General spherically symmetric elastic stars in Relativity

The relativistic theory of elasticity is reviewed within the spherically symmetric context with a view towards the modeling of star interiors possessing elastic properties such as theones expected in neutron stars. Emphasis is placed on generality in the main sections of the paper, and the results are then applied to specific examples. Along the way, a few general results for spacetimes admitting isometries are deduced, and their consequences are fully exploited in the case of spherical symmetry relating them next to the the case in which the material content of the spacetime is some elastic material. This paper extends and generalizes the pioneering work by Magli and Kijowski [1], Magli [2] and [3], and complements, in a sense, that by Karlovini and Samuelsson in their interesting series of papers [4], [5] and [6].Comment: 23 page

The megalithic building of S.Erasmo di Cesi: architecture, astronomy, and landscape

Abstract. One of the most enigmatic megalithic buildings of Italy is the structure which lies on the S. Erasmo hill near Cesi, in Umbria, a huge complex encompassing an area of around 8000 square meters and enclosed by refined cyclopean walls. Although its date is uncertain, suggested dates comprise the Iron Age and archaic period, down to the third century B.C. The building’s function is also uncertain. Usually identified as a fortified structure, in fact there is a megalithic platform at the southern end of the enclosure which could have served as foundation of a temple or palace and, from the top of Monte Torre Maggiore, a complex of temples dating from the fourth century B.C. overlooks the hill. Similar combinations of megalithic buildings resting half-way to temples placed on high peaks are known to exist. In order to clarify the function of this structure and its position in relation to the surrounding landscape, with particular attention to its visibility and to the directions of visibility from the complex, as well as to the possible astronomical alignments, we present a multi-disciplinary approach to the study of the S. Erasmo complex, which includes the mapping of the sky at the various possible epochs of construction, the creation of a digital model of the landscape in forms of digital maps using Geographic Information System technologies, and a 3D model using various 3D software packages

NIR image colorization with graph-convolutional neural networks

Colorization of near-infrared (NIR) images is a challenging problem due to the different material properties at the infared wavelenghts, thus reducing the correlation with visible images. In this paper, we study how graph-convolutional neural networks allow exploiting a more powerful inductive bias than standard CNNs, in the form of non-local self-similiarity. Its impact is evaluated by showing how training with mean squared error only as loss leads to poor results with a standard CNN, while the graph-convolutional network produces significantly sharper and more realistic colorizations

RAN-GNNs: Breaking the Capacity Limits of Graph Neural Networks

Graph neural networks (GNNs) have become a staple in problems addressing learning and analysis of data defined over graphs. However, several results suggest an inherent difficulty in extracting better performance by increasing the number of layers. Recent works attribute this to a phenomenon peculiar to the extraction of node features in graph-based tasks, i.e., the need to consider multiple neighborhood sizes at the same time and adaptively tune them. In this article, we investigate the recently proposed randomly wired architectures in the context of GNNs. Instead of building deeper networks by stacking many layers, we prove that employing a randomly wired architecture can be a more effective way to increase the capacity of the network and obtain richer representations. We show that such architectures behave like an ensemble of paths, which are able to merge contributions from receptive fields of varied size. Moreover, these receptive fields can also be modulated to be wider or narrower through the trainable weights over the paths. We also provide extensive experimental evidence of the superior performance of randomly wired architectures over multiple tasks and five graph convolution definitions, using recent benchmarking frameworks that address the reliability of previous testing methodologies

Signal Compression via Neural Implicit Representations

Existing end-to-end signal compression schemes using neural networks are largely based on an autoencoder-like structure, where a universal encoding function creates a compact latent space and the signal representation in this space is quantized and stored. Recently, advances from the field of 3D graphics have shown the possibility of building implicit representation networks, i.e., neural networks returning the value of a signal at a given query coordinate. In this paper, we propose using neural implicit representations as a novel paradigm for signal compression with neural networks, where the compact representation of the signal is defined by the very weights of the network. We discuss how this compression framework works, how to include priors in the design, and highlight interesting connections with transform coding. While the framework is general, and still lacks maturity, we already show very competitive performance on the task of compressing point cloud attributes, which is notoriously challenging due to the irregularity of the domain, but becomes trivial in the proposed framework

Rebounce and Black hole formation in a Gravitational Collapse Model with Vanishing Radial Pressure

We examine spherical gravitational collapse of a matter model with vanishing radial pressure and non-zero tangential pressure. It is seen analytically that the collapsing cloud either forms a black hole or disperses depending on values of the initial parameters which are initial density, tangential pressure and velocity profile of the cloud. A threshold of black hole formation is observed near which a scaling relation is obtained for the mass of black hole, assuming initial profiles to be smooth. The similarities in the behaviour of this model at the onset of black hole formation with that of numerical critical behaviour in other collapse models are indicated.Comment: 15 pages, To be published in Gen.Rel.Gra