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

The effect of dynamic recrystallisation on the rheology and microstructures of partially molten rocks

This work was founded by the joint project “Rheology of the continental crust in collision”, funded by the Procope scheme of PHC Egide in France and by the DAAD PPP scheme in Germany. M-GL acknowledges the support of the Juan de la Cierva programme of the Government of Spain’s Ministry for Science, Innovation and Universities. EGR acknowledges the support of the Beatriu de Pinós programme of the Government of Catalonia's Secretariat for Universities and Research of the Department of Economy and Knowledge (2016 BP 00208). This work benefited from discussions with Pi L. Jolivet and E. Burov within the ERC project RHEOLITH. We thank Elisabetta Mariani and Marcin Dabrowski for their helpful comments, together with the editorial guidance of Dave Healy and Bill Dunne.Peer reviewedPostprin

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

Neurochemical Changes in the Mouse Hippocampus Underlying the Antidepressant Effect of Genetic Deletion of P2X7 Receptors.

Recent investigations have revealed that the genetic deletion of P2X7 receptors (P2rx7) results in an antidepressant phenotype in mice. However, the link between the deficiency of P2rx7 and changes in behavior has not yet been explored. In the present study, we studied the effect of genetic deletion of P2rx7 on neurochemical changes in the hippocampus that might underlie the antidepressant phenotype. P2X7 receptor deficient mice (P2rx7-/-) displayed decreased immobility in the tail suspension test (TST) and an attenuated anhedonia response in the sucrose preference test (SPT) following bacterial endotoxin (LPS) challenge. The attenuated anhedonia was reproduced through systemic treatments with P2rx7 antagonists. The activation of P2rx7 resulted in the concentration-dependent release of [3H]glutamate in P2rx7+/+ but not P2rx7-/- mice, and the NR2B subunit mRNA and protein was upregulated in the hippocampus of P2rx7-/- mice. The brain-derived neurotrophic factor (BDNF) expression was higher in saline but not LPS-treated P2rx7-/- mice; the P2rx7 antagonist Brilliant blue G elevated and the P2rx7 agonist benzoylbenzoyl ATP (BzATP) reduced BDNF level. This effect was dependent on the activation of NMDA and non-NMDA receptors but not on Group I metabotropic glutamate receptors (mGluR1,5). An increased 5-bromo-2-deoxyuridine (BrdU) incorporation was also observed in the dentate gyrus derived from P2rx7-/- mice. Basal level of 5-HT was increased, whereas the 5HIAA/5-HT ratio was lower in the hippocampus of P2rx7-/- mice, which accompanied the increased uptake of [3H]5-HT and an elevated number of [3H]citalopram binding sites. The LPS-induced elevation of 5-HT level was absent in P2rx7-/- mice. In conclusion there are several potential mechanisms for the antidepressant phenotype of P2rx7-/- mice, such as the absence of P2rx7-mediated glutamate release, elevated basal BDNF production, enhanced neurogenesis and increased 5-HT bioavailability in the hippocampus

Argon redistribution during a metamorphic cycle: Consequences for determining cooling rates

40Ar/39Ar thermochronology is commonly used to constrain the rates and times of cooling in exhumed metamorphic terranes, with ages usually linked to temperature via Dodson's closure temperature (TC) formulation. Whilst many metamorphic 40Ar/39Ar data are consistent with the timing of crystallisation or cooling within a chronological framework defined by other, higher temperature, chronometers, other 40Ar/39Ar data are more difficult to interpret. We report white mica and biotite single grain fusion and laser ablation 40Ar/39Ar ages from felsic gneisses from the Western Gneiss Region, Norway. The rocks record isothermal decompression from peak eclogite-facies conditions (white mica stable) to amphibolite-facies conditions (biotite stable) at c. 700 °C. White mica and biotite yield dispersed single grain fusion dates from 416 to 373 Ma and 437 to 360 Ma respectively. In-situ laser ablation analyses provide a similar range, with white mica spot ages ranging from 424 to 370 Ma and biotite spot ages ranging from 437 to 370 Ma. The dates span the duration of the metamorphic cycle suggested by previous studies, and cannot be reconciled with the results of simple models of Ar loss by diffusion during cooling. Samples that show evidence for different physical processes, such as the chemical breakdown of white mica, partial melting, and fluid ingress, generated different age populations to samples that did not experience or record obvious petrological evidence for these processes. Samples that record significant recrystallization and deformation yielded younger white mica (but older biotite) single grain fusion ages than more pristine samples. Amphibolite-facies gneisses that preserve evidence for significant partial melting generated younger biotite ages than samples that recorded evidence for significant hydration. Our data support other reported observations that high-temperature metamorphic mica 40Ar/39Ar dates cannot be assumed to record the timing of cooling through a specific temperature window. Careful assessment of the petrographic context of the dated minerals and consideration of their post-crystallisation history may provide a more robust insight into whether ‘age’ links to ‘stage’ in a temporally meaningful way

Quantifying the causes and consequences of variation in satellite‐derived population indices: a case study of emperor penguins

Very high-resolution satellite (VHR) imagery is a promising tool for estimating the abundance of wildlife populations, especially in remote regions where traditional surveys are limited by logistical challenges. Emperor penguins Aptenodytes forsteri were the first species to have a circumpolar population estimate derived via VHR imagery. Here we address an untested assumption from Fretwell et al. (2012) that a single image of an emperor penguin colony is a reasonable representation of the colony for the year the image was taken. We evaluated satellite-related and environmental variables that might influence the calculated area of penguin pixels to reduce uncertainties in satellite-based estimates of emperor penguin populations in the future. We focused our analysis on multiple VHR images from three representative colonies: Atka Bay, Stancomb-Wills (Weddell Sea sector) and Coulman Island (Ross Sea sector) between September and December during 2011. We replicated methods in Fretwell et al. (2012), which included using supervised classification tools in ArcGIS 10.7 software to calculate area occupied by penguins (hereafter referred to as ‘population indices’) in each image. We found that population indices varied from 2 to nearly 6-fold, suggesting that penguin pixel areas calculated from a single image may not provide a complete understanding of colony size for that year. Thus, we further highlight the important roles of: (i) sun azimuth and elevation through image resolution and (ii) penguin patchiness (aggregated vs. distributed) on the calculated areas. We found an effect of wind and temperature on penguin patchiness. Despite intra-seasonal variability in population indices, simulations indicate that reliable, robust population trends are possible by including satellite-related and environmental covariates and aggregating indices across time and space. Our work provides additional parameters that should be included in future models of population size for emperor penguins