Geological evidence indicates that grounded ice sheets reached sea level at all latitudes during two long-lived Cryogenian (58 and ≥5 My) glaciations. Combined uranium-lead and rhenium-osmium dating suggests that the older (Sturtian) glacial onset and both terminations were globally synchronous. Geochemical data imply that CO₂ was 10² PAL (present atmospheric level) at the younger termination, consistent with a global ice cover. Sturtian glaciation followed breakup of a tropical supercontinent, and its onset coincided with the equatorial emplacement of a large igneous province. Modeling shows that the small thermal inertia of a globally frozen surface reverses the annual mean tropical atmospheric circulation, producing an equatorial desert and net snow and frost accumulation elsewhere. Oceanic ice thickens, forming a sea glacier that flows gravitationally toward the equator, sustained by the hydrologic cycle and by basal freezing and melting. Tropical ice sheets flow faster as CO₂ rises but lose mass and become sensitive to orbital changes. Equatorial dust accumulation engenders supraglacial oligotrophic meltwater ecosystems, favorable for cyanobacteria and certain eukaryotes. Meltwater flushing through cracks enables organic burial and submarine deposition of airborne volcanic ash. The subglacial ocean is turbulent and well mixed, in response to geothermal heating and heat loss through the ice cover, increasing with latitude. Terminal carbonate deposits, unique to Cryogenian glaciations, are products of intense weathering and ocean stratification. Whole-ocean warming and collapsing peripheral bulges allow marine coastal flooding to continue long after ice-sheet disappearance. The evolutionary legacy of Snowball Earth is perceptible in fossils and living organisms.

We propose an approach for analyzing signals with long-range correlations by decomposing the signal increment series into magnitude and sign series and analyzing their scaling properties. We show that signals with identical long-range correlations can exhibit different time organization for the magnitude and sign. We find that the magnitude series relates to the nonlinear properties of the original time series, while the sign series relates to the linear properties. We apply our approach to the heartbeat interval series and find that the magnitude series is long-range correlated, while the sign series is anticorrelated and that both magnitude and sign series may have clinical applications.

We analyze daily prices of 29 commodities and 2449 stocks, each over a period of $\approx 15$ years. We find that the price fluctuations for commodities have a significantly broader multifractal spectrum than for stocks. We also propose that multifractal properties of both stocks and commodities can be attributed mainly to the broad probability distribution of price fluctuations and secondarily to their temporal organization. Furthermore, we propose that, for commodities, stronger higher order correlations in price fluctuations result in broader multifractal spectra.

This paper is the outcome of a workshop held in Rome in November 2011 on the occasion of the 25th anniversary of the POEM (Physical Oceanography of the Eastern Mediterranean) program. In the workshop discussions, a number of unresolved issues were identified for the physical and biogeochemical properties of the Mediterranean Sea as a whole, i.e., comprising the Western and Eastern sub-basins. Over the successive two years, the related ideas were discussed among the group of scientists who participated in the workshop and who have contributed to the writing of this paper. Three major topics were identified, each of them being the object of a section divided into a number of different sub-sections, each addressing a specific physical, chemical or biological issue: 1. Assessment of basin-wide physical/biochemical properties, of their variability and interactions. 2. Relative importance of external forcing functions (wind stress, heat/moisture fluxes, forcing through straits) vs. internal variability. 3. Shelf/deep sea interactions and exchanges of physical/biogeochemical properties and how they affect the sub-basin circulation and property distribution. Furthermore, a number of unresolved scientific/methodological issues were also identified and are reported in each sub-section after a short discussion of the present knowledge. They represent the collegial consensus of the scientists contributing to the paper. Naturally, the unresolved issues presented here constitute the choice of the authors and therefore they may not be exhaustive and/or complete. The overall goal is to stimulate a broader interdisciplinary discussion among the scientists of the Mediterranean oceanographic community, leading to enhanced collaborative efforts and exciting future discoveries.