Riemannian Ricci curvature lower bounds in metric measure spaces with σ\sigma-finite measure

Using techniques of optimal transportation and gradient flows in metric spaces, we extend the notion of Riemannian Curvature Dimension condition $RCD(K,\infty)$ introduced (in case the reference measure is finite) by Giuseppe Savare', the first and the second author, to the case the reference measure is $\sigma$-finite; in this way the theory includes natural examples as the euclidean $n$-dimensional space endowed with the Lebesgue measure, and noncompact manifolds with bounded geometry endowed with the Riemannian volume measure. Another major goal of the paper is to simplify the axiomatization of $RCD(K,\infty)$ (even in case of finite reference measure) replacing the assumption of strict $CD(K,\infty)$ with the classic notion of $CD(K,\infty)$.Comment: 42 pages; final version (minor changes to the old one, in particular we added some more preliminaries and explanations) to be published in Transactions of the AM

On the thermal and thermodynamic (In)stability of methylammonium lead halide perovskites

The interest of the scientific community on methylammonium lead halide perovskites (MAPbX3, X = Cl, Br, I) for hybrid organic-inorganic solar cells has grown exponentially since the first report in 2009. This fact is clearly justified by the very high efficiencies attainable (reaching 20% in lab scale devices) at a fraction of the cost of conventional photovoltaics. However, many problems must be solved before a market introduction of these devices can be envisaged. Perhaps the most important to be addressed is the lack of information regarding the thermal and thermodynamic stability of the materials towards decomposition, which are intrinsic properties of them and which can seriously limit or even exclude their use in real devices. In this work we present and discuss the results we obtained using non-ambient X-ray diffraction, Knudsen effusion-mass spectrometry (KEMS) and Knudsen effusion mass loss (KEML) techniques on MAPbCl3, MAPbBr3 and MAPbI3. The measurements demonstrate that all the materials decompose to the corresponding solid lead (II) halide and gaseous methylamine and hydrogen halide, and the decomposition is well detectable even at moderate temperatures (~60 °C). Our results suggest that these materials may be problematic for long term operation of solar devices

Co-digestion of macroalgae for biogas production: an LCA-based environmental evaluation

Algae represent a favourable and potentially sustainable source of biomass for bioenergy-based industrial pathways in the future. The study, performed on a real pilot plant implemented in Augusta (Italy) within the frame of the BioWALK4Biofuels project, aims to figure out whether seaweed (macroalgae) cultivated in near-shore open ponds could be considered a beneficial aspect as a source of biomass for biogas production within the co-digestion with local agricultural biological waste. The LCA results confirm that the analysed A and B scenarios (namely the algae-based co-digestion scenario and agricultural mix feedstock scenario) present an environmental performance more favourable than that achieved with conventional non-renewable-based technologies (specifically natural gas - Scenario C). Results show that the use of seaweed (Scenario A) represent a feasible solution in order to replace classical biomass used for biofuel production from a land-based feedstock. The improvement of the environmental performances is quantifiable on 10% respect to Scenario B, and 38 times higher than Scenario

Euclidean spaces as weak tangents of infinitesimally Hilbertian metric mea- sure spaces with Ricci curvature bounded below

We show that in any infinitesimally Hilbertian $CD^*(K,N)$-space at almost every point there exists a Euclidean weak tangent, i.e. there exists a sequence of dilations of the space that converges to a Euclidean space in the pointed measured Gromov-Hausdorff topology. The proof follows by considering iterated tangents and the splitting theorem for infinitesimally Hilbertian $CD^*(0, N)$-spaces

What is the best spatial distribution to model base station density? A deep dive into two european mobile networks

This paper studies the base station (BS) spatial distributions across different scenarios in urban, rural, and coastal zones, based on real BS deployment data sets obtained from two European countries (i.e., Italy and Croatia). Basically, this paper takes into account different representative statistical distributions to characterize the probability density function of the BS spatial density, including Poisson, generalized Pareto, Weibull, lognormal, and \alpha -Stable. Based on a thorough comparison with real data sets, our results clearly assess that the \alpha -Stable distribution is the most accurate one among the other candidates in urban scenarios. This finding is confirmed across different sample area sizes, operators, and cellular technologies (GSM/UMTS/LTE). On the other hand, the lognormal and Weibull distributions tend to fit better the real ones in rural and coastal scenarios. We believe that the results of this paper can be exploited to derive fruitful guidelines for BS deployment in a cellular network design, providing various network performance metrics, such as coverage probability, transmission success probability, throughput, and delay

Corrigendum: On the thermal and thermodynamic (in)stability of methylammonium lead halide perovskites

NO ABSTRAC

Preoperative staging of colorectal cancer using virtual colonoscopy: correlation with surgical results

The aim of this study was to evaluate the clinical usefulness of computed tomography colonography (CTC) in the preoperative staging in patients with abdominal pain for occlusive colorectal cancer (CRC) and to compare the results of CTC with the surgical ones

Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows

Aim of this paper is to discuss convergence of pointed metric measure spaces in absence of any compactness condition. We propose various definitions, show that all of them are equivalent and that for doubling spaces these are also equivalent to the well known measured-Gromov-Hausdorff convergence. Then we show that the curvature conditions CD(K, 1e) and RCD(K, 1e) are stable under this notion of convergence and that the heat flow passes to the limit as well, both in the Wasserstein and in the L2-framework. We also prove the variational convergence of Cheeger energies in the naturally adapted \u393-Mosco sense and the convergence of the spectra of the Laplacian in the case of spaces either uniformly bounded or satisfying the RCD(K, 1e) condition with K>0. When applied to Riemannian manifolds, our results allow for sequences with diverging dimensions