Nonnegative polynomials and their Carath\'eodory number

In 1888 Hilbert showed that every nonnegative homogeneous polynomial with real coefficients of degree $2d$ in $n$ variables is a sum of squares if and only if $d=1$ (quadratic forms), $n=2$ (binary forms) or $(n,d)=(3,2)$ (ternary quartics). In these cases, it is interesting to compute canonical expressions for these decompositions. Starting from Carath\'eodory's Theorem, we compute the Carath\'eodory number of Hilbert cones of nonnegative quadratic and binary forms.Comment: 9 pages. Discrete & Computational Geometry (2014

Spectrum Trading: An Abstracted Bibliography

This document contains a bibliographic list of major papers on spectrum trading and their abstracts. The aim of the list is to offer researchers entering this field a fast panorama of the current literature. The list is continually updated on the webpage \url{http://www.disp.uniroma2.it/users/naldi/Ricspt.html}. Omissions and papers suggested for inclusion may be pointed out to the authors through e-mail (\textit{[email protected]})

Analysis of cloud storage prices

Cloud storage is fast securing its role as a major repository for both consumers and business customers. Many companies now offer storage solutions, sometimes for free for limited amounts of capacity. We have surveyed the pricing plans of a selection of major cloud providers and compared them using the unit price as the means of comparison. All the providers, excepting Amazon, adopt a bundling pricing scheme; Amazon follows instead a block-declining pricing policy. We compare the pricing plans through a double approach: a pointwise comparison for each value of capacity, and an overall comparison using a two-part tariff approximation and a Pareto-dominance criterion. Under both approaches, most providers appear to offer pricing plans that are more expensive and can be excluded from a procurement selection in favour of a limited number of dominant providers.Comment: 17 pages, 17 figures, 17 reference

A new nonlocal nonlinear diffusion equation for image denoising and data analysis

In this paper we introduce and study a new feature-preserving nonlinear anisotropic diffusion for denoising signals. The proposed partial differential equation is based on a novel diffusivity coefficient that uses a nonlocal automatically detected parameter related to the local bounded variation and the local oscillating pattern of the noisy input signal. We provide a mathematical analysis of the existence of the solution of our nonlinear and nonlocal diffusion equation in the two dimensional case (images processing). Finally, we propose a numerical scheme with some numerical experiments which demonstrate the effectiveness of the new method