A metric property of umbilic points

In the space $\mathbb U^4$ of cubic forms of surfaces, regarded as a $G$-space and endowed with a natural invariant metric, the ratio of the volumes of those representing umbilic points with negative to those with positive indexes is evaluated in terms of the asymmetry of the metric, defined here. A connection of this ratio with that reported by Berry and Hannay (1977) in the domain of Statistical Physics, is discussed.Comment: 8 pages, 1 figur

Optimal Policy Derivation for Transmission Duty-Cycle Constrained LPWAN

Low-power wide-area network (LPWAN) technologies enable Internet of Things (IoT) devices to efficiently and robustly communicate over long distances, thus making them especially suited for industrial environments. However, the stringent regulations on the usage of certain industrial, scientific, and medical bands in many countries in which LPWAN operate limit the amount of time IoT motes can occupy the shared bands. This is particularly challenging in industrial scenarios, where not being able to report some detected events might result in the failure of critical assets. To alleviate this, and by mathematically modeling LPWAN-based IoT motes, we have derived optimal transmission policies that maximize the number of reported events (prioritized by their importance) while still complying with current regulations. The proposed solution has been customized for two widely known LPWAN technologies: 1) LoRa and 2) Sigfox. Analytical results reveal that our solution is feasible and performs remarkably close to the theoretical limit for a wide range of network activity patterns

Sigma pole position and errors of a once and twice subtracted dispersive analysis of pi-pi scattering data

We show how the new precise data on kaon decays together with forward dispersion relations, sum rules and once- and twice-subtracted Roy's equations allow for a precise determination of the sigma meson pole position. We present a comparison and a study of the different sources of uncertainties when using either once- or twice-subtracted Roy's equations to analyze the data. Finally we present a preliminary determination of the sigma pole from the constrained dispersive data analysis.Comment: 4 pages, 6 figures. Contribution to the proceedings of the QCD08 14th International QCD Conference. 7-12th July 2008 Montpellier (France); one reference removed, changed errors in Eqs (4), (5) and (7