Critical Points for Elliptic Equations with Prescribed Boundary Conditions

This paper concerns the existence of critical points for solutions to second order elliptic equations of the form $\nabla\cdot \sigma(x)\nabla u=0$ posed on a bounded domain $X$ with prescribed boundary conditions. In spatial dimension $n=2$, it is known that the number of critical points (where $\nabla u=0$) is related to the number of oscillations of the boundary condition independently of the (positive) coefficient $\sigma$. We show that the situation is different in dimension $n\geq3$. More precisely, we obtain that for any fixed (Dirichlet or Neumann) boundary condition for $u$ on $\partial X$, there exists an open set of smooth coefficients $\sigma(x)$ such that $\nabla u$ vanishes at least at one point in $X$. By using estimates related to the Laplacian with mixed boundary conditions, the result is first obtained for a piecewise constant conductivity with infinite contrast, a problem of independent interest. A second step shows that the topology of the vector field $\nabla u$ on a subdomain is not modified for appropriate bounded, sufficiently high-contrast, smooth coefficients $\sigma(x)$. These results find applications in the class of hybrid inverse problems, where optimal stability estimates for parameter reconstruction are obtained in the absence of critical points. Our results show that for any (finite number of) prescribed boundary conditions, there are coefficients $\sigma(x)$ for which the stability of the reconstructions will inevitably degrade.Comment: 26 pages, 4 figure

Volumetric analysis of carotid plaque components and cerebral microbleeds: a correlative study

PURPOSE: The purpose of this work was to explore the association between carotid plaque volume (total and the subcomponents) and cerebral microbleeds (CMBs). MATERIALS AND METHODS: Seventy-two consecutive (male 53; median age 64) patients were retrospectively analyzed. Carotid arteries were studied by using a 16-detector-row computed tomography scanner whereas brain was explored with a 1.5 Tesla system. CMBs were studied using a T2*-weighted gradient-recalled echo sequence. CMBs were classified as from absent (grade 1) to severe (grade 4). Component types of the carotid plaque were defined according to the following Hounsfield unit (HU) ranges: lipid less than 60 HU; fibrous tissue from 60 to 130 HU; calcification greater than 130 HU, and plaque volumes of each component were calculated. Each carotid artery was analyzed by 2 observers. RESULTS: The prevalence of CMBs was 35.3%. A statistically significant difference was observed between symptomatic (40%) and asymptomatic (11%) patients (P value = .001; OR = 6.07). Linear regression analysis demonstrated an association between the number of CMBs and the symptoms (P = .0018). Receiver operating characteristics curve analysis found an association between the carotid plaque subcomponents and CMBs (Az = .608, .621, and .615 for calcified, lipid, and mixed components, respectively), and Mann-Whitney test confirmed this association in particular for the lipid components (P value = .0267). CONCLUSIONS: Results of this study confirm the association between CMBs and symptoms and that there is an increased number of CMBs in symptomatic patients. Moreover, we found that an increased volume of the fatty component is associated with the presence and number of CMBs

Direct measurement of DNA-mediated adhesion between lipid bilayers

Multivalent interactions between deformable mesoscopic units are ubiquitous in biology, where membrane macromolecules mediate the interactions between neighbouring living cells and between cells and solid substrates. Lately, analogous artificial materials have been synthesised by functionalising the outer surface of compliant Brownian units, for example emulsion droplets and lipid vesicles, with selective linkers, in particular short DNA sequences. This development extended the range of applicability of DNA as a selective glue, originally applied to solid nano and colloidal particles. On very deformable lipid vesicles, the coupling between statistical effects of multivalent interactions and mechanical deformation of the membranes gives rise to complex emergent behaviours, as we recently contributed to demonstrate [Parolini et al., Nature Communications, 2015, 6, 5948]. Several aspects of the complex phenomenology observed in these systems still lack a quantitative experimental characterisation and fundamental understanding. Here we focus on the DNA-mediated multivalent interactions of a single liposome adhering to a flat supported bilayer. This simplified geometry enables the estimate of the membrane tension induced by the DNA-mediated adhesive forces acting on the liposome. Our experimental investigation is completed by morphological measurements and the characterisation of the DNA-melting transition, probed by in-situ F\"{o}rster Resonant Energy Transfer spectroscopy. Experimental results are compared with the predictions of an analytical theory that couples the deformation of the vesicle to a full description of the statistical mechanics of mobile linkers. With at most one fitting parameter, our theory is capable of semi-quantitatively matching experimental data, confirming the quality of the underlying assumptions.Comment: 16 pages, 7 figure

Evaluation of radiative transfer schemes for mesoscale model data assimilation: a case study

International audienceThe assimilation of Special Sensor Microwave Imager (SSM/I) data into the Mesoscale Model 5 (MM5) allows for improving the weather forecast. However the results suggested an update the Radiative Transfer Equation (RTE) within the three-dimensional variational (3DVAR) algorithm which is tailored for non rainy conditions only. To this purpose, a new RTE algorithm is tested, in order to account for radiometric response in rainy regions. The new brightness temperatures (TB) are estimated by using hydrometeor profiles from the MM5 mesoscale model, running with two different microphysical parameterizations. The goodness of the results is assessed by comparing the new TB with those of the original RTE algorithm in the 3DVAR code and the SSM/I observed data. The results confirm a better reliability of the new RTE compared to the old one

Association between carotid artery and abdominal aortic aneurysm plaque

The correlation between AAA and carotid artery plaque is unknown and a common etiology and pathophysiology is suspected by some authors. The purpose of this work was to explore the association between the features of a) carotid artery plaque and b) abdominal aortic aneurysm (AAA) plaques using multi-detector-CT Angiography (MDCTA). Forty-eight (32 males; median age 72 years) patients studied using a 16-detectors CT scanner were retrospectively analyzed. A region of interest (ROI) ≥ 2 mm2 was used to quantify the HU value of the plaque by two readers independently. Inter-observer reproducibility was calculated and Pearson correlation analysis was performed. The Bland-Altman plots showed the inter-observer reproducibility to be good. The Pearson correlation was 0.224 (95 % CI = 0.071 to 0.48), without statistically significant association between HU measured in the carotid artery plaque and in the AAA plaques (p = 0.138); after exclusion of the calcified plaques from the analysis, the rho values resulted 0.494 (95 % CI = 0.187 to 0.713) with a statistically significant association (p = 0.003). In this study, we found an association between the features of the non calcific carotid plaque and the features of AAA plaque

Effect of biomass features on oxygen transfer in conventional activated sludge and membrane bioreactor systems

The aim of the present study was to compare the oxygen transfer efficiency in a conventional activated sludge and a membrane bioreactor system. The oxygen transfer was evaluated by means of the oxygen transfer coefficient (kLa)20 and α-factor calculation, under different total suspended solids concentration, extracellular polymeric substances, sludge apparent viscosity and size of the flocs. The (kLa)20 and α-factor showed an exponential decreasing trend with total suspended solid, with a stronger (kLa)20 dependence in the conventional activated sludge than the membrane bioreactor. It was noted that the (kLa)20 in the conventional activated sludge become comparable to that in membrane bioreactor when the TSS concentration in the conventional activated sludge was higher than 5 gTSS L-1. Operating under high carbon to nitrogen ratio, the (kLa)20 increased in both conventional activated sludge and membrane bioreactor because of the sludge deflocculation and a weaker dependence of (kLa)20 with total suspended solid was noted. The results indicated that the most important parameters on the oxygen transfer efficiency were in order: the total suspended solid concentration, flocs size, sludge apparent viscosity, the protein to polysaccharides ratio and extracellular polymeric substances content. Based on the influence of the main biomass features affecting the (kLa)20 and considering the typical operating conditions in both systems, those of membrane bioreactor appeared to be more favorable to oxygen transfer efficiency compared to conventional activated sludge process

Versatile multiplexed super-resolution imaging of nanostructures by Quencher-Exchange-PAINT

This is the final version of the article. Available from Springer Verlag via the DOI in this record.The optical super-resolution technique DNA-PAINT (Point Accumulation Imaging in Nanoscale Topography) provides a flexible way to achieve imaging of nanoscale structures at ∼10-nanometer resolution. In DNA-PAINT, fluorescently labeled DNA “imager” strands bind transiently and with high specificity to complementary target “docking” strands anchored to the structure of interest. The localization of single binding events enables the assembly of a super-resolution image, and this approach effectively circumvents photobleaching. The solution exchange of imager strands is the basis of Exchange-PAINT, which enables multiplexed imaging that avoids chromatic aberrations. Fluid exchange during imaging typically requires specialized chambers or washes, which can disturb the sample. Additionally, diffusional washout of imager strands is slow in thick samples such as biological tissue slices. Here, we introduce Quencher-Exchange-PAINT—a new approach to Exchange-PAINT in regular open-top imaging chambers—which overcomes the comparatively slow imager strand switching via diffusional imager washout. Quencher-Exchange-PAINT uses “quencher” strands, i.e., oligonucleotides that prevent the imager from binding to the targets, to rapidly reduce unwanted single-stranded imager concentrations to negligible levels, decoupled from the absolute imager concentration. The quencher strands contain an effective dye quencher that reduces the fluorescence of quenched imager strands to negligible levels. We characterized Quencher-Exchange-PAINT when applied to synthetic, cellular, and thick tissue samples. Quencher-Exchange-PAINT opens the way for efficient multiplexed imaging of complex nanostructures, e.g., in thick tissues, without the need for washing steps. [Figure not available: see fulltext.]The work was supported by funding from the Human Frontier Science Program (No. 0027/2013) and the Engineering and Physical Sciences Research Council of the UK (No. EP/N008235/1)

Effectiveness of an automatic tracking software in underwater motion analysis

Tracking of markers placed on anatomical landmarks is a common practice in sports science to perform the kinematic analysis that interests both athletes and coaches. Although different software programs have been developed to automatically track markers and/or features, none of them was specifically designed to analyze underwater motion. Hence, this study aimed to evaluate the effectiveness of a software developed for automatic tracking of underwater movements (DVP), based on the Kanade-Lucas-Tomasi feature tracker. Twenty-one video recordings of different aquatic exercises (n = 2940 markers' positions) were manually tracked to determine the markers' center coordinates. Then, the videos were automatically tracked using DVP and a commercially available software (COM). Since tracking techniques may produce false targets, an operator was instructed to stop the automatic procedure and to correct the position of the cursor when the distance between the calculated marker's coordinate and the reference one was higher than 4 pixels. The proportion of manual interventions required by the software was used as a measure of the degree of automation. Overall, manual interventions were 10.4% lower for DVP (7.4%) than for COM (17.8%). Moreover, when examining the different exercise modes separately, the percentage of manual interventions was 5.6% to 29.3% lower for DVP than for COM. Similar results were observed when analyzing the type of marker rather than the type of exercise, with 9.9% less manual interventions for DVP than for COM. In conclusion, based on these results, the developed automatic tracking software presented can be used as a valid and useful tool for underwater motion analysis. Key PointsThe availability of effective software for automatic tracking would represent a significant advance for the practical use of kinematic analysis in swimming and other aquatic sports.An important feature of automatic tracking software is to require limited human interventions and supervision, thus allowing short processing time.When tracking underwater movements, the degree of automation of the tracking procedure is influenced by the capability of the algorithm to overcome difficulties linked to the small target size, the low image quality and the presence of background clutters.The newly developed feature-tracking algorithm has shown a good automatic tracking effectiveness in underwater motion analysis with significantly smaller percentage of required manual interventions when compared to a commercial software