Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below

This paper is devoted to a deeper understanding of the heat flow and to the refinement of calculus tools on metric measure spaces (X,d,m). Our main results are: - A general study of the relations between the Hopf-Lax semigroup and Hamilton-Jacobi equation in metric spaces (X,d). - The equivalence of the heat flow in L^2(X,m) generated by a suitable Dirichlet energy and the Wasserstein gradient flow of the relative entropy functional in the space of probability measures P(X). - The proof of density in energy of Lipschitz functions in the Sobolev space W^{1,2}(X,d,m). - A fine and very general analysis of the differentiability properties of a large class of Kantorovich potentials, in connection with the optimal transport problem. Our results apply in particular to spaces satisfying Ricci curvature bounds in the sense of Lott & Villani [30] and Sturm [39,40], and require neither the doubling property nor the validity of the local Poincar\'e inequality.Comment: Minor typos corrected and many small improvements added. Lemma 2.4, Lemma 2.10, Prop. 5.7, Rem. 5.8, Thm. 6.3 added. Rem. 4.7, Prop. 4.8, Prop. 4.15 and Thm 4.16 augmented/reenforced. Proof of Thm. 4.16 and Lemma 9.6 simplified. Thm. 8.6 corrected. A simpler axiomatization of weak gradients, still equivalent to all other ones, has been propose

Sex hormones in SARS-CoV-2 susceptibility: key players or confounders?

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection has a clear sex disparity in clinical outcomes. Hence, the interaction between sex hormones, virus entry receptors and immune responses has attracted major interest as a target for the prevention and treatment of SARS-CoV-2 infections. This Review summarizes the current understanding of the roles of androgens, oestrogens and progesterone in the regulation of virus entry receptors and disease progression of coronavirus disease 2019 (COVID-19) as well as their therapeutic value. Although many experimental and clinical studies have analysed potential mechanisms by which female sex hormones might provide protection against SARS-CoV-2 infectivity, there is currently no clear evidence for a sex-specific expression of virus entry receptors. In addition, reports describing an influence of oestrogen, progesterone and androgens on the course of COVID-19 vary widely. Current data also do not support the administration of oestradiol in COVID-19. The conflicting evidence and lack of consensus results from a paucity of mechanistic studies and clinical trials reporting sex-disaggregated data. Further, the influence of variables beyond biological factors (sex), such as sociocultural factors (gender), on COVID-19 manifestations has not been investigated. Future research will have to fill this knowledge gap as the influence of sex and gender on COVID-19 will be essential to understanding and managing the long-term consequences of this pandemic

From log Sobolev to Talagrand: a quick proof

We provide yet another proof of the Otto-Villani theorem from the log Sobolev inequality to the Talagrand transportation cost inequality valid in arbitrary metric measure spaces. The argument relies on the recent develop- ment [2] identifying gradient flows in Hilbert space and in Wassertein space, emphasizing one key step as precisely the root of the Otto-Villani theorem. The approach does not require the doubling property or the validity of the local Poincar\ue9 inequality

The Abresch-Gromoll inequality in a non-smooth setting

We prove that the Abresch-Gromoll inequality holds on infinitesimally Hilbertian CD(K,N) spaces in the same form as the one available on smooth Riemannian manifolds

Optimal maps and exponentiation on finite dimensional spaces with Ricci curvature bounded from below

We prove existence and uniqueness of optimal maps on $RCD^*(K,N)$ spaces under the assumption that the starting measure is absolutely continuous. We also discuss how this result naturally leads to the notion of exponentiation. \ua9 2015, Mathematica Josephina, Inc

Fermi Large Area Telescope Constraints on the Gamma-ray Opacity of the Universe

The Extragalactic Background Light (EBL) includes photons with wavelengths from ultraviolet to infrared, which are effective at attenuating gamma rays with energy above ~10 GeV during propagation from sources at cosmological distances. This results in a redshift- and energy-dependent attenuation of the gamma-ray flux of extragalactic sources such as blazars and Gamma-Ray Bursts (GRBs). The Large Area Telescope onboard Fermi detects a sample of gamma-ray blazars with redshift up to z~3, and GRBs with redshift up to z~4.3. Using photons above 10 GeV collected by Fermi over more than one year of observations for these sources, we investigate the effect of gamma-ray flux attenuation by the EBL. We place upper limits on the gamma-ray opacity of the Universe at various energies and redshifts, and compare this with predictions from well-known EBL models. We find that an EBL intensity in the optical-ultraviolet wavelengths as great as predicted by the "baseline" model of Stecker et al. (2006) can be ruled out with high confidence.Comment: 42 pages, 12 figures, accepted version (24 Aug.2010) for publication in ApJ; Contact authors: A. Bouvier, A. Chen, S. Raino, S. Razzaque, A. Reimer, L.C. Reye

The 2018 report of the Lancet Countdown on health and climate change: shaping the health of nations for centuries to come

The Lancet Countdown: tracking progress on health and climate change was established to provide an independent, global monitoring system dedicated to tracking the health dimensions of the impacts of, and the response to, climate change. The Lancet Countdown tracks 41 indicators across five domains: climate change impacts, exposures, and vulnerability; adaptation, planning, and resilience for health; mitigation actions and health co-benefits; finance and economics; and public and political engagement. This report is the product of a collaboration of 27 leading academic institutions, the UN, and intergovernmental agencies from every continent. The report draws on world-class expertise from climate scientists, ecologists, mathematicians, geographers, engineers, energy, food, livestock, and transport experts, economists, social and political scientists, public health professionals, and. doctors. The Lancet Countdown’s work builds on decades of research in this field, and was first proposed in the 2015 Lancet Commission on health and climate change,1 which documented the human impacts of climate change and provided ten global recommendations to respond to this public health emergency and secure the public health benefits available (panel 1)

Using RNA-seq to determine the transcriptional landscape and the hypoxic response of the pathogenic yeast Candida parapsilosis

<p>Abstract</p> <p>Background</p> <p><it>Candida parapsilosis </it>is one of the most common causes of <it>Candida </it>infection worldwide. However, the genome sequence annotation was made without experimental validation and little is known about the transcriptional landscape. The transcriptional response of <it>C. parapsilosis </it>to hypoxic (low oxygen) conditions, such as those encountered in the host, is also relatively unexplored.</p> <p>Results</p> <p>We used next generation sequencing (RNA-seq) to determine the transcriptional profile of <it>C. parapsilosis </it>growing in several conditions including different media, temperatures and oxygen concentrations. We identified 395 novel protein-coding sequences that had not previously been annotated. We removed > 300 unsupported gene models, and corrected approximately 900. We mapped the 5' and 3' UTR for thousands of genes. We also identified 422 introns, including two introns in the 3' UTR of one gene. This is the first report of 3' UTR introns in the Saccharomycotina. Comparing the introns in coding sequences with other species shows that small numbers have been gained and lost throughout evolution. Our analysis also identified a number of novel transcriptional active regions (nTARs). We used both RNA-seq and microarray analysis to determine the transcriptional profile of cells grown in normoxic and hypoxic conditions in rich media, and we showed that there was a high correlation between the approaches. We also generated a knockout of the <it>UPC2 </it>transcriptional regulator, and we found that similar to <it>C. albicans</it>, Upc2 is required for conferring resistance to azole drugs, and for regulation of expression of the ergosterol pathway in hypoxia.</p> <p>Conclusion</p> <p>We provide the first detailed annotation of the <it>C. parapsilosis </it>genome, based on gene predictions and transcriptional analysis. We identified a number of novel ORFs and other transcribed regions, and detected transcripts from approximately 90% of the annotated protein coding genes. We found that the transcription factor Upc2 role has a conserved role as a major regulator of the hypoxic response in <it>C. parapsilosis </it>and <it>C. albicans</it>.</p

Gamma-ray and radio properties of six pulsars detected by the fermi large area telescope

We report the detection of pulsed γ-rays for PSRs J0631+1036, J0659+1414, J0742-2822, J1420-6048, J1509-5850, and J1718-3825 using the Large Area Telescope on board the Fermi Gamma-ray Space Telescope (formerly known as GLAST). Although these six pulsars are diverse in terms of their spin parameters, they share an important feature: their γ-ray light curves are (at least given the current count statistics) single peaked. For two pulsars, there are hints for a double-peaked structure in the light curves. The shapes of the observed light curves of this group of pulsars are discussed in the light of models for which the emission originates from high up in the magnetosphere. The observed phases of the γ-ray light curves are, in general, consistent with those predicted by high-altitude models, although we speculate that the γ-ray emission of PSR J0659+1414, possibly featuring the softest spectrum of all Fermi pulsars coupled with a very low efficiency, arises from relatively low down in the magnetosphere. High-quality radio polarization data are available showing that all but one have a high degree of linear polarization. This allows us to place some constraints on the viewing geometry and aids the comparison of the γ-ray light curves with high-energy beam models

Detection of High-Energy Gamma-Ray Emission from the Globular Cluster 47 Tucanae with Fermi

Gamma-Ray Pulsar Bonanza Most of the pulsars we know about were detected through their radio emission; a few are known to pulse gamma rays but were first detected at other wavelengths (see the Perspective by Halpern ). Using the Fermi Gamma-Ray Space Telescope, Abdo et al. (p. 840 , published online 2 July; see the cover) report the detection of 16 previously unknown pulsars based on their gamma-ray emission alone. Thirteen of these coincide with previously unidentified gamma-ray sources, solving the 30-year-old mystery of their identities. Pulsars are fast-rotating neutron stars. With time they slow down and cease to radiate; however, if they are in a binary system, they can have their spin rates increased by mass transfer from their companion stars, starting a new life as millisecond pulsars. In another study, Abdo et al. (p. 845 ) report the detection of gamma-ray emission from the globular cluster 47 Tucanae, which is coming from an ensemble of millisecond pulsars in the cluster's core. The data imply that there are up to 60 millisecond pulsars in 47 Tucanae, twice as many as predicted by radio observations. In a further companion study, Abdo et al. (p. 848 , published online 2 July) searched Fermi Large Area Telescope data for pulsations from all known millisecond pulsars outside of stellar clusters, finding gamma-ray pulsations for eight of them. Their properties resemble those of other gamma-ray pulsars, suggesting that they share the same basic emission mechanism. Indeed, both sets of pulsars favor emission models in which the gamma rays are produced in the outer magnetosphere of the neutron star