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

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

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

Invariance of the essential spectra of operator pencils

The essential spectrum of operator pencils with bounded coefficients in a Hilbert space is studied. Sufficient conditions in terms of the operator coefficients of two pencils are derived which guarantee the same essential spectrum. This is done by exploiting a strong relation between an operator pencil and a specific linear subspace (linear relation)

Metabotyping of docosahexaenoic acid - Treated alzheimer's disease cell model

10.1371/journal.pone.0090123PLoS ONE92-POLN

Moonlighting Newborn Screening Markers: The Incidental Discovery of a Second-Tier Test for Pompe Disease

Purpose: To describe a novel biochemical marker in dried blood spots suitable to improve the specificity of newborn screening for Pompe disease. Methods: The new marker is a ratio calculated between the creatine/creatinine (Cre/Crn) ratio as the numerator and the activity of acid α-glucosidase (GAA) as the denominator. Using Collaborative Laboratory Integrated Reports (CLIR), the new marker was incorporated in a dual scatter plot that can achieve almost complete segregation between Pompe disease and false-positive cases. Results: The (Cre/Crn)/GAA ratio was measured in residual dried blood spots of five Pompe cases and was found to be elevated (range 4.41–13.26; 99%ile of neonatal controls: 1.10). Verification was by analysis of 39 blinded specimens that included 10 controls, 24 samples with a definitive classification (16 Pompe, 8 false positives), and 5 with genotypes of uncertain significance. The CLIR tool showed 100% concordance of classification for the 24 known cases. Of the remaining five cases, three p.V222M homozygotes, a benign variant, were classified by CLIR as false positives; two with genotypes of unknown significance, one likely informative, were categorized as Pompe disease. Conclusion: The CLIR tool inclusive of the new ratio could have prevented at least 12 of 13 (92%) false-positive outcomes

A Role for the RNA Chaperone Hfq in Controlling Adherent-Invasive Escherichia coli Colonization and Virulence

Adherent-invasive Escherichia coli (AIEC) has been linked with the onset and perpetuation of inflammatory bowel diseases. The AIEC strain LF82 was originally isolated from an ileal biopsy from a patient with Crohn's disease. The pathogenesis of LF82 results from its abnormal adherence to and subsequent invasion of the intestinal epithelium coupled with its ability to survive phagocytosis by macrophages once it has crossed the intestinal barrier. To gain further insight into AIEC pathogenesis we employed the nematode Caenorhabditis elegans as an in vivo infection model. We demonstrate that AIEC strain LF82 forms a persistent infection in C. elegans, thereby reducing the host lifespan significantly. This host killing phenotype was associated with massive bacterial colonization of the nematode intestine and damage to the intestinal epithelial surface. C. elegans killing was independent of known LF82 virulence determinants but was abolished by deletion of the LF82 hfq gene, which encodes an RNA chaperone involved in mediating posttranscriptional gene regulation by small non-coding RNAs. This finding reveals that important aspects of LF82 pathogenesis are controlled at the posttranscriptional level by riboregulation. The role of Hfq in LF82 virulence was independent of its function in regulating RpoS and RpoE activity. Further, LF82Δhfq mutants were non-motile, impaired in cell invasion and highly sensitive to various chemical stress conditions, reinforcing the multifaceted function of Hfq in mediating bacterial adaptation. This study highlights the usefulness of simple non-mammalian infection systems for the identification and analysis of bacterial virulence factors