Sharp estimates on the first Dirichlet eigenvalue of nonlinear elliptic operators via maximum principle

In this paper we study optimal lower and upper bounds for functionals involving the first Dirichlet eigenvalue $\lambda_{F}(p,\Omega)$ of the anisotropic $p$-Laplacian, $1<p<+\infty$. Our aim is to enhance how, by means of the $\mathcal P$-function method, it is possible to get several sharp estimates for $\lambda_{F}(p,\Omega)$ in terms of several geometric quantities associated to the domain. The $\mathcal P$-function method is based on a maximum principle for a suitable function involving the eigenfunction and its gradient

Seamless Positioning and Navigation in Urban Environment

L'abstract è presente nell'allegato / the abstract is in the attachmen

Temporal witnesses of non-classicality and conservation laws

A general entanglement-based witness of non-classicality has recently been proposed, which can be applied to testing quantum effects in gravity. This witness is based on generating entanglement between two quantum probes via a mediator. In this paper we provide a "temporal" variant of this witness, using a single quantum probe to assess the non-classicality of the mediator. Within the formalism of quantum theory, we show that if a system $M$ is capable of inducing a coherent dynamical evolution of a quantum system $Q$, in the presence of a conservation law, then $M$ must be non-classical. This argument supports witnesses of non-classicality relying on a single quantum probe, which can be applied to a number of open issues, notably in quantum gravity or quantum biology.Comment: 7 pages, 1 figur

New geomatics techniques for bees monitoring: the BEEMS project

Bees provide essential pollination services to natural ecosystems and agricultural crops. However, bee populations, both wild and farmed, are in decline around the world. To better manage and restore bee populations, long-term monitoring programs are needed. Direct monitoring of bees is expensive, time-consuming and requires a high level of expertise. Therefore, economic indicators for bee diversity and community composition are essential. The BEEMS Project, a project of Scientific and Technological Cooperation between Italy and Israel (Scientific Track 2019), aims to evaluate the cost-benefit ratio of new aerial Geomatics techniques compared to classical terrestrial methods to collect biotic and abiotic indicators of diversity bees and the composition of their communities. This work aims to present the project's progress, focusing on the Geomatics techniques applied to collect environmental data and produce spatial information useful for the work's progress

THE USE OF OPEN SOURCE SOFTWARE FOR MONITORING BEE DIVERSITY IN NATURAL SYSTEMS: THE BEEMS PROJECT

Abstract. This work wants to highlight the results obtained during the BEEMS (Monitoring Bee Diversity in Natural System) project, which the main goal was to answer the following question: Which biotic and abiotic indicators of floral and nesting resources best reflect the diversity of bee species and community composition in the Israeli natural environment? The research was oriented towards the cost-effectiveness analysis of new aerial geomatics techniques and classical ground-based methods for collecting the indicators described above, based only on open-source software for data analysis. Two complementary study systems in central Israel have been considered: the Alexander Stream National Park, an area undergoing an ecological restoration project in a sandy ecosystem, and the Judean foothills area, to the South of Tel Aviv. In each study system, different surveys of bees, flowers, nesting substrates and soil, using classical field measurement methods have been conducted. Simultaneously, an integrated aero photogrammetric survey, acquiring different spectral responses of the land surface by means of Uncrewed Aerial Vehicle (UAV) imaging systems have been performed. The multispectral sensors have provided surface spectral response out of the visible spectrum, while the photogrammetric reconstruction has provided three-dimensional information. Thanks to Artificial Intelligence algorithms and the richness of the data acquired, a methodology for Land Cover Classification has been developed. The results obtained by ground surveys and advanced geomatics tools have been compared and overlapped. The results are promising and show a good fit between the two approaches, and high performance of the geomatics tools in providing valuable ecological data

Efficiency and localisation for the first Dirichlet eigenfunction

Bounds are obtained for the efficiency or mean to peak ratio $E(\Omega)$ for the first Dirichlet eigenfunction (positive) for open, connected sets $\Omega$ with finite measure in Euclidean space $\R^m$. It is shown that (i) localisation implies vanishing efficiency, (ii) a vanishing upper bound for the efficiency implies localisation, (iii) localisation occurs for the first Dirichlet eigenfunctions for a wide class of elongating bounded, open, convex and planar sets, (iv) if $\Omega_n$ is any quadrilateral with perpendicular diagonals of lengths $1$ and $n$ respectively, then the sequence of first Dirichlet eigenfunctions localises, and $E(\Omega_n)=O\big(n^{-2/3}\log n\big)$. This disproves some claims in the literature. A key technical tool is the Feynman-Kac formula.Comment: 18 page

Single-Baseline RTK Positioning Using Dual-Frequency GNSS Receivers Inside Smartphones

Global Navigation Satellite System (GNSS) positioning is currently a common practice thanks to the development of mobile devices such as smartphones and tablets. The possibility to obtain raw GNSS measurements, such as pseudoranges and carrier-phase, from these instruments has opened new windows towards precise positioning using smart devices. This work aims to demonstrate the positioning performances in the case of a typical single-base Real-Time Kinematic (RTK) positioning while considering two different kinds of multi-frequency and multi-constellation master stations: a typical geodetic receiver and a smartphone device. The results have shown impressive performances in terms of precision in both cases: with a geodetic receiver as the master station, the reachable precisions are several mm for all 3D components while if a smartphone is used as the master station, the best results can be obtained considering the GPS+Galileo constellations, with a precision of about 2 cm both for 2D and Up components in the case of L1+L5 frequencies, or 3 cm for 2D components and 2 cm for the Up, in the case of an L1 frequency. Moreover, it has been demonstrated that it is not feasible to reach the phase ambiguities fixing: despite this, the precisions are still good and also the obtained 3D accuracies of positioning solutions are less than 1 m. So, it is possible to affirm that these results are very promising in the direction of cooperative positioning using smartphone devices

LAYING THE FOUNDATION FOR AN ARTIFICIAL NEURAL NETWORK FOR PHOTOGRAMMETRIC RIVERINE BATHYMETRY

Abstract. This work aims to test the effectiveness of artificial intelligence for correcting water refraction in shallow inland water using very high-resolution images collected by Unmanned Aerial Systems (UAS) and processed through a total FOSS workflow. The tests focus on using synthetic information extracted from the visible component of the electromagnetic spectrum. An artificial neural network is created using data of three morphologically similar alpine rivers. The RGB information, the SfM depth and seven radiometric indices are calculated and stacked in an 11-bands raster (input dataset). The depths are calculated as the difference between the Up component of the bathymetry cross-sections and the water surface quotas and constitute the dependent variable of the regression. The dataset is then scaled. The observations of one of the analyzed case studies are used as the unseen dataset to test the generalization capability of the model. The remaining observations are divided into test (20%) and training (80%) datasets. The generated NN is a 3-layer MLP model with one hidden layer and the Rectified Linear Unit (ReLU) and sigmoid activation functions. The weights are initialized to small Gaussian random values, and kernel regularizers, L1 and L2, are added to reduce the overfitting. Weights are updated with the Adam search technique, and the mean squared error is the loss function. The importance and significance of 11 variables are assessed. The model has a 0.70 r-squared score on the test dataset and 0.77 on the training dataset. The MAE is 0.06 and the RMSE 0.08, similar results obtained from the unseen dataset. Although the good metrics, the model shows some difficulties generalizing swallow depths

Blow-up solutions for some nonlinear elliptic equations involving a Finsler-Laplacian

In this paper we prove existence results and asymptotic behavior for strong solutions of the nonlinear elliptic problem with first order terms