Resolution of Born Scattering in Curve Geometries: Aspect-Limited Observations and Excitations

In inverse scattering problems, the most accurate possible imaging results require plane waves impinging from all directions and scattered fields observed in all observation directions around the object. Since this full information is infrequently available in actual applications, this paper is concerned with the mathematical analysis and numerical simulations to estimate the achievable resolution in object reconstruction from the knowledge of the scattered far-field when limited data are available at a single frequency. The investigation focuses on evaluating the Number of Degrees of Freedom (NDF) and the Point Spread Function (PSF), which accounts for reconstructing a point-like unknown and depends on the NDF. The discussion concerns objects belonging to curve geometries, in this case, circumference and square scatterers. In addition, since the exact evaluation of the PSF can only be accomplished numerically, an approximated closed-form evaluation is introduced and compared with the exact one. The approximation accuracy of the PSF is verified by numerical results, at least within its main lobe region, which is the most critical as far as the resolution discussion is concerned. The main result of the analysis is the space variance of the PSF for the considered geometries, showing that the resolution is different over the investigation domain. Finally, two numerical applications of the PSF concept are shown, and their relevance in the presence of noisy data is outlined.In inverse scattering problems, the most accurate possible imaging results require plane waves impinging from all directions and scattered fields observed in all observation directions around the object. Since this full information is infrequently available in actual applications, this paper is concerned with the mathematical analysis and numerical simulations to estimate the achievable resolution in object reconstruction from the knowledge of the scattered far-field when limited data are available at a single frequency. The investigation focuses on evaluating the Number of Degrees of Freedom (NDF) and the Point Spread Function (PSF), which accounts for reconstructing a point-like unknown and depends on the NDF. The discussion concerns objects belonging to curve geometries, in this case, circumference and square scatterers. In addition, since the exact evaluation of the PSF can only be accomplished numerically, an approximated closed-form evaluation is introduced and compared with the exact one. The approximation accuracy of the PSF is verified by numerical results, at least within its main lobe region, which is the most critical as far as the resolution discussion is concerned. The main result of the analysis is the space variance of the PSF for the considered geometries, showing that the resolution is different over the investigation domain. Finally, two numerical applications of the PSF concept are shown, and their relevance in the presence of noisy data is outlined

Existence results for an impulsive abstract partial differential equation with state-dependent delay

AbstractIn this paper, we establish the existence of mild solutions for a class of impulsive abstract partial functional differential equation with state-dependent delay

A Test of Gravitational Theories Including Torsion with the BepiColombo Radio Science Experiment

Within the framework of the relativity experiment of the ESA/JAXA BepiColombo mission to Mercury, which was launched at the end of 2018, we describe how a test of alternative theories of gravity, including torsion can be set up. Following March et al. (2011), the effects of a non-vanishing spacetime torsion have been parameterized by three torsion parameters, t(1), t(2), and t(3). These parameters can be estimated within a global least squares fit, together with a number of parameters of interest, such as post-Newtonian parameters gamma and beta, and the orbits of Mercury and the Earth. The simulations have been performed by means of the ORBIT14 orbit determination software, which was developed by the Celestial Mechanics Group of the University of Pisa for the analysis of the BepiColombo radio science experiment. We claim that the torsion parameters can be determined by means of the relativity experiment of BepiColombo at the level of some parts in 10(-4), which is a significant result for constraining gravitational theories that allow spacetime torsion

Electromagnetic inversion for subsurface applications under the distorted Born approximation

The problem of reconstructing dielectric permittivity of a buried object from the knowledge of the scattered field is considered for a two-dimensional rectangular geometry at a fixed frequency. The linearization of the mathematical relationship between the dielectric permittivity function and the scattered field about a constant reference profile function and the approximation of actual internal field with the unperturbed field leads to the so-called Distorted Born Approximation. To analyze the limitations and capabilities of the linear inversion algorithms, we investigate the class of the retrievable profiles. This analysis makes it possible to point out that a very reduced number of independent data is available, so requiring to employ regularization techniques in order to perform in a reliable and stable way the linear inversions. In this paper we present a general algorithm consisting in a regularized Singular Value Decomposition of the matrix resulting from a discretization of the problem. Finally, numerical results of linear inversions are given

Random Graph-Homomorphisms and Logarithmic Degree

A graph homomorphism between two graphs is a map from the vertex set of one graph to the vertex set of the other graph, that maps edges to edges. In this note we study the range of a uniformly chosen homomorphism from a graph G to the infinite line Z. It is shown that if the maximal degree of G is `sub-logarithmic', then the range of such a homomorphism is super-constant. Furthermore, some examples are provided, suggesting that perhaps for graphs with super-logarithmic degree, the range of a typical homomorphism is bounded. In particular, a sharp transition is shown for a specific family of graphs C_{n,k} (which is the tensor product of the n-cycle and a complete graph, with self-loops, of size k). That is, given any function psi(n) tending to infinity, the range of a typical homomorphism of C_{n,k} is super-constant for k = 2 log(n) - psi(n), and is 3 for k = 2 log(n) + psi(n)

Large-Scale Distribution of the European Seahorses (Hippocampus Rafinesque, 1810): A Systematic Review

Human pressures on marine ecosystems have caused extensive degradation of marine habitats and several local extinctions. Overexploitation and destructive fishing practices are responsible for biodiversity loss in many coastal ecosystems. The definition of conservation programs in marine fish requires comprehensive knowledge on large-scale geographical distribution, while considering distribution/abundance patterns in relation to key environmental variables. Due to their life-cycle traits, the two European seahorses (Hippocampus guttulatus and H. hippocampus), as with other congeneric species, are particularly sensitive to the effects of anthropogenic activities and habitat changes. However, information on the ecological distribution of these two species is scattered, patchy, and mainly focused on small-scale studies. In this paper, we followed an international standard protocol for systematic reviews (the PRISMA protocol) to provide a detailed assessment of the two species’ geographical distribution in relation to the environmental characteristics. According to the 134 analyzed studies, Hippocampus guttulatus is more common in confined areas, while H. hippocampus is found in marine shelf waters. With several interspecific differences, seagrasses were the most used holdfasts of both species. The EUNIS codes (European nature information system) referring to a specific and unique habitat were discussed as a potential tool for defining the ecological distribution of the two species. The obtained results and their future implementation could help plan conservation actions

Predicting economic resilience of territories in Italy during the COVID-19 first lockdown

This paper aims to predict the economic resilience to crises of territories based on local pre-existing socioeco-nomic characteristics. Specifically, we consider the case of Italian municipalities during the first wave of the COVID-19 pandemic, leveraging a large-scale dataset of cardholders performing transactions in Point-of-Sales. Based on a set of machine learning classifiers, we show that network-based measures and variables related to the social, economic, demographic and environmental dimensions are relevant predictors of the economic resilience of Italian municipalities to the crisis. In particular, we find accurate classification performance both in balanced and un-balanced scenarios, as well as in the case we restrict the analysis to specific geographical areas. Our analysis predicts that territories with larger income per capita, soil consumption, concentration of real estate activities and commuting network centrality in terms of closeness and Pagerank constitute the set of most affected areas, experiencing the strongest reduction of economic activities during the COVID-19 pandemic. Overall, we provide an application of an early-warning system able to provide timely evidence to policymakers about the detrimental effects generated by natural disasters and severe crisis episodes, thus contributing to optimize public decision support systems

Bouguer gravity field of the Tuscan Archipelago (central Italy)

In this paper, we present a new Bouguer gravity map of the Northern Tuscan offshore (central Italy), based on original gravity data acquired on the islands of the Tuscan Archipelago. Our dataset integrates 274 unpublished gravity field measurements with 126 available marine gravity data of the northern Tyrrhenian Sea. The Bouguer anomaly map shows a westward and southward increase of the regional gravity field associated with the uplift of the Moho boundary from central Apennines towards the Tyrrhenian Sea. At a local scale, several Bouguer anomalies are well associated with the igneous plutons of the Elba, Montecristo and Capraia islands, as a result of a deep density contrast between the granitoid intrusive rocks and the embedding metamorphic basement. The presented Bouguer anomaly map represents a useful tool for future studies of the complex geological and geodynamical setting of the Tuscan Archipelago and of the buried and deep igneous structures