On the multiplicity of the second eigenvalue of the Laplacian in non simply connected domains--with some numerics--

We revisit an interesting example proposed by Maria Hoffmann-Ostenhof, the second author and Nikolai Nadirashvili of a bounded domain in R2 for which the second eigenvalue of the Dirichlet Laplacian has multiplicity three. We also analyze carefully the first eigenvalues of the Laplacian in the case of the disk with two symmetric cracks placed on a smaller concentric disk in function of their size.Comment: 9 figure

Retinoid acid receptors in human colorectal cancer: An unexpected link with patient outcome.

International audienceThe status of the three retinoic acid receptors (RARs) α, β and γ in human colorectal cancer (CRC) has not as yet been examined. RARs are in part responsible for the actions of the retinoids (vitamin A and its derivatives), which are essential for human health and survival due to their extensive involvement in numerous cellular processes, in particular in epithelial morphology. The present study examined the expression of the three RARs in CRC using immunohistochemical analysis of paraffin-embedded tissue sections. RAR expression in tumor (T) and adjacent non-tumor (NT) specimens from stage I (n=6), stage II (n=34), stage III (n=26) and stage IV (n=14) CRC patients was compared with that in normal mucous membranes (n=10) from control individuals. The findings were correlated with tumor grade, treatment response (progression during treatment, remission, chemoresistance) and survival as clinicopathological parameters. RARα and γ expression was decreased with CRC stage in the T tissues (P=0.016 and P=0.052, respectively), suggesting that they may be used as predictive markers. RARβ expression in the NT tissues was associated with a more favorable prognosis (P=0.04). These results provide important information on the tumor microenvironment (the area adjacent to tumor cells)

A new role under sortilin's belt in cancer.

The neurotensin receptor-3 also known as sortilin was the first member of the small family of vacuolar protein sorting 10 protein domain (Vps10p) discovered two decades ago in the human brain. The expression of sortilin is not confined to the nervous system but sortilin is ubiquitously expressed in many tissues. Sortilin has multiple roles in the cell as a receptor or a co-receptor, in protein transport of many interacting partners to the plasma membrane, to the endocytic pathway and to the lysosomes for protein degradation. Sortilin could be considered as the cells own shuttle system. In many human diseases including neurological diseases and cancer, sortilin expression has been shown to be deregulated. In addition, some studies have highlighted that the extracellular domain of sortilin is shedded into the culture media by an unknown mechanism. Sortilin can be released in exosomes and appears to control some mechanisms of exosome biogenesis. In lung cancer cells, sortilin can associate with two receptor tyrosine kinase receptors called the TES complex found in exosomes. Exosomes carrying the TES complex can convey a microenvironment control through the activation of ErbB signaling pathways and the release of angiogenic factors. Deregulation of sortilin function is now emerging to be implicated in four major human diseases- cardiovascular disease, Type 2 diabetes mellitus, Alzheimer’s disease and cancer

Neurotrophins are expressed in giant cell arteritis lesions and may contribute to vascular remodeling

International audienceIntroduction: Giant cell arteritis (GCA) is characterized by intimal hyperplasia leading to ischaemic manifestations that involve large vessels. Neurotrophins (NTs) and their receptors (NTRs) are protein factors for growth, differentiation and survival of neurons. They are also involved in the migration of vascular smooth muscle cells (VSMCs). Our aim was to investigate whether NTs and NTRs are involved in vascular remodelling of GCA.Methods: We included consecutive patients who underwent a temporal artery biopsy for suspected GCA. We developed an enzymatic digestion method to obtain VSMCs from smooth muscle cells in GCA patients and controls. Neurotrophin protein and gene expression and functional assays were studied from these VSMCs. Neurotrophin expression was also analysed by immunohistochemistry in GCA patients and controls.Results: Whereas temporal arteries of both GCA patients (n = 22) and controls (n = 21) expressed nerve growth factor (NGF), brain-derived neurotrophic factor (BDNF), tropomyosin receptor kinase B (TrkB) and sortilin, immunostaining was more intense in GCA patients, especially in the media and intima, while neurotrophin-3 (NT-3) and P75 receptor (P75NTR) were only detected in TA from GCA patients. Expression of TrkB, a BDNF receptor, was higher in GCA patients with ischaemic complications. Serum NGF was significantly higher in GCA patients (n = 28) vs. controls (n = 48), whereas no significant difference was found for BDNF and NT-3. NGF and BDNF enhanced GCA-derived temporal artery VSMC proliferation and BDNF facilitated migration of temporal artery VSMCs in patients with GCA compared to controls.Conclusions: Our results suggest that NTs and NTRs are involved in vascular remodelling of GCA. In GCA-derived temporal artery VSMC, NGF promoted proliferation and BDNF enhanced migration by binding to TrkB and p75NTR receptors. Further experiments are needed on a larger number of VSMC samples to confirm these results

Études numériques du spectre d'un opérateur de Schrödinger avec champ magnétique constant

Les deux premieres parties concernent le calcul de la premiere valeur propre de familles d'op erateurs de Neumann en utilisant les diff erences finies et les el ements finis. La troisieme partie porte sur un probleme de valeurs propres faisant intervenir un op erateur de Schr odinger avec champ magn etique constant issu de la th eorie de Ginzburg-Landau et concernant la supraconductivit e de certains mat eriaux. Pour la r esolution num erique, une m ethode bas ee sur les el ements finis avec int egration num erique est utilis ee. L'existence des solutions du probleme variationnel spectral a et e etablie. La quatrieme partie porte sur la mise en oeuvre de la r esolution num erique du probleme pr ec edent. Les r esultats num eriques concernant la localisation de l' etat fondamental de l'op erateur de Schr odinger avec champ magn etique constant dans diff erents domaines (carr es, disques, ellipses, polygones) sont conformes a la th eorie : la concentration des electrons supraconducteurs au voisinage des points dont la courbure est maximale.NANTES-BU Sciences (441092104) / SudocSudocFranceF

Modélisation et simulation de l'activité électrique du coeur dans le thorax, analyse numérique et méthodes de volumes finis

Cette thèse s'inscrit dans le cadre de la modélisation en bio-mathématiques et dans celui de l'analyse numérique et du calcul scientifique. Le modèle bidomaine décrit l'activité électrique du coeur. Cette activité est complexe : elle relève à l'échelle cellulaire de processus biochimiques et à l'échelle macroscopique de la structure anisotrope des tissus cardiaques, des caractéristiques du thorax. Une application fondamentale du modèle est la simulation d'électrocardiogrammes. Des méthodes de calcul type volumes finis sont développées pour la résolution du modèle. Dans un premier temps, la stabilité et la convergence de schémas volumes finis classiques est établie, en théorie et numériquement, pour une version simplifiée du modèle bidomaine. Pour faire face à des difficultés conceptuelles et pratiques du modèle complet (anisotropie des tissus, conditions limites, maillages non structurés distordus), une seconde classe de schémas 2D-3D, cell-vertex centered, est mise au point et testée.The two purposes of that PhD thesis are firstly the modeling in the field of bio mathematics and secondly numerical analysis and scientific computing. The bidomain model describes the electrical activity of the heart. This activity is complex : at the cellular scale it is based on biochemical processes and at the macroscopic scale on the anisotropic structure of the cardiac tissues and the torso characteristics. A fundamental application for that model is the simulation of electrocardiograms. Finite volumes methods have been developed to solve the model. First of all the stability and the convergence of a classical finite volumes scheme is proved, theoretically and numerically, for a simplified version of the bidomain model. To handle with conceptual and practical difficulties of the complete model (tissues anisotropy, limit conditions, distorted and unstructured meshes), a second class of finite volumes schemes in 2D or 3D, called cell-vertex centered, has been elaborated and tested.NANTES-BU Sciences (441092104) / SudocSudocFranceF

Etude théorique et approximation numérique d'un problème inverse de transfert de chaleur

Nous nous intéressons à l étude d un problème d analyse des transferts de chaleur qui modélise une opération de soudage. L approche que nous considérons ne s occupe que de la partie solide de la plaque. Elle consiste à résoudre un problème à frontière libre. Pour cela, nous proposons une formulation en optimisation de forme. Le problème d état est gouverné par un opérateur qui, pour certaines données, n est pas coercif. Cela complique l étude de la continuité du problème d état. Nous surmontons cette difficulté en utilisant le degré topologique de Leray-Shauder, ainsi nous montrons l existence d un domaine optimal. Ensuite, nous considérons une discrétisation de ce problème basée sur les éléments finis linéaires. Nous prouvons alors que le problème discret admet une solution et nous montrons qu une sous-suite des solutions de ce problème convergence vers la solution du problème continu. Enfin, nous présentons des résultats numériques réalisés par deux méthodes : la méthode déterministe basée sur le calcul du gradient de forme, et les algorithmes génétiques combinés avec la logique floue et le calcul parallèle. Ainsi une étude comparative de ces deux méthodes aux niveaux qualitatif et quantitatif a été présentée.We are interested in studying a heat transfer problem which modeling a welding process. The approach that we consider deals only with the solid part of the plate. It consists in solving a free boundary problem. For this, we propose a shape optimization formulation. The state problem governed by an operator which for some data is not coercif. This complicates the study of the continuity of the state problem.We overcome this difficulty using the topological degree of Leray-Schauder and we show the existence of an optimal domain. Next, we consider a discretization of this problem based on linear finite elements. We prove that the approximate problem is solvable and we show that a subsequence of the solution of this approximate problem converges to the solution of the continuous problem. Finally, we present numerical results achieved by two methods : the deterministic method based on the gradient-likes method and genetic algorithms combined with fuzzy logic and parallel computing. A comparative study of two methods for qualitative and quantitative levels was presented.NANTES-BU Sciences (441092104) / SudocSudocFranceF

On the multiplicity of the second eigenvalue of the Laplacian in non simply connected domains - with some numerics -

We revisit an interesting example proposed by Maria Hoffmann-Ostenhof, the second author and Nikolai Nadirashvili of a bounded domain in R-2 for which the second eigenvalue of the Dirichlet Laplacian has multiplicity 3. We also analyze carefully the first eigenvalues of the Laplacian in the case of the disk with two symmetric cracks placed on a smaller concentric disk in function of their size

Sortilin mediates the release and transfer of exosomes in concert with two tyrosine kinase receptors.

International audience: The transfer of exosomes containing both genetic and protein materials is necessary for the control of cancer cell microenvironment to promote tumor angiogenesis. The nature and function of proteins found in the exosomal cargo, their mechanisms in membrane transport and related signaling events are not clearly understood. In this study, we demonstrate in human lung cancer A549 cells, that the exosome release mechanism is closely linked to a multifaceted receptor, neurotensin (NT) receptor-3 also called sortilin. Sortilin is already known to be important for cancer cell function. Here, we report for the first time its role in the assembly of a tyrosine kinase complex and subsequent exosome release. This novel complex (TES complex) found in exosomes results in the linkage of two tyrosine kinase receptors, TrkB and EGFR with sortilin. Using in vitro models, we demonstrate that this complex containing sortilin exhibits a control on endothelial cells and angiogenesis activation through exosome transfer