Spectral stability of higher order uniformly elliptic operators

We prove estimates for the variation of the eigenvalues of uniformly elliptic operators with homogeneous Dirichlet or Neumann boundary conditions upon variation of the open set on which an operator is defined. We consider operators of arbitrary even order and open sets admitting arbitrary strong degeneration. The main estimate is expressed via a natural and easily computable distance between open sets with continuous boundaries. Another estimate is obtained via the lower Hausdorff-Pompeiu deviation of the boundaries, which in general may be much smaller than the usual Hausdorff-Pompeiu distance. Finally, in the case of diffeomorphic open sets we obtain an estimate even without the assumption of continuity of the boundaries

Jensen-Shannon divergence as a measure of distinguishability between mixed quantum states

We discuss an alternative to relative entropy as a measure of distance between mixed quantum states. The proposed quantity is an extension to the realm of quantum theory of the Jensen-Shannon divergence (JSD) between probability distributions. The JSD has several interesting properties. It arises in information theory and, unlike the Kullback-Leibler divergence, it is symmetric, always well defined and bounded. We show that the quantum JSD (QJSD) shares with the relative entropy most of the physically relevant properties, in particular those required for a "good" quantum distinguishability measure. We relate it to other known quantum distances and we suggest possible applications in the field of the quantum information theory.Comment: 14 pages, corrected equation 1

Real time monitoring of water quality in an agricultural area with salinity problems

Agriculture is a highly water-demanding sector. Developed in recent years, the precision farming approach allows to optimize irrigation without compromising crops productivity. WSN networks are a key element of this approach because they allow to monitor continuously large number of parameters providing the possibility of a real-time intervention on field management practices. The WSN networks can be used to measure traditional parameters such as precipitation, soil moisture, or irradiation and others such as the quality of irrigation water and groundwater. The qualitative monitoring of these parameters is essential when the cultivation is carried out under complex conditions such as those represented by soils with salinization problem. This work fits this context by presenting the results of the first 13 months of an experimental campaign aimed at the measurement of soil, water (quality of irrigation and drainage water of the fields) and groundwater parameters by a WSN system. This paper analyzes results of this activity and provides practical suggestions to ensure a more efficient system

Sharp spectral stability estimates via the Lebesgue measure of domains for higher order elliptic operators

We prove sharp stability estimates for the variation of the eigenvalues of non-negative self-adjoint elliptic operators of arbitrary even order upon variation of the open sets on which they are defined. These estimates are expressed in terms of the Lebesgue measure of the symmetric difference of the open sets. Both Dirichlet and Neumann boundary conditions are considered

The ligand-receptor interactions based on silicon technology

We explored the use of porous silicon (pSi) technology for the construction of a biotechnological device, in which the ligand-receptor interactions are revealed by means of laser optical measurements. Here we report the settling of chemical procedures for the functionalization of the silicon wafers and for the subsequent anchoring of biological molecules such as a purified murine monoclonal antibody (UN1 mAb), an antibody anti-P8 protein of M13 phage and an antibody anti-A20 murine lymphoma cell line. The optical analysis of the interaction on the biochips between the bound biomolecules and their corresponding ligands indicated that the pSi is suitable for thi

Scaling rules in optomechanical semiconductor micropillars

International audienceSemiconductor pillar microcavities have recently emerged as a promising optomechanical platform in the unprecedented 20-GHz frequency range. Currently established models for the mechanical behavior of micropillars, however, rely on complete numerical simulations or semianalytical approaches, which makes their application to experiments notoriously difficult. Here we overcome this challenge with an effective model by reducing the full, hybridized mechanical mode picture of a micropillar to an approach that captures the observed global trends. We show experimentally the validity of this approach by studying the lateral size dependence of the frequency, amplitude, and lifetime of the mechanical modes of square-section pillar microcavities, using room-temperature pump-probe microscopy. General scaling rules for these quantities are found and explained through simple phenomenological models of the physical phenomena involved. We show that the energy shift ω m of the modes due to confinement is dependent on the inverse of their frequency ω 0 and lateral size L (ω m ∝ 1/ω 0 L 2) and that the mode lifetime τ is linear with pillar size and inversely proportional to their frequency (τ ∝ L/ω 0). The mode amplitude is in turn inversely proportional to the lateral size of the considered resonators. This is related to the dependence of the optomechanical coupling rate (g 0 ∝ 1/L) with the spatial extent of the confined electromagnetic and mechanical fields. Using a numerical model based on the finite-element method, we determine the magnitude and size dependence of g 0 and, by combining the results with the experimental data, we discuss the attainable single-photon cooperativity in these systems. The effective models proposed and the scaling rules found constitute an important tool in micropillar optomechanics and in the future development of more complex micropillar based devices

Cortical Oxygenation during a Motor Task to Evaluate Recovery in Subacute Stroke Patients: A Study with Near-Infrared Spectroscopy

In subacute stroke patients we studied cortical oxygenation changes by near-infrared spectroscopy (NIRS) during a motor task performed with the hemiparetic arm (15 s of reaching and grasping, 45 s of rest, repeated 6 times). Twenty-three subjects were included at baseline, compared with six healthy subjects, and restudied after 6 weeks of rehabilitation. Motor/premotor cortical changes in oxyhemoglobin detected by NIRS were quantified as the area under the curve (AUC) for the total cortex (TOT-AUC) and for both affected (AFF-AUC) and unaffected hemispheres (UN-AUC). The ratio between AUC and the number of task repetitions performed identified the cortical metabolic cost (CMC) or the oxygenation increase for a single movement. Fugl–Meyer assessment of the upper extremity (FMA-UE) was also performed. At baseline, both total and hemispheric CMC were significantly higher in stroke patients than in healthy subjects and inversely correlated with FMA-UE. After rehabilitation, changes in total-CMC and unaffected-CMC, but not Affected-CMC, were inversely correlated with variations in the FMA-UE score. A value > 5000 a.u. for the ratio baseline TOT-CMC /days since stroke was associated with not reaching the clinically important difference for FMA-UE after rehabilitation. In subacute stroke the CMC, a biomarker assessed by NIRS during a motor task with the hemiparetic arm, may describe cortical time/treatment reorganization and favor patient selection for rehabilitation

On the metric character of the quantum Jensen-Shannon divergence

In a recent paper, the generalization of the Jensen Shannon divergence (JSD) in the context of quantum theory has been studied (Phys. Rev. A 72, 052310 (2005)). This distance between quantum states has shown to verify several of the properties required for a good distinguishability measure. Here we investigate the metric character of this distance. More precisely we show, formally for pure states and by means of simulations for mixed states, that its square root verifies the triangle inequality.Comment: 8 pages, 1 figures, numerical results substantially improved in Sec. III. To appear in Phys. Rev.