Distributed soft thresholding for sparse signal recovery

In this paper, we address the problem of distributed sparse recovery of signals acquired via compressed measurements in a sensor network. We propose a new class of distributed algorithms to solve Lasso regression problems, when the communication to a fusion center is not possible, e.g., due to communication cost or privacy reasons. More precisely, we introduce a distributed iterative soft thresholding algorithm (DISTA) that consists of three steps: an averaging step, a gradient step, and a soft thresholding operation. We prove the convergence of DISTA in networks represented by regular graphs, and we compare it with existing methods in terms of performance, memory, and complexity.Comment: Revised version. Main improvements: extension of the convergence theorem to regular graphs; new numerical results and comparisons with other algorithm

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

GPU-Accelerated Algorithms for Compressed Signals Recovery with Application to Astronomical Imagery Deblurring

Compressive sensing promises to enable bandwidth-efficient on-board compression of astronomical data by lifting the encoding complexity from the source to the receiver. The signal is recovered off-line, exploiting GPUs parallel computation capabilities to speedup the reconstruction process. However, inherent GPU hardware constraints limit the size of the recoverable signal and the speedup practically achievable. In this work, we design parallel algorithms that exploit the properties of circulant matrices for efficient GPU-accelerated sparse signals recovery. Our approach reduces the memory requirements, allowing us to recover very large signals with limited memory. In addition, it achieves a tenfold signal recovery speedup thanks to ad-hoc parallelization of matrix-vector multiplications and matrix inversions. Finally, we practically demonstrate our algorithms in a typical application of circulant matrices: deblurring a sparse astronomical image in the compressed domain

Genericity of blackhole formation in the gravitational collapse of homogeneous self-interacting scalar fields

The gravitational collapse of a wide class of self-interacting homogeneous scalar fields models is analyzed. The class is characterized by certain general conditions on the scalar field potential, which, in particular, include both asymptotically polynomial and exponential behaviors. Within this class, we show that the generic evolution is always divergent in a finite time, and then make use of this result to construct radiating star models of the Vaidya type. It turns out that blackholes are generically formed in such models.Comment: 18 pages, 4 figure

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

New mathematical framework for spherical gravitational collapse

A theorem, giving necessary and sufficient condition for naked singularity formation in spherically symmetric non static spacetimes under hypotheses of physical acceptability, is formulated and proved. The theorem relates existence of singular null geodesics to existence of regular curves which are super-solutions of the radial null geodesic equation, and allows us to treat all the known examples of naked singularities from a unified viewpoint. New examples are also found using this approach, and perspectives are discussed.Comment: 8 pages, LaTeX2

Network coding meets multimedia: a review

While every network node only relays messages in a traditional communication system, the recent network coding (NC) paradigm proposes to implement simple in-network processing with packet combinations in the nodes. NC extends the concept of "encoding" a message beyond source coding (for compression) and channel coding (for protection against errors and losses). It has been shown to increase network throughput compared to traditional networks implementation, to reduce delay and to provide robustness to transmission errors and network dynamics. These features are so appealing for multimedia applications that they have spurred a large research effort towards the development of multimedia-specific NC techniques. This paper reviews the recent work in NC for multimedia applications and focuses on the techniques that fill the gap between NC theory and practical applications. It outlines the benefits of NC and presents the open challenges in this area. The paper initially focuses on multimedia-specific aspects of network coding, in particular delay, in-network error control, and mediaspecific error control. These aspects permit to handle varying network conditions as well as client heterogeneity, which are critical to the design and deployment of multimedia systems. After introducing these general concepts, the paper reviews in detail two applications that lend themselves naturally to NC via the cooperation and broadcast models, namely peer-to-peer multimedia streaming and wireless networkin