Geometric bounds on the growth rate of null-controllability cost for the heat equation in small time

Given a control region $\Omega$ on a compact Riemannian manifold $M$, we consider the heat equation with a source term $g$ localized in $Omega$. It is known that any initial data in $L^2(M)$ can be stirred to 0 in an arbitrarily small time $T$ by applying a suitable control $g$ in $L^2([0,T]xOmega)$, and, as $T$ tends to 0, the norm of $g$ grows like $e^(C/T)$ times the norm of the data. We investigate how $C$ depends on the geometry of $Omega$. We prove $C\geq d^{2}/4$ where $d$ is the largest distance of a point in $M$ from $\Omega$. When $M$ is a segment of length $L$ controlled at one end, we prove $C\leq alpha L^{2}$ for some $alpha < 2$. Moreover, this bound implies $C\leq alpha L_{Omega}^2$ where $L_{Omega}$ is the length of the longest generalized geodesic in $M$ which does not intersect $\Omega$. The control transmutation method used in proving this last result is of a broader interest.Comment: 26 pages, uses elsart.sty, typos and section 5.3 correcte

mRNA binding protein staufen 1-dependent regulation of pyramidal cell spine morphology via NMDA receptor-mediated synaptic plasticity

Staufens (Stau) are RNA-binding proteins involved in mRNA transport, localization, decay and translational control. The Staufen 1 (Stau1) isoform was recently identified as necessary for the protein synthesis-dependent late phase long-term potentiation (late-LTP) and for the maintenance of mature dendritic spines and synaptic activity in hippocampal CA1 pyramidal cells, strongly suggesting a role of mRNA regulation by Stau1 in these processes. However, the causal relationship between these impairments in synaptic function (spine shape and basal synaptic activity) and plasticity (late-LTP) remains unclear. Here, we determine that the effects of Stau1 knockdown on spine shape and size are mimicked by blocking NMDA receptors (or elevating extracellular Mg2+) and that Stau1 knockdown in the presence of NMDA receptor blockade (or high Mg2+) has no further effect on spine shape and size. Moreover, the effect of Stau1 knockdown on late-LTP cannot be explained by these effects, since when tested in normal medium, slice cultures that had been treated with high Mg2+ (to impair NMDA receptor function) in combination with a control siRNA still exhibited late-LTP, while siRNA to Stau1 was still effective in blocking late-LTP. Our results indicate that Stau1 involvement in spine morphogenesis is dependent on ongoing NMDA receptor-mediated plasticity, but its effects on late-LTP are independent of these changes. These findings clarify the role of Stau1-dependent mRNA regulation in physiological and morphological changes underlying long-term synaptic plasticity in pyramidal cells

Comparison of Destructive Methods to Appraise the Mechanical Integrity of a Concrete Surface

peer reviewedDepending on the technique being used, the concrete removal operation prior to repair can be harmful to the residual concrete skin left on the structure. Whenever a tight bond between the repair and the old concrete is required, the soundness of the prepared surface should thus be assessed. Although this is widely recognized, there is no standard method intended to characterize the integrity of a concrete substrate after concrete removal. This paper presents the results of an investigation intended to assess and compare quantitatively different test methods, namely the Schmidt rebound hammer, the pull-out test and the pull-off test, to evaluate superficial mechanical integrity of a substrate after concrete removal operations. Although it does not yield a precise evaluation of compressive strength, the Schmidt rebound hammer test is recognized as a useful tool for performing quick surveys to assess concrete uniformity. The pull-off test is very well correlated with the splitting-tensile test, but it is not suited for vertical and overhead surfaces. The Capo pull-out test has limited interest for surface preparation, as it is applicable to flat surfaces only. Conversely, the accelerated pull-out test showed interesting potential as a simple and relatively rapid means for assessing the mechanical integrity of a concrete surface prior to repair for any type of concrete surface. More work is definitely required to refine the procedures and develop performance criteria. Nevertheless, it appears from the results generated in this study that the combination Schmidt hammer / pull-off test could fill the needs for the evaluation of horizontal surfaces after concrete removal, while the combination Schmidt hammer / accelerated pull-out test could be used effectively on vertical and overhead surfaces.Coopération scientifique WBI/Québe

On the null-controllability of the heat equation in unbounded domains

We make two remarks about the null-controllability of the heat equation with Dirichlet condition in unbounded domains. Firstly, we give a geometric necessary condition (for interior null-controllability in the Euclidean setting)which implies that one can not go infinitely far away from the control region without tending to the boundary (if any), but also applies when the distance to the control region is bounded. The proof builds on heat kernel estimates. Secondly, we describe a class of null-controllable heat equations on unbounded product domains. Elementary examples include an infinite strip in the plane controlled from one boundary and an infinite rod controlled from an internal infinite rod. The proof combines earlier results on compact manifolds with a new lemma saying that the null-controllability of an abstract control system and its null-controllability cost are not changed by taking its tensor product with a system generated by a non-positive self-adjoint operator.Comment: References [CdMZ01, dTZ00] added, abstract modifie

Non-structural controllability of linear elastic systems with structural damping

13 pages, a4paper, no figures. Note added in proof: After our article was accepted for publication, we became aware of a paper to appear in Asymptotic Analysis: "Internal null-controllability for a structurally damped beam equation" by Julian Edward and Louis Tebou. This paper concerns (18) when $M$ is a segment and focuses on the limit $\rho\to 0$. We claim that our Theorem~2 generalizes the main result of this paper (n.b. $L_{\Omega}1 and some C_p>0. Indeed, this fast controllability cost estimate is proved for more general linear elastic systems with structural damping and non-structural controls satisfying a spectral observability condition. Moreover, under some geometric optics condition on the subdomain allowing to apply the control transmutation method, this estimate is improved into p=1 and the dependence of C_p on the subdomain is made explicit. These results are analogous to the optimal ones known for the heat flow

From experimentation to the simulation of hygrothermal properties of walls insulated with straw

Le projet aPROpaille, dont les premiers résultats sont présentés ici, vise à améliorer la connaissance générale sur le comportement hygrothermique de mur dont l’isolation est principalement réalisée en paille. Outre une caractérisation globale des propriétés de la paille et de deux types d’enduits à base d’argile, une campagne d’essais a permis de déterminer les propriétés hygrothermiques de ces matériaux: porosité, courbe de sorption, perméabilité à la vapeur d’eau, absorption capillaire, absorption d’eau totale, chaleur massique et conductivité thermique. La détermination de ces paramètres a parfois nécessité la mise en place de protocoles ou de matériels inédits. Des simulations basées sur les propriétés définies dans la campagne d’essais sont également présentées. Les résultats obtenus montrent l’influence du type d’argile et de l’orientation des brins de paille.First results of aPROpaille project are presented. The goal of this project is to improve the knowledge about hygrothermal performances of walls in which thermal insulation is mainly provided by straw. Besides an overall properties characterization of straw and two types of earth plaster, a series of tests was performed to determine the hygrothermal properties of these materials: porosity, sorption curve, water vapour diffusion, capillary absorption, total water absorption, specific heat and thermal conductivity. The determination of these parameters required sometimes the implementation of unusual protocols or unreleased materials. Numerical simulations based on the properties defined in the test campaign are also presented. Results clearly point out the influence of the type of plaster and the orientation of fibres into straw bale.aPROpaill

rAAV-Mediated Overexpression of SOX9 and TGF-β via Carbon Dot-Guided Vector Delivery Enhances the Biological Activities in Human Bone Marrow-Derived Mesenchymal Stromal Cells

Scaffold-assisted gene therapy is a highly promising tool to treat articular cartilage lesions upon direct delivery of chondrogenic candidate sequences. The goal of this study was to examine the feasibility and benefits of providing highly chondroreparative agents, the cartilage-specific sex-determining region Y-type high-mobility group 9 (SOX9) transcription factor or the transforming growth factor beta (TGF-β), to human bone marrow-derived mesenchymal stromal cells (hMSCs) via clinically adapted, independent recombinant adeno-associated virus (rAAV) vectors formulated with carbon dots (CDs), a novel class of carbon-dominated nanomaterials. Effective complexation and release of a reporter rAAV-lacZ vector was achieved using four different CDs elaborated from 1-citric acid and pentaethylenehexamine (CD-1); 2-citric acid, poly(ethylene glycol) monomethyl ether (MW 550 Da), and N,N-dimethylethylenediamine (CD-2); 3-citric acid, branched poly(ethylenimine) (MW 600 Da), and poly(ethylene glycol) monomethyl ether (MW 2 kDa) (CD-3); and 4-citric acid and branched poly(ethylenimine) (MW 600 Da) (CD-4), allowing for the genetic modification of hMSCs. Among the nanoparticles, CD-2 showed an optimal ability for rAAV delivery (up to 2.2-fold increase in lacZ expression relative to free vector treatment with 100% cell viability for at least 10 days, the longest time point examined). Administration of therapeutic (SOX9, TGF-β) rAAV vectors in hMSCs via CD-2 led to the effective overexpression of each independent transgene, promoting enhanced cell proliferation (TGF-β) and cartilage matrix deposition (glycosaminoglycans, type-II collagen) for at least 21 days relative to control treatments (CD-2 lacking rAAV or associated to rAAV-lacZ), while advantageously restricting undesirable type-I and -X collagen deposition. These results reveal the potential of CD-guided rAAV gene administration in hMSCs as safe, non-invasive systems for translational strategies to enhance cartilage repair

The interaction between lipid derivatives of colchicine and tubulin: Consequences of the interaction of the alkaloid with lipid membranes

AbstractColchicine is a potent antimitotic poison which is well known to prevent microtubule assembly by binding tubulin very tightly. Colchicine also possesses anti-inflammatory properties which are not well understood yet. Here we show that colchicine tightly interacts with lipid layers. The physical and biological properties of three different lipid derivatives of colchicine are investigated parallel to those of membrane lipids in the presence of colchicine. Upon insertion in the fatty alkyl chains, colchicine rigidifies the lipid monolayers in a fluid phase and fluidifies rigid monolayers. Similarly X-ray diffraction data show that lecithin–water phases are destabilized by colchicine. In addition, an unexpectedly drastic enhancement of the photoisomerization rate of colchicine into lumicolchicine in the lipid environment is observed and further supports insertion of the alkaloid in membranes. Finally the interaction of colchicine with lipids makes the drug inaccessible to tubulin. The possible in vivo significance of these results is discussed

Design of Functionalized Lipids and Evidence for Their Binding to Photosystem II Core Complex by Oxygen Evolution Measurements, Atomic Force Microscopy, and Scanning Near-Field Optical Microscopy

AbstractPhotosystem II core complex (PSII CC) absorbs light energy and triggers a series of electron transfer reactions by oxidizing water while producing molecular oxygen. Synthetic lipids with different alkyl chains and spacer lengths bearing functionalized headgroups were specifically designed to bind the QB site and to anchor this large photosynthetic complex (240 kDa) in order to attempt two-dimensional crystallization. Among the series of different compounds that have been tested, oxygen evolution measurements have shown that dichlorophenyl urea (DCPU) binds very efficiently to the QB site of PSII CC, and therefore, that moiety has been linked covalently to the headgroup of synthetic lipids. The analysis of the monolayer behavior of these DCPU-lipids has allowed us to select ones bearing long spacers for the anchoring of PSII CC. Oxygen evolution measurements demonstrated that these long-spacer DCPU-lipids specifically bind to PSII CC and inhibit electron transfer. With the use of atomic force microscopy (AFM) and scanning near-field optical microscopy (SNOM), it was possible to visualize domains of PSII CC bound to DCPU-lipid monolayers. SNOM imaging has enabled us to confirm that domains observed by AFM were composed of PSII CC. Indeed, the SNOM topography images presented similar domains as those observed by AFM, but in addition, it allowed us to determine that these domains are fluorescent. Electron microscopy of these domains, however, has shown that the bound PSII CC was not crystalline