Statistical stability and limit laws for Rovella maps

We consider the family of one-dimensional maps arising from the contracting Lorenz attractors studied by Rovella. Benedicks-Carleson techniques were used by Rovella to prove that there is a one-parameter family of maps whose derivatives along their critical orbits increase exponentially fast and the critical orbits have slow recurrent to the critical point. Metzger proved that these maps have a unique absolutely continuous ergodic invariant probability measure (SRB measure). Here we use the technique developed by Freitas and show that the tail set (the set of points which at a given time have not achieved either the exponential growth of derivative or the slow recurrence) decays exponentially fast as time passes. As a consequence, we obtain the continuous variation of the densities of the SRB measures and associated metric entropies with the parameter. Our main result also implies some statistical properties for these maps.Comment: 1 figur

Some remarks on the geometry of the Standard Map

We define and compute hyperbolic coordinates and associated foliations which provide a new way to describe the geometry of the standard map. We also identify a uniformly hyperbolic region and a complementary 'critical' region containing a smooth curve of tangencies between certain canonical 'stable' foliations.Comment: 25 pages, 11 figure

Geometry of expanding absolutely continuous invariant measures and the liftability problem

We show that for a large class of maps on manifolds of arbitrary finite dimension, the existence of a Gibbs-Markov-Young structure (with Lebesgue as the reference measure) is a necessary as well as sufficient condition for the existence of an invariant probability measure which is absolutely continuous measure (with respect to Lebesgue) and for which all Lyapunov exponents are positive.Comment: 21 pages; final versio

COVID-19 one year into the pandemic: from genetics and genomics to therapy, vaccination, and policy

COVID-19 has engulfed the world and it will accompany us all for some time to come. Here, we review the current state at the milestone of 1 year into the pandemic, as declared by the WHO (World Health Organization). We review several aspects of the on-going pandemic, focusing first on two major topics: viral variants and the human genetic susceptibility to disease severity. We then consider recent and exciting new developments in therapeutics, such as monoclonal antibodies, and in prevention strategies, such as vaccines. We also briefly discuss how advances in basic science and in biotechnology, under the threat of a worldwide emergency, have accelerated to an unprecedented degree of the transition from the laboratory to clinical applications. While every day we acquire more and more tools to deal with the on-going pandemic, we are aware that the path will be arduous and it will require all of us being community-minded. In this respect, we lament past delays in timely full investigations, and we call for bypassing local politics in the interest of humankind on all continents

Genetic predisposition to hemophagocytic lymphohistiocytosis: report on 500 patients from the Italian registry

Background Hemophagocytic lymphohistiocytosis (HLH) is a rare life-threatening disease affecting mostly children but also adults and characterized by hyperinflammatory features. A subset of patients, referred to as having familial hemophagocytic lymphohistiocytosis (FHL), have various underlying genetic abnormalities, the frequencies of which have not been systematically determined previously. Objective This work aims to further our understanding of the pathogenic bases of this rare condition based on an analysis of our 25 years of experience. Methods From our registry, we have analyzed a total of 500 unselected patients with HLH. Results Biallelic pathogenic mutations defining FHL were found in 171 (34%) patients; the proportion of FHL was much higher (64%) in patients given a diagnosis during the first year of life. Taken together, mutations of the genes PRF1 (FHL2) and UNC13D (FHL3) accounted for 70% of cases of FHL. Overall, a genetic diagnosis was possible in more than 90% of our patients with FHL. Perforin expression and the extent of degranulation have been more useful for diagnosing FHL than hemophagocytosis and the cytotoxicity assay. Of 281 (56%) patients classified as having "sporadic" HLH, 43 had monoallelic mutations in one of the FHL-defining genes. Given this gene dosage effect, FHL is not strictly recessive. Conclusion We suggest that the clinical syndrome HLH generally results from the combined effects of an exogenous trigger and genetic predisposition. Within this combination, different weights of exogenous and genetic factors account for the wide disease spectrum that ranges from HLH secondary to severe infection to FHL

Large deviations for non-uniformly expanding maps

We obtain large deviation results for non-uniformly expanding maps with non-flat singularities or criticalities and for partially hyperbolic non-uniformly expanding attracting sets. That is, given a continuous function we consider its space average with respect to a physical measure and compare this with the time averages along orbits of the map, showing that the Lebesgue measure of the set of points whose time averages stay away from the space average decays to zero exponentially fast with the number of iterates involved. As easy by-products we deduce escape rates from subsets of the basins of physical measures for these types of maps. The rates of decay are naturally related to the metric entropy and pressure function of the system with respect to a family of equilibrium states. The corrections added to the published version of this text appear in bold; see last section for a list of changesComment: 36 pages, 1 figure. After many PhD students and colleagues having pointed several errors in the statements and proofs, this is a correction to published article answering those comments. List of main changes in a new last sectio

Gateways as inter-modal nodes in different ages: The Venetian region, eighteenth to twentieth centuries

This paper focuses on the theoretical implications of a regional case studyfor the analysis of transportation networks and gateway functions. Thestarting point is the result of a research on the changing role of gateways,and on the relocation of the gateway function from one city to a series ofcities in the Venetian region from the eighteenth to the twentieth century.Against this evolution, I test the validity and usefulness of a definition of thegateway as a point of inter-modal exchange for its historical interpretation.Changing transport technologies involve different organisations of inter-modal exchanges, and imply more or less intense economic functions ofgateway cities. These changes intertwine with political events and deci-sions, and more general economic changes: they could at the same time beread as an effect of these transformations, and as a causal factor. From this perspective, a study of intermodality shows to be useful to shed new lighton specific changes in the structure of urban hierarchie