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

Approximate computing design exploration through data lifetime metrics

When designing an approximate computing system, the selection of the resources to modify is key. It is important that the error introduced in the system remains reasonable, but the size of the design exploration space can make this extremely difficult. In this paper, we propose to exploit a new metric for this selection: data lifetime. The concept comes from the field of reliability, where it can guide selective hardening: the more often a resource handles "live" data, the more critical it be-comes, the more important it will be to protect it. In this paper, we propose to use this same metric in a new way: identify the less critical resources as approximation targets in order to minimize the impact on the global system behavior and there-fore decrease the impact of approximation while increasing gains on other criteria

Arm-stroke descriptor variability during 200-M front crawl swimming

The present study aimed to explore the variability of the arm-stroke temporal descriptors between and within laps during middle-distance swimming event using IMMUs. Eight male swimmers performed a 200-m maximum front-crawl in which the inter-lap and intra-lap variability of velocity, stroke rate, stroke-phases duration and arm-coordination index were measured through five units of IMMU. An algorithm computes the 3D coordinates of the wrist by means the IMMU orientation and the kinematic chain of upper arm biomechanical model, and it recognizes the start events of the four arm-stroke phases. Velocity and stroke rate had a mean value of 1.47 ± 0.10 m·s−1 and 32.94 ± 4.84 cycles·min−1, respectively, and a significant decrease along the 200-m (p < 0.001; η2 = 0.80 and 0.47). The end of each lap showed significantly lower stroke rate compared to the start and the middle segment (p < 0.05; η2 = 0.55). No other significant inter-lap and intra-lap differences were detected. The two main findings are: (i) IMMUs technology can be an effective solution to continuously monitor the temporal descriptors during the swimming trial; (ii) swimmers are able to keep stable their temporal technique descriptors in a middle-distance event, despite the decrease of velocity and stroke rate

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

Comparing microphysical/dynamical outputs by different cloud resolving models: impact on passive microwave precipitation retrieval from satellite

International audienceMesoscale cloud resolving models (CRM's) are often utilized to generate consistent descriptions of the microphysical structure of precipitating clouds, which are then used by physically-based algorithms for retrieving precipitation from satellite-borne microwave radiometers. However, in principle, the simulated upwelling brightness temperatures (TB's) and derived precipitation retrievals generated by means of different CRM's with different microphysical assumptions, may be significantly different even when the models simulate well the storm dynamical and rainfall characteristics. In this paper, we investigate this issue for two well-known models having different treatment of the bulk microphysics, i.e. the UW-NMS and the MM5. To this end, the models are used to simulate the same 24-26 November 2002 flood-producing storm over northern Italy. The model outputs that best reproduce the structure of the storm, as it was observed by the Advanced Microwave Scanning Radiometer (AMSR) onboard the EOS-Aqua satellite, have been used in order to compute the upwelling TB's. Then, these TB's have been utilized for retrieving the precipitation fields from the AMSR observations. Finally, these results are compared in order to provide an indication of the CRM-effect on precipitation retrieval

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