A family of generalized quantum entropies: definition and properties

We present a quantum version of the generalized $(h,\phi)$-entropies, introduced by Salicr\'u \textit{et al.} for the study of classical probability distributions. We establish their basic properties, and show that already known quantum entropies such as von Neumann, and quantum versions of R\'enyi, Tsallis, and unified entropies, constitute particular classes of the present general quantum Salicr\'u form. We exhibit that majorization plays a key role in explaining most of their common features. We give a characterization of the quantum $(h,\phi)$-entropies under the action of quantum operations, and study their properties for composite systems. We apply these generalized entropies to the problem of detection of quantum entanglement, and introduce a discussion on possible generalized conditional entropies as well.Comment: 26 pages, 1 figure. Close to published versio

On a Babu\u161ka Paradox for Polyharmonic Operators: Spectral Stability and Boundary Homogenization for Intermediate Problems

We analyse the spectral convergence of high order elliptic differential operators subject to singular domain perturbations and homogeneous boundary conditions of intermediate type. We identify sharp assumptions on the domain perturbations improving, in the case of polyharmonic operators of higher order, conditions known to be sharp in the case of fourth order operators. The optimality is proved by analysing in detail a boundary homogenization problem, which provides a smooth version of a polyharmonic Babuska paradox

Tuning the potential drop at graphene/protic ionic liquid interface by molecular structure engineering

Ionic liquids (ILs) have been extensively employed in many applications involving interfaces with carbon-based electrodes, such as energy storage devices (batteries or supercapacitors) or electrocatalytic devices, where the way each ion of the IL interacts with the electrode has a strong impact on the overall performance of the device. For instance, the amount of potential difference between the electrode and the bulk of the IL is highly sensitive to the IL composition and it is directly related to the device capacitance. The selection of the most suited pair of ions often proceeds by time-consuming and costly trial-and-error approaches. It is necessary to understand the atomistic features of the interface to determine the effect of each ion on the potential drop. By classical molecular dynamics simulations, we show that it is possible to quickly infer the interface potential arising at the carbon electrode by carefully inspecting the molecular structure of the IL. The ion orientation at the interface is, in fact, determined by the distribution of charges within the molecules. Depending on where charges are located, ions can either lie flat or perpendicular to the interface to minimize the surface energy. The interface potential is found to be mainly determined by ion-ion interactions dictating the interface energy minimization process, whereas ion-electrode interactions are found to enforce higher ordering and charge layers stacking but not to induce selective adsorption of an ion over the other

Gradient based sequential Markov chain Monte Carlo for multitarget tracking with correlated measurements

Measurements in wireless sensor networks (WSNs) are often correlated both in space and in time. This paper focuses on tracking multiple targets in WSNs by taking into consideration these measurement correlations. A sequential Markov Chain Monte Carlo (SMCMC) approach is proposed in which a Metropolis within Gibbs refinement step and a likelihood gradient proposal are introduced. This SMCMC filter is applied to case studies with cellular network received signal strength data in which the shadowing component correlations in space and time are estimated. The efficiency of the SMCMC approach compared to particle filtering, as well as the gradient proposal compared to a basic prior proposal, are demonstrated through numerical simulations. The accuracy improvement with the gradient-based SMCMC is above 90% when using a low number of particles. Thanks to its sequential nature, the proposed approach can be applied to various WSN applications, including traffic mobility monitoring and prediction

Sequential Markov Chain Monte Carlo for multi-target tracking with correlated RSS measurements

In this paper, we present a Bayesian approach to accurately track multiple objects based on Received Signal Strength (RSS) measurements. This work shows that taking into account the spatial correlations of the observations caused by the random shadowing effect can induce significant tracking performance improvements, especially in very noisy scenarios. Additionally, the superiority of the proposed Sequential Markov Chain Monte Carlo (SMCMC) method over the more common Sequential Importance Resampling (SIR) technique is empirically demonstrated through numerical simulations in which multiple targets have to be tracked

Spectral analysis of the biharmonic operator subject to Neumann boundary conditions on dumbbell domains

We consider the biharmonic operator subject to homogeneous boundary conditions of Neumann type on a planar dumbbell domain which consists of two disjoint domains connected by a thin channel. We analyse the spectral behaviour of the operator, characterizing the limit of the eigenvalues and of the eigenprojections as the thickness of the channel goes to zero. In applications to linear elasticity, the fourth order operator under consideration is related to the deformation of a free elastic plate, a part of which shrinks to a segment. In contrast to what happens with the classical second order case, it turns out that the limiting equation is here distorted by a strange factor depending on a parameter which plays the role of the Poisson coefficient of the represented plate.Comment: To appear in "Integral Equations and Operator Theory