Polynomial growth of volume of balls for zero-entropy geodesic systems

The aim of this paper is to state and prove polynomial analogues of the classical Manning inequality relating the topological entropy of a geodesic flow with the growth rate of the volume of balls in the universal covering. To this aim we use two numerical conjugacy invariants, the {\em strong polynomial entropy $h_{pol}$} and the {\em weak polynomial entropy $h_{pol}^*$}. Both are infinite when the topological entropy is positive and they satisfy $h_{pol}^*\leq h_{pol}$. We first prove that the growth rate of the volume of balls is bounded above by means of the strong polynomial entropy and we show that for the flat torus this inequality becomes an equality. We then study the explicit example of the torus of revolution for which we can give an exact asymptotic equivalent of the growth rate of volume of balls, which we relate to the weak polynomial entropy.Comment: 22 page

Declining water resources in response to global warming and changes in atmospheric circulation patterns over southern Mediterranean France

Warming trends are responsible for an observed decrease of water discharge in southern France (northwestern Mediterranean). Ongoing climate change and the likely increase of water demand threaten the availability of water resources over the coming decades. Drought indices like the Reconnaissance Drought Index (RDI) are increasingly used in climate characterization studies, but little is known about the relationships between these indices, water resources, and the overall atmospheric circulation patterns. In this study, we investigate the relationships between the RDI, water discharge, and four atmospheric teleconnection patterns (TPs) for six coastal river basins in southern France, both for the historical period of the last 60 years and for a worst-case climatic scenario (RCP8.5) reaching the year 2100. We combine global and regional climate model (CGM and RCM, respectively) outputs with a set of observed climatic and hydrological data in order to investigate the past relationships between the RDI, water discharge, and TPs and to project their potential evolution in space and time. Results indicate that annual water discharge can be reduced by −49 % to −88 % by the end of the century under the extreme climate scenario conditions. Due to unequal links with TPs, the hydroclimatic evolution is unevenly distributed within the study area. Indeed a clustering analysis performed with the RDI time series detects two major climate clusters, separating the eastern and western part of the study region. The former indicates stronger relationships with the Atlantic TPs (e.g. the North Atlantic Oscillation (NAO) and the Scandinavian Oscillation (Scand) patterns), whereas the latter is more closely related to the Mediterranean TPs (Mediterranean Oscillation (MO) and Western Mediterranean Oscillation (WeMO)). The future climate simulations predict an antagonistic evolution in both clusters which are likely driven by decreasing trends of Scand and WeMO. The former provokes a general tendency of lower P in both clusters during spring, summer, and autumn, whereas the latter might partly compensate for this evolution by enhanced precipitation in the eastern cluster during autumn and winter. However, compared to observations, representation of the Mediterranean TPs WeMO and MO in the considered climate models is less satisfactory compared to the Atlantic TPs NAO and Scand, and further improvement of the model simulations therefore requires better representations of the Mediterranean TPs.</p

Ice-sheet melt drove methane emissions in the Arctic during the last two interglacials

Circum-Arctic glacial ice is melting in an unprecedented mode, and release of currently trapped geological methane may act as a positive feedback on ice-sheet retreat during global warming. Evidence for methane release during the penultimate (Eemian, ca. 125 ka) interglacial, a period with less glacial sea ice and higher temperatures than today, is currently absent. Here, we argue that based on foraminiferal isotope studies on drill holes from offshore Svalbard, Norway, methane leakage occurred upon the abrupt Eurasian ice-sheet wastage during terminations of the last (Weichselian) and penultimate (Saalian) glaciations. Progressive increase of methane emissions seems to be first recorded by depleted benthic foraminiferal δ13C. This is quickly followed by the precipitation of methane-derived authigenic carbonate as overgrowth inside and outside foraminiferal shells, characterized by heavy δ18O and depleted δ13C of both benthic and planktonic foraminifera. The similarities between the events observed over both terminations advocate for a common driver for the episodic release of geological methane stocks. Our favored model is recurrent leakage of shallow gas reservoirs below the gas hydrate stability zone along the margin of western Svalbard that can be reactivated upon initial instability of the grounded, marine-based ice sheets. Analogous to this model, with the current acceleration of the Greenland ice melt, instabilities of existing methane reservoirs below and nearby the ice sheet are likely

Petrophysical properties across scales and compositions

The scales at which observations from geophysical imaging are made are orders of magnitude larger than those made in field-based studies of fossil subduction and collision zones. Even more so, the determination of petrophysical properties of rocks is typically based on millimeter to centimeter-scale samples, and the so-obtained information is then used to inform large-scale geophysical imaging studies. Information on how such properties can be up-scaled to geophysically relevant scales is rare, underlining the need to combine petrophysical properties with structural data, obtained from relevant field analogues. We provide results from three field analogues; (1) Tenda massif, Corsica, (2) Monte Mucrone, Sesia Zone, western Alps, and (3) Holsnøy, Lindås nappe, Scandinavian Caledonides. The bulk rock compositions cover a gradient from felsic (1-2) to mafic (3), as would be expected in the upper and lower continental crust, respectively. Petrophysical properties (P and S wave velocities and their ratios and anisotropies) were determined by direct measurement (ultrasonic pulse transmission technique) and calculated (based on texture data from neutron diffraction measurements). The data set is then used for numerical modeling (finite element method) of meter to kilometer-scale structural associations as mapped in the field (3). The obtained results show that high-pressure metamorphism of mafic rocks results in significant increase in both P and S wave velocities, that in principle would generate a sufficient impedance contrast to be imaged by seismic methods. While structures observed in the field are typically below the scale of geophysical imaging techniques, our considerations of bulk petrophysical properties indicate that significant anisotropy may still be detectable on the kilometer scale. On the other hand, the increase of P and S wave velocities of felsic rocks during high pressure metamorphism is much smaller, however, as such compositions have a higher potential to form rocks with high mica contents, they display a large variability in seismic anisotropy, hinting at the potential to link relatively low seismic velocities, combined with high anisotropy to fluid intake during metamorphism

Recycling Argon through Metamorphic Reactions: the Record in Symplectites

The 40Ar/39Ar ages of metamorphic micas that crystallized at high temperatures are commonly interpreted as cooling ages, with grains considered to have lost 40Ar via thermally-driven diffusion into the grain boundary network. Recently reported laser-ablation data suggest that the spatial distribution of Ar in metamorphic micas does not always conform to the patterns predicted by diffusion theory and that despite high metamorphic temperatures, argon was not removed efficiently from the local system during metamorphic evolution. In the Western Gneiss Region (WGR), Norway, felsic gneisses preserve microtextural evidence for the breakdown of phengite to biotite and plagioclase symplectites during near isothermal decompression from c. 20–25 to c. 8–12 kbar at ~700°C. These samples provide an ideal natural laboratory to assess whether the complete replacement of one K-bearing mineral by another at high temperatures completely ‘resets’ the Ar clock, or whether there is some inheritance of 40Ar in the neo-crystallized phase. The timing of the high-temperature portion of the WGR metamorphic cycle has been well constrained in previous studies. However, the timing of cooling following the overprint is still much debated. In-situ laser ablation spot dating in phengite, biotite-plagioclase symplectites and coarser, texturally later biotite yielded 40Ar/39Ar ages that span much of the metamorphic cycle. Together these data show that despite residence at temperatures of ~700°C, Ar is not completely removed by diffusive loss or during metamorphic recrystallization. Instead, Ar released during phengite breakdown appears to be partially reincorporated into the newly crystallizing biotite and plagioclase (or is trapped in fluid inclusions in those phases) within a close system. Our data show that the microtextural and petrographic evolution of the sample being dated provides a critical framework in which local 40Ar recycling can be tracked, thus potentially allowing 40Ar/39Ar dates to be linked more accurately to metamorphic history

Phenotypic covariance of longevity, immunity and stress resistance in the Caenorhabditis nematodes

Background \ud Ageing, immunity and stresstolerance are inherent characteristics of all organisms. In animals, these traits are regulated, at least in part, by forkhead transcription factors in response to upstream signals from the Insulin/Insulin– like growth factor signalling (IIS) pathway. In the nematode Caenorhabditis elegans, these phenotypes are molecularly linked such that activation of the forkhead transcription factor DAF-16 both extends lifespan and simultaneously increases immunity and stress resistance. It is known that lifespan varies significantly among the Caenorhabditis species but, although DAF-16 signalling is highly conserved, it is unclear whether this phenotypic linkage occurs in other species. Here we investigate this phenotypic covariance by comparing longevity, stress resistance and immunity in four \ud Caenorhabditis species. \ud \ud Methodology/Principal Findings \ud We show using phenotypic analysis of DAF-16 influenced phenotypes that among four closely related Caenorhabditis nematodes, the gonochoristic species (Caenorhabditis remanei and Caenorhabditis brenneri) have diverged \ud significantly with a longer lifespan, improved stress resistance and higher immunity than the hermaphroditic species (C. elegans and Caenorhabditis briggsae). Interestingly, we also observe significant differences in expression levels between the daf-16 homologues in these species using Real-Time PCR, which positively correlate with the observed phenotypes. Finally, we provide additional evidence in support of a role for DAF-16 in regulating phenotypic coupling by using a combination of wildtype isolates, constitutively active daf-16 mutants and bioinformatic analysis. \ud \ud Conclusions \ud The gonochoristic species display a significantly longer lifespan (p < 0.0001)and more robust immune and stress response (p<0.0001, thermal stress; p<0.01, heavy metal stress; p<0.0001, pathogenic stress) than the hermaphroditic species. Our data suggests that divergence in DAF-16 mediated phenotypes may underlie many of the differences observed between these four species of Caenorhabditis nematodes. These findings are further supported by the correlative higher daf-16 expression levels among the gonochoristic species and significantly higher lifespan, immunity and stress tolerance in the constitutively active daf-16 hermaphroditic mutants

Phenotypic covariance of Longevity, Immunity and Stress Resistance in the Caenorhabditis Nematodes

Background: Ageing, immunity and stresstolerance are inherent characteristics of all organisms. In animals, these traits are regulated, at least in part, by forkhead transcription factors in response to upstream signals from the Insulin/Insulin–like growth factor signalling (IIS) pathway. In the nematode Caenorhabditis elegans, these phenotypes are molecularly linked such that activation of the forkhead transcription factor DAF-16 both extends lifespan and simultaneously increases immunity and stress resistance. It is known that lifespan varies significantly among the Caenorhabditis species but, although DAF-16 signalling is highly conserved, it is unclear whether this phenotypic linkage occurs in other species. Here we investigate this phenotypic covariance by comparing longevity, stress resistance and immunity in four Caenorhabditis species. \ud \ud Methodology/Principal Findings: We show using phenotypic analysis of DAF-16 influenced phenotypes that among four closely related Caenorhabditis nematodes, the gonochoristic species (Caenorhabditis remanei and Caenorhabditis brenneri) have diverged significantly with a longer lifespan, improved stress resistance and higher immunity than the hermaphroditic species (C. elegans and Caenorhabditis briggsae). Interestingly, we also observe significant differences in expression levels between the daf-16 homologues in these species using Real-Time PCR, which positively correlate with the observed phenotypes. Finally, we provide additional evidence in support of a role for DAF-16 in regulating phenotypic coupling by using a combination of wildtype isolates, constitutively active daf-16 mutants and bioinformatic analysis. \ud \ud Conclusions: The gonochoristic species display a significantly longer lifespan (p<0.0001) and more robust immune and stress response (p<0.0001, thermal stress; p<0.01, heavy metal stress; p<0.0001, pathogenic stress) than the hermaphroditic species. Our data suggests that divergence in DAF-16 mediated phenotypes may underlie many of the differences observed between these four species of Caenorhabditis nematodes. These findings are further supported by the correlative higher daf-16 expression levels among the gonochoristic species and significantly higher lifespan, immunity and stress tolerance in the constitutively active daf-16 hermaphroditic mutants