The method of fundamental solutions for three-dimensional inverse geometric elasticity problems

We investigate the numerical reconstruction of smooth star-shaped voids (rigid inclusions and cavities) which are compactly contained in a three-dimensional isotropic linear elastic medium from a single set of Cauchy data (i.e. nondestructive boundary displacement and traction measurements) on the accessible outer boundary. This inverse geometric problem in three-dimensional elasticity is approximated using the method of fundamental solutions (MFS). The parameters describing the boundary of the unknown void, its centre, and the contraction and dilation factors employed for selecting the fictitious surfaces where the MFS sources are to be positioned, are taken as unknowns of the problem. In this way, the original inverse geometric problem is reduced to finding the minimum of a nonlinear least-squares functional that measures the difference between the given and computed data, penalized with respect to both the MFS constants and the derivative of the radial coordinates describing the position of the star-shaped void. The interior source points are anchored and move with the void during the iterative reconstruction procedure. The feasibility of this new method is illustrated in several numerical examples

A general wavelet-based profile decomposition in the critical embedding of function spaces

We characterize the lack of compactness in the critical embedding of functions spaces $X\subset Y$ having similar scaling properties in the following terms : a sequence $(u_n)_{n\geq 0}$ bounded in $X$ has a subsequence that can be expressed as a finite sum of translations and dilations of functions $(\phi_l)_{l>0}$ such that the remainder converges to zero in $Y$ as the number of functions in the sum and $n$ tend to $+\infty$. Such a decomposition was established by G\'erard for the embedding of the homogeneous Sobolev space $X=\dot H^s$ into the $Y=L^p$ in $d$ dimensions with $0<s=d/2-d/p$, and then generalized by Jaffard to the case where $X$ is a Riesz potential space, using wavelet expansions. In this paper, we revisit the wavelet-based profile decomposition, in order to treat a larger range of examples of critical embedding in a hopefully simplified way. In particular we identify two generic properties on the spaces $X$ and $Y$ that are of key use in building the profile decomposition. These properties may then easily be checked for typical choices of $X$ and $Y$ satisfying critical embedding properties. These includes Sobolev, Besov, Triebel-Lizorkin, Lorentz, H\"older and BMO spaces.Comment: 24 page

Polymer multilayer films obtained by electrochemically catalyzed click chemistry.

We report the covalent layer-by-layer construction of polyelectrolyte multilayer (PEM) films by using an efficient electrochemically triggered Sharpless click reaction. The click reaction is catalyzed by Cu(I) which is generated in situ from Cu(II) (originating from the dissolution of CuSO(4)) at the electrode constituting the substrate of the film. The film buildup can be controlled by the application of a mild potential inducing the reduction of Cu(II) to Cu(I) in the absence of any reducing agent or any ligand. The experiments were carried out in an electrochemical quartz crystal microbalance cell which allows both to apply a controlled potential on a gold electrode and to follow the mass deposited on the electrode through the quartz crystal microbalance. Poly(acrylic acid) (PAA) modified with either alkyne (PAA(Alk)) or azide (PAA(Az)) functions grafted onto the PAA backbone through ethylene glycol arms were used to build the PEM films. Construction takes place on gold electrodes whose potentials are more negative than a critical value, which lies between -70 and -150 mV vs Ag/AgCl (KCl sat.) reference electrode. The film thickness increment per bilayer appears independent of the applied voltage as long as it is more negative than the critical potential, but it depends upon Cu(II) and polyelectrolyte concentrations in solution and upon the reduction time of Cu(II) during each deposition step. An increase of any of these latter parameters leads to an increase of the mass deposited per layer. For given buildup conditions, the construction levels off after a given number of deposition steps which increases with the Cu(II) concentration and/or the Cu(II) reduction time. A model based on the diffusion of Cu(II) and Cu(I) ions through the film and the dynamics of the polyelectrolyte anchoring on the film, during the reduction period of Cu(II), is proposed to explain the major buildup features.journal articleresearch support, non-u.s. gov't2010 Feb 16importe

Studying complex interventions : reflections from the FEMHealth project on evaluating fee exemption policies in West Africa and Morocco

Peer reviewedPublisher PD

Ensemble approach for generalized network dismantling

Finding a set of nodes in a network, whose removal fragments the network below some target size at minimal cost is called network dismantling problem and it belongs to the NP-hard computational class. In this paper, we explore the (generalized) network dismantling problem by exploring the spectral approximation with the variant of the power-iteration method. In particular, we explore the network dismantling solution landscape by creating the ensemble of possible solutions from different initial conditions and a different number of iterations of the spectral approximation.Comment: 11 Pages, 4 Figures, 4 Table

Urinary Exosomal microRNA-451-5p Is a Potential Early Biomarker of Diabetic Nephropathy in Rats

Non-invasive renal signatures can help in serial monitoring of diabetic patients. We tested whether urinary exosomal (UE) microRNA (miR) analysis could non-invasively predict renal pathology in diabetic rats during the course of diabetes. Diabetes mellitus (DM) was induced in male Wistar rats by a single intraperitoneal injection of streptozotocin (STZ, 50 mg/kg body weight). Non-diabetic control (CTRL) rats were injected with vehicle. Insulin (INS) treatment (5U/d, s.c.) was provided to 50% of the DM rats. Urine samples were collected at weeks 3, 6, and 9 following injections and UE prepared. An increase in miR-451-5p and miR-16, observed by pilot small RNA sequencing of UE RNA, was confirmed by quantitative real-time polymerase chain reaction (qPCR) and selected for further study. Subsets of rats were euthanized after 3, 6, and 9 weeks of diabetes for renal pathology analysis, including determination of the tubulointerstitial fibrotic index (TFI) and glomerulosclerotic index (GI) scores. qPCR showed a substantial rise in miR-451-5p in UE from DM rats during thecourse of diabetes, with a significant rise (median fold change >1000) between 3 and 6 weeks. Moreover, UE miR-451-5p at 6 weeks predicted urine albumin at 9 weeks (r = 0.76). A delayed but significant rise was also observed for miR-16. In contrast, mean urine albumin only increased 21% between 3 and 6 weeks (non-significant rise), and renal TFI and GI were unchanged till 9 weeks. Renal expression of miR-451-5p and miR-16 (at 10 weeks) did not correlate with urine levels, and moreover, was negatively associated with indices of renal pathology (r�-0.70, p = 0.005 for TFI and r�-0.6, p�0.02 for GI). Overall, a relative elevation in renal miR-451-5p and miR-16 in diabetes appeared protective against diabetes- induced kidney fibrosis; while UE miR-451-5p may hold prognostic value as an earlyand sensitive non-invasive indicator of renal diseas