Decay of correlations for maps with uniformly contracting fibers and logarithm law for singular hyperbolic attractors

We consider two dimensional maps preserving a foliation which is uniformly contracting and a one dimensional associated quotient map having exponential convergence to equilibrium (iterates of Lebesgue measure converge exponentially fast to physical measure). We prove that these maps have exponential decay of correlations over a large class of observables. We use this result to deduce exponential decay of correlations for the Poincare maps of a large class of singular hyperbolic flows. From this we deduce logarithm laws for these flows.Comment: 39 pages; 03 figures; proof of Theorem 1 corrected; many typos corrected; improvements on the statements and comments suggested by a referee. Keywords: singular flows, singular-hyperbolic attractor, exponential decay of correlations, exact dimensionality, logarithm la

New ophthalmosaurid ichthyosaurs from the European lower cretaceous demonstrate extensive ichthyosaur survival across the Jurassic–Cretaceous boundary

Background Ichthyosauria is a diverse clade of marine amniotes that spanned most of the Mesozoic. Until recently, most authors interpreted the fossil record as showing that three major extinction events affected this group during its history: one during the latest Triassic, one at the Jurassic–Cretaceous boundary (JCB), and one (resulting in total extinction) at the Cenomanian-Turonian boundary. The JCB was believed to eradicate most of the peculiar morphotypes found in the Late Jurassic, in favor of apparently less specialized forms in the Cretaceous. However, the record of ichthyosaurs from the Berriasian–Barremian interval is extremely limited, and the effects of the end-Jurassic extinction event on ichthyosaurs remains poorly understood. Methodology/Principal Findings Based on new material from the Hauterivian of England and Germany and on abundant material from the Cambridge Greensand Formation, we name a new ophthalmosaurid, Acamptonectes densus gen. et sp. nov. This taxon shares numerous features with Ophthalmosaurus, a genus now restricted to the Callovian–Berriasian interval. Our phylogenetic analysis indicates that Ophthalmosauridae diverged early in its history into two markedly distinct clades, Ophthalmosaurinae and Platypterygiinae, both of which cross the JCB and persist to the late Albian at least. To evaluate the effect of the JCB extinction event on ichthyosaurs, we calculated cladogenesis, extinction, and survival rates for each stage of the Oxfordian–Barremian interval, under different scenarios. The extinction rate during the JCB never surpasses the background extinction rate for the Oxfordian–Barremian interval and the JCB records one of the highest survival rates of the interval. Conclusions/Significance There is currently no evidence that ichthyosaurs were affected by the JCB extinction event, in contrast to many other marine groups. Ophthalmosaurid ichthyosaurs remained diverse from their rapid radiation in the Middle Jurassic to their total extinction at the beginning of the Late Cretaceous

Budget impact analysis of medicines : updated systematic review and implications

This evaluation determines whether published studies to date meet the key characteristics identified for budget impact analyses (BIA) for medicines, accomplished through a systematic review and assessment against identified key characteristics. Studies from 2001 to 2015 on "budget impact analysis" with "drug" interventions were assessed, selected based on their titles/abstracts and full texts, with their characteristics checked according to key criteria. Out of 1984 studies, 92 were identified. Of these, 95% were published in Europe and the USA. 2012 saw the largest number of publications (16%) with a decline thereafter. 48% met up to 6 or 7 out of the 9 key characteristics. Only 22% stated no conflict of interest. The results indicate low adherence to the key characteristics that should be considered for BIAs and strong conflict of interest. This is an issue since BIAs can be of fundamental importance in managing the entry of new medicines including reimbursement decisions

Multiscale Systems, Homogenization, and Rough Paths:VAR75 2016: Probability and Analysis in Interacting Physical Systems

In recent years, substantial progress was made towards understanding convergence of fast-slow deterministic systems to stochastic differential equations. In contrast to more classical approaches, the assumptions on the fast flow are very mild. We survey the origins of this theory and then revisit and improve the analysis of Kelly-Melbourne [Ann. Probab. Volume 44, Number 1 (2016), 479-520], taking into account recent progress in $p$-variation and c\`adl\`ag rough path theory.Comment: 27 pages. Minor corrections. To appear in Proceedings of the Conference in Honor of the 75th Birthday of S.R.S. Varadha