The fundamental theorem of affine geometry

We deal with a natural generalization of the classical Fundamental Theorem of Affine Geometry to the case of non bijective maps. This extension geometrically characterizes semiaffine morphisms. It was obtained by W. Zick in 1981, although it is almost unknown. Our aim is to present and discuss a simplified proof of this result

Moduli spaces for finite-order jets of Riemannian metrics

We construct the moduli space of r-jets at a point of Riemannian metrics on a smooth manifold. The construction is closely related to the problem of classification of jet metrics via differential invariants. The moduli space is proved to be a differentiable space which admits a finite canonical stratification into smooth manifolds. A complete study on the stratification of moduli spaces is carried out for metrics in dimension n=2.Comment: 25 pages, corrected typos, partially changed content with an appendix adde

Noise induced transitions in semiclassical cosmology

A semiclassical cosmological model is considered which consists of a closed Friedmann-Robertson-Walker in the presence of a cosmological constant, which mimics the effect of an inflaton field, and a massless, non-conformally coupled quantum scalar field. We show that the back-reaction of the quantum field, which consists basically of a non local term due to gravitational particle creation and a noise term induced by the quantum fluctuations of the field, are able to drive the cosmological scale factor over the barrier of the classical potential so that if the universe starts near zero scale factor (initial singularity) it can make the transition to an exponentially expanding de Sitter phase. We compute the probability of this transition and it turns out to be comparable with the probability that the universe tunnels from "nothing" into an inflationary stage in quantum cosmology. This suggests that in the presence of matter fields the back-reaction on the spacetime should not be neglected in quantum cosmology.Comment: LaTex, 33.tex pages, no figure

Complement component C4 structural variation and quantitative traits contribute to sex-biased vulnerability in systemic sclerosis

Altres ajuts: Fondo Europeo de Desarrollo Regional (FEDER), "A way of making Europe".Copy number (CN) polymorphisms of complement C4 play distinct roles in many conditions, including immune-mediated diseases. We investigated the association of C4 CN with systemic sclerosis (SSc) risk. Imputed total C4, C4A, C4B, and HERV-K CN were analyzed in 26,633 individuals and validated in an independent cohort. Our results showed that higher C4 CN confers protection to SSc, and deviations from CN parity of C4A and C4B augmented risk. The protection contributed per copy of C4A and C4B differed by sex. Stronger protection was afforded by C4A in men and by C4B in women. C4 CN correlated well with its gene expression and serum protein levels, and less C4 was detected for both in SSc patients. Conditioned analysis suggests that C4 genetics strongly contributes to the SSc association within the major histocompatibility complex locus and highlights classical alleles and amino acid variants of HLA-DRB1 and HLA-DPB1 as C4-independent signals

Para-infectious brain injury in COVID-19 persists at follow-up despite attenuated cytokine and autoantibody responses

To understand neurological complications of COVID-19 better both acutely and for recovery, we measured markers of brain injury, inflammatory mediators, and autoantibodies in 203 hospitalised participants; 111 with acute sera (1–11 days post-admission) and 92 convalescent sera (56 with COVID-19-associated neurological diagnoses). Here we show that compared to 60 uninfected controls, tTau, GFAP, NfL, and UCH-L1 are increased with COVID-19 infection at acute timepoints and NfL and GFAP are significantly higher in participants with neurological complications. Inflammatory mediators (IL-6, IL-12p40, HGF, M-CSF, CCL2, and IL-1RA) are associated with both altered consciousness and markers of brain injury. Autoantibodies are more common in COVID-19 than controls and some (including against MYL7, UCH-L1, and GRIN3B) are more frequent with altered consciousness. Additionally, convalescent participants with neurological complications show elevated GFAP and NfL, unrelated to attenuated systemic inflammatory mediators and to autoantibody responses. Overall, neurological complications of COVID-19 are associated with evidence of neuroglial injury in both acute and late disease and these correlate with dysregulated innate and adaptive immune responses acutely

Lichenometry on Adelaide Island, Antarctic Peninsula : size-frequency studies, growth rates and snowpatches

This paper presents new lichenometric population data from the Antarctic Peninsula (67°S), and describes a new approach to lichen growth-rate calibration in locations where dated surfaces are extremely rare. We use historical aerial photography and field surveys to identify sites of former perennial snowpatches where lichen populations now exist. As an independent check on lichen mortality by snowkill, and the timing of snow patch disappearance, we use a positive-degree day (PDD) approach based on monthly climate data from Rothera Research Station. We find that maximum growth rates for lichens <40 mm in diameter on Adelaide Island are around 0.8 mm/yr. Furthermore, we propose that our combined methodology may be more widely applicable to the Polar Regions where the construction of lichenometric dating (age-size) curves remains a problem

Studies on the growth of Rhizocarpon geographicum in NW Scotland, and some implications for lichenometry

Scotland, a maritime subpolar environment (55–60°N), has seen relatively few applications of lichenometry – even though it offers much potential. Perhaps surprisingly, direct measurements of Rhizocarpon geographicum growth rates in Scotland are so far lacking. This study reports on the growth of this crustose areolate species from two sites in Assynt, NW Scotland, between 2002 and 2009. Repeat photography of 23 non-competing thalli growing under identical environmental conditions on a single vertical surface over 5 years at Inchnadamph showed growth rates to be a function of size – with larger thalli (10–30 mm) growing significantly faster than the smallest thalli (10 mm are 0.67 mm yr−1 (s.d. = 0.16). Studies on a second vertical surface near Lochinver, over 7 years, yielded complex growth data on a more mature population of R. geographicum thalli (10 mm) are slower (0.29 mm yr−1; s.d. = 0.12) than those at Inchnadamph. However, at this site, competition with other species rules out any meaningful comparison of growth rates between the two sites. Other growth processes were monitored over the five to seven-year study period, including hypothallus growth, areolae development, thallus coalescence, and inter-species competition – all have important implications for the use of Rhizocarpon species in lichenometry