Insights into the explosive eruption history of the Campanian volcanoes prior to the Campanian Ignimbrite eruption

The Campanian Volcanic Zone (CVZ) comprises multiple active volcanoes and includes the highly productive Campi Flegrei and Ischia caldera systems. These caldera volcanoes have produced probably the largest eruptions in Europe in the past 200 ka, such as the Monte Epomeo Green Tuff (MEGT; Ischia) at ca. 56 ka and the Campanian Ignimbrite (CI; Campi Flegrei) at ca. 40 ka, which form widespread isochrons across the Mediterranean region. These closely-spaced volcanic centres erupt phonolitic to trachytic glass compositions that are similar, and thus it can be challenging to correlate tephra deposits to specific volcanic sources. Here we present a detailed tephrostratigraphy for pre-CI eruption activity using the units preserved within a sequence at the coastal Acquamorta outcrop, on the western side of the CI caldera rim. Both the MEGT and CI units are present in the section, and they bracket twelve eruption units that were logged and sampled. New major and trace element glass chemistry data have been acquired for these Acquamorta tephra deposits. Three eruption deposits from Ischia and nine from Campi Flegrei are identified, which helps constrain the tempo of volcanic activity of these centres between the large caldera-forming eruptions. The three Ischia tephra deposits between the MEGT and the CI are indistinguishable based on both major and trace element glass chemistry and cannot be correlated to a specific or known eruption in this interval, such as the Schiappone tephra. The compositional variations between the Campi Flegrei eruptions reveal temporal shifts in the composition of the tephra deposits that reflect changes in the magmatic system prior to the CI eruption. These deposits indicate that there were at least nine eruptions at Campi Flegrei within 16 ka of the enormous CI eruption, and suggest that there was no significant period of repose before the caldera generating eruption

Strontium ranelate reduces the risk of vertebral fracture in young postmenopausal women with severe osteoporosis

Early osteoporotic fractures have a great impact on disease progression, the first fracture being a major risk factor for further fractures. Strontium ranelate efficacy against vertebral fractures is presently assessed in a subset of women aged 50-65 years

An elementary approach to rigorous approximation of invariant measures

We describe a framework in which is possible to develop and implement algorithms for the approximation of invariant measures of dynamical systems with a given bound on the error of the approximation. Our approach is based on a general statement on the approximation of fixed points for operators between normed vector spaces, allowing an explicit estimation of the error. We show the flexibility of our approach by applying it to piecewise expanding maps and to maps with indifferent fixed points. We show how the required estimations can be implemented to compute invariant densities up to a given error in the $L^{1}$ or $L^\infty$ distance. We also show how to use this to compute an estimation with certified error for the entropy of those systems. We show how several related computational and numerical issues can be solved to obtain working implementations, and experimental results on some one dimensional maps.Comment: 27 pages, 10 figures. Main changes: added a new section in which we apply our method to Manneville-Pomeau map