true for axisymmetric domains which are convex in the direction orthogonal to the axis of symmetry. We also show that this inequality cannot be true in more general situations. However we prove that $\int_{\partial\Omega} |H|\,dA \geq \sqrt{4\pi A(\partial\Omega)}$ remains true for any axisymmetric domain

Semaine d'Etude Mathématiques et Entreprises 5 : Reconstruction de couches géologiques à partir de données discrètes

Ce rapport synthétise le travail de recherche mis en oeuvre durant la cinquième Semaine d'Etude Maths-Entreprises à l'Ecole des Mines de Nancy. Le sujet a été proposé par le consortium GOCAD: comment reconstituer efficacement le sous-sol terrestre à partir de données discrètes éparses ? Un état de l'art est d'abord effectué sur les différentes méthodes existantes : cokrigeage statistique (Calcagno et al., 2008), discrétisation numérique (Caumon et al., 2013) et modélisation physique entre deux horizons géologiques (Hjelle and Petersen, 2011). Ensuite, nous avons tenté d'adapter l'approche (Hjelle and Petersen, 2011) à notre problématique. Il s'agit de représenter chaque couche géologique par les points d'annulation d'une fonction dont l'évolution est gérée par une loi qui contient les informations connues et permettra la reconstitution in fine du sous-sol. Finalement, on effectue la résolution numérique de l'équation de Hamilton-Jacobi associée à cette loi de propagation, s'aidant de (Osher and Fedkiw, 2003). Par souci de simplicité et surtout par manque de temps, le modèle sera résolu numériquement en 2-D et sans failles

Voltage Imaging of Cortical Oscillations in Layer 1 with Two-Photon Microscopy

Membrane voltage oscillations in layer 1 (L1) of primary sensory cortices might be important indicators of cortical gain control, attentional focusing, and signal integration. However, electric field recordings are hampered by the low seal resistance of electrodes close to the brain surface. To study L1 membrane voltage oscillations, we synthesized a new voltage-sensitive dye, di1-ANNINE-6plus, that can diffuse into tissue. We applied it with a new surgery, leaving the dura intact but allowing injection of large quantities of staining solution, and imaged cortical membrane potential oscillations with two-photon microscopy depth-resolved (25 to 100 microm below dura) in anesthetized and awake mice. We found delta (0.5-4 Hz), theta (4-10 Hz), low beta (10-20 Hz), and low gamma (30-40 Hz) oscillations. All oscillations were stronger in awake animals. While the power of delta, theta, and low beta oscillations increased with depth, the power of low gamma was more constant throughout L1. These findings identify L1 as an important coordination hub for the dynamic binding process of neurons mediated by oscillations

Identification of Antigenic Proteins from Lichtheimia corymbifera for Farmer's Lung Disease Diagnosis.

The use of recombinant antigens has been shown to improve both the sensitivity and the standardization of the serological diagnosis of Farmer's lung disease (FLD). The aim of this study was to complete the panel of recombinant antigens available for FLD serodiagnosis with antigens of Lichtheimia corymbifera, known to be involved in FLD. L. corymbifera proteins were thus separated by 2D electrophoresis and subjected to western blotting with sera from 7 patients with FLD and 9 healthy exposed controls (HEC). FLD-associated immunoreactive proteins were identified by mass spectrometry based on a protein database specifically created for this study and subsequently produced as recombinant antigens. The ability of recombinant antigens to discriminate patients with FLD from controls was assessed by ELISA performed with sera from FLD patients (n = 41) and controls (n = 43) recruited from five university hospital pneumology departments of France and Switzerland. Forty-one FLD-associated immunoreactive proteins from L. corymbifera were identified. Six of them were produced as recombinant antigens. With a sensitivity and specificity of 81.4 and 77.3% respectively, dihydrolipoyl dehydrogenase was the most effective antigen for discriminating FLD patients from HEC. ELISA performed with the putative proteasome subunit alpha type as an antigen was especially specific (88.6%) and could thus be used for FLD confirmation. The production of recombinant antigens from L. corymbifera represents an additional step towards the development of a standardized ELISA kit for FLD diagnosis

Functional phenotypes determined by fluctuation-based clustering of lung function measurements in healthy and asthmatic cohort participants

Asthma is characterised by inflammation and reversible airway obstruction. However, these features are not always closely related. Fluctuations of daily lung function contain information on asthma phenotypes, exacerbation risk and response to long-acting β-agonists.; In search of subgroups of asthmatic participants with specific lung functional features, we developed and validated a novel clustering approach to asthma phenotyping, which exploits the information contained within the fluctuating behaviour of twice-daily lung function measurements.; Forced expiratory volume during the first second (FEV1) and peak expiratory flow (PEF) were prospectively measured over 4 weeks in 696 healthy and asthmatic school children (Protection Against Allergy - Study in Rural Environments (PASTURE)/EFRAIM cohort), and over 1 year in 138 asthmatic adults with mild-to-moderate or severe asthma (Pan-European Longitudinal Assessment of Clinical Course and BIOmarkers in Severe Chronic AIRway Disease (BIOAIR) cohort). Using enrichment analysis, we explored whether the method identifies clinically meaningful, distinct clusters of participants with different lung functional fluctuation patterns.; In the PASTURE/EFRAIM dataset, we found four distinct clusters. Two clusters were enriched in children with well-known clinical characteristics of asthma. In cluster 3, children from a farming environment predominated, whereas cluster 4 mainly consisted of healthy controls. About 79% of cluster 3 carried the asthma-risk allele rs7216389 of the 17q21 locus. In the BIOAIR dataset, we found two distinct clusters clearly discriminating between individuals with mild-to-moderate and severe asthma.; Our method identified dynamic functional asthma and healthy phenotypes, partly independent of atopy and inflammation but related to genetic markers on the 17q21 locus. The method can be used for disease phenotyping and possibly endotyping. It may identify participants with specific functional abnormalities, potentially needing a different therapeutic approach

omega-3 fatty acids contribute to the asthma-protective effect of unprocessed cow's milk

Background: Living on a farm has repeatedly been shown to protect children from asthma and allergies. A major factor involved in this effect is consumption of unprocessed cow's milk obtained directly from a farm. However, this phenomenon has never been shown in a longitudinal design, and the responsible milk components are still unknown. Objectives: We sought to assess the asthma-protective effect of unprocessed cow's milk consumption in a birth cohort and to determine whether the differences in the fatty acid (FA) composition of unprocessed farm milk and industrially processed milk contributed to this effect. Methods: The Protection Against Allergy-Study in Rural Environments (PASTURE) study followed 1133 children living in rural areas in 5 European countries from birth to age 6 years. In 934 children milk consumption was assessed by using yearly questionnaires, and samples of the ``usually'' consumed milk and serum samples of the children were collected at age 4 years. Doctor-diagnosed asthma was parent reported at age 6 years. In a nested case-control study of 35 asthmatic and 49 nonasthmatic children, 42 FAs were quantified in milk samples. Results: The risk of asthma at 6 years of age was reduced by previous consumption of unprocessed farm milk compared with shop milk (adjusted odds ratio for consumption at 4 years, 0.26; 95% CI,0.10-0.67). Part of the effect was explained by the higher fat content of farm milk, particularly the higher levels of omega-3 polyunsaturated FAs (adjusted odds ratio, 0.29; 95% CI,0.11-0.81). Conclusion: Continuous farm milk consumption in childhood protects against asthma at school age partially by means of higher intake of omega-3 polyunsaturated FAs, which are precursors of anti-inflammatory mediators.Peer reviewe