Unified entropic measures of quantum correlations induced by local measurements

We introduce quantum correlations measures based on the minimal change in unified entropies induced by local rank-one projective measurements, divided by a factor that depends on the generalized purity of the system in the case of non-additive entropies. In this way, we overcome the issue of the artificial increasing of the value of quantum correlations measures based on non-additive entropies when an uncorrelated ancilla is appended to the system without changing the computability of our entropic correlations measures with respect to the previous ones. Moreover, we recover as limiting cases the quantum correlations measures based on von Neumann and R\'enyi entropies (i.e., additive entropies), for which the adjustment factor becomes trivial. In addition, we distinguish between total and semiquantum correlations and obtain some relations between them. Finally, we obtain analytical expressions of the entropic correlations measures for typical quantum bipartite systems.Comment: 10 pages, 1 figur

On a classical spectral optimization problem in linear elasticity

We consider a classical shape optimization problem for the eigenvalues of elliptic operators with homogeneous boundary conditions on domains in the $N$-dimensional Euclidean space. We survey recent results concerning the analytic dependence of the elementary symmetric functions of the eigenvalues upon domain perturbation and the role of balls as critical points of such functions subject to volume constraint. Our discussion concerns Dirichlet and buckling-type problems for polyharmonic operators, the Neumann and the intermediate problems for the biharmonic operator, the Lam\'{e} and the Reissner-Mindlin systems.Comment: To appear in the proceedings of the workshop `New Trends in Shape Optimization', Friedrich-Alexander Universit\"{a}t Erlangen-Nuremberg, 23-27 September 201

Hyperhomocysteinemia in L-dopa treated patients with Parkinson's disease: potential implications in cognitive dysfunction and dementia?

Abstract: Background: Hyperhomocysteinemia has been associated with cognitive dysfunction and dementia. The incidence of dementia in Parkinson’s Disease (PD) patients is higher than in the general population and plasma Homocysteine concentrations are increased in L-dopa treated PD patients. Objective: We evaluated the possible correlations between L-Dopa related hyperhomocysteinemia and cognitive dysfunction in PD. Methods: A Medline literature search was performed to identify all published studies on Homocysteine and cognitive dysfunction and dementia during the course of PD from 1966 to 31/03/2010. Results: Sixteen studies were found for review; ten studies focused on homocysteine and cognitive dysfunction in PD patients, five on homocysteine and PD dementia and two on homocysteine and markers of neurodegeneration in PD. The design of the study was retrospective in 14 studies, while 2 had a prospective design, with a variable follow-up period (from 24-weeks to 2 years). In most of the studies plasma homocysteine levels significantly correlated with cognitive functions, dementia and markers of neurodegeneration in PD patients. However, some studies did not confirm these findings. Several factors may concur to explain these partially conflicting results, including the retrospective design of the studies, their small sample size, their high percentage of excluded patients, and the use of a wide range of neuropsychological tasks in assessment of cognitive dysfunctions across the available studies. Conclusions: Available data seem to indicate a potential role of L-dopa related hyperhomocysteinemia on cognitive impairment and dementia during the course of PD

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

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

On an interior Calder\'{o}n operator and a related Steklov eigenproblem for Maxwell's equations

We discuss a Steklov-type problem for Maxwell's equations which is related to an interior Calder\'{o}n operator and an appropriate Dirichlet-to-Neumann type map. The corresponding Neumann-to-Dirichlet map turns out to be compact and this provides a Fourier basis of Steklov eigenfunctions for the associated energy spaces. With an approach similar to that developed by Auchmuty for the Laplace operator, we provide natural spectral representations for the appropriate trace spaces, for the Calder\'{o}n operator itself and for the solutions of the corresponding boundary value problems subject to electric or magnetic boundary conditions on a cavity.Comment: Submitted for publication to Siam Journal on Mathematical Analysis on 21 March 2019, revised on 12 May 2020, accepted for publication on 16 July 202

Nanoparticle Surface Functionalization: How to Improve Biocompatibility and Cellular Internalization

The use of nanoparticles (NP) in diagnosis and treatment of many human diseases, including cancer, is of increasing interest. However, cytotoxic effects of NPs on cells and the uptake efficiency significantly limit their use in clinical practice. The physico-chemical properties of NPs including surface composition, superficial charge, size and shape are considered the key factors that affect the biocompatibility and uptake efficiency of these nanoplatforms. Thanks to the possibility of modifying physico-chemical properties of NPs, it is possible to improve their biocompatibility and uptake efficiency through the functionalization of the NP surface. In this review, we summarize some of the most recent studies in which NP surface modification enhances biocompatibility and uptake. Furthermore, the most used techniques used to assess biocompatibility and uptake are also reported