Long-time behaviour of degenerate diffusions: UFG-type SDEs and time-inhomogeneous hypoelliptic processes

We study the long time behaviour of a large class of diffusion processes on $R^N$, generated by second order differential operators of (possibly) degenerate type. The operators that we consider {\em need not} satisfy the H\"ormander condition. Instead, they satisfy the so-called UFG condition, introduced by Herman, Lobry and Sussman in the context of geometric control theory and later by Kusuoka and Stroock, this time with probabilistic motivations. In this paper we study UFG diffusions and demonstrate the importance of such a class of processes in several respects: roughly speaking i) we show that UFG processes constitute a family of SDEs which exhibit multiple invariant measures and for which one is able to describe a systematic procedure to determine the basin of attraction of each invariant measure (equilibrium state). ii) We use an explicit change of coordinates to prove that every UFG diffusion can be, at least locally, represented as a system consisting of an SDE coupled with an ODE, where the ODE evolves independently of the SDE part of the dynamics. iii) As a result, UFG diffusions are inherently "less smooth" than hypoelliptic SDEs; more precisely, we prove that UFG processes do not admit a density with respect to Lebesgue measure on the entire space, but only on suitable time-evolving submanifolds, which we describe. iv) We show that our results and techniques, which we devised for UFG processes, can be applied to the study of the long-time behaviour of non-autonomous hypoelliptic SDEs and therefore produce several results on this latter class of processes as well. v) Because processes that satisfy the (uniform) parabolic H\"ormander condition are UFG processes, our paper contains a wealth of results about the long time behaviour of (uniformly) hypoelliptic processes which are non-ergodic, in the sense that they exhibit multiple invariant measures.Comment: 66 page

Review of geographical stocks of tropical dolphins (Stenella spp. and Delphinus delphis) in the eastern Pacific

Information on geographical variation is reviewed for Stenella attenuata, S. longirostris, S. coeruleoalba, and Delphinus delphis in the eastern tropical Pacific, and boundaries for potential management units are proposed. National Marine Fisheries Service and Inter-American Tropical Tuna Commission sighting records made from 1979 to 1983 which were outside boundaries used in a 1979 assessment were examined for validity. Tagging returns and morphological data were also analyzed. Several stock ranges are expanded or combined. Three management units are proposed for S. attenuata: the coastal, northern offshore, and southern offshore spoiled dolphins. Four management units are proposed for S. longirostris: the Costa Rican, eastern, northern whitebelly, and southern whitebelly spinner dolphins. Two provisional management units are proposed for S. coeruleoalba: the northern and southern striped dolphins. Five management units (two of which are provisional) are proposed for D. delphis: the Baja neritic, northern, central, southern, and Guerrero common dolphins. Division into management units was based on morphological stock differences and distributional breaks. (PDF file contains 34 pages.

On small time asymptotics for rough differential equations driven by fractional Brownian motions

We survey existing results concerning the study in small times of the density of the solution of a rough differential equation driven by fractional Brownian motions. We also slightly improve existing results and discuss some possible applications to mathematical finance.Comment: This is a survey paper, submitted to proceedings in the memory of Peter Laurenc

Assessing the Association between Serum Ferritin, Transferrin Saturation, and C-Reactive Protein in Northern Territory Indigenous Australian Patients with High Serum Ferritin on Maintenance Haemodialysis

Copyright © 2017 SandawanaWilliam Majoni et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Objective. To determine the significance of high serum ferritin observed in Indigenous Australian patients on maintenance haemodialysis in the Northern Territory, we assessed the relationship between ferritin and transferrin saturation (TSAT) as measures of iron status and ferritin and C-reactive protein (CRP) as markers of inflammation. Methods. We performed a retrospective cohort analysis of data from adult patients (≥18 years) on maintenance haemodialysis (>3 months) from 2004 to 2011. Results. There were 1568 patients. The mean age was 53.9 (11.9) years. 1244 (79.3%) were Indigenous. 44.2% () were male. Indigenous patients were younger (mean age [52.3 (11.1) versus 57.4 (15.2), ]) and had higher CRP [14.7 mg/l (7–35) versus 5.9 mg/l (1.9–17.5), ], higher median serum ferritin [1069 µg/l (668–1522) versus 794.9 µg/l (558.5–1252.0), ], but similar transferrin saturation [26% (19–37) versus 28% (20–38), ]. We observed a small positive correlation between ferritin and TSAT (, ), no correlation between ferritin and CRP ( = 0.001, ), and positive association between high serum ferritin and TSAT (), Indigenous ethnicity (), urea reduction ratio (), and gender () after adjustment in mixed regression analysis. Conclusion. Serum ferritin and TSAT may inadequately reflect iron status in this population. The high ferritin was poorly explained by inflammation

Centre Vortices in SU(3)

Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence.We investigate the effectiveness of using smearing as a means to generate a preconditioning transformation for gauge fields prior to fixing to Maximal Centre Gauge. This still leaves the gaugefixed field in the original gauge orbit. As expected, we find that this preconditioning leads to higher maxima of the gauge-fixing condition, resulting in lower numbers of P-vortices. We also find that removing vortices appears to give a loss of confinement for all cases but that the string tension as measured from vortex-only configurations drops from about 65% to as low as 26% when using the preconditioning method

Different genome stability proteins underpin primed and naïve adaptation in E. coli CRISPR-Cas immunity

CRISPR-Cas is a prokaryotic immune system built from capture and integration of invader DNA into CRISPR (Clustered Regularly Interspaced Short Palindromic Repeats) loci, termed ‘Adaptation’, which is dependent on Cas1 and Cas2 proteins. In Escherichia coli, Cascade-Cas3 degrades invader DNA to effect immunity, termed ‘Interference’. Adaptation can interact with interference (‘primed’), or is independent of it (‘naïve’). We demonstrate that primed adaptation requires the RecG helicase and PriA protein to be present. Genetic analysis of mutant phenotypes suggests that RecG is needed to dissipate R-loops at blocked replication forks. Additionally, we identify that DNA polymerase I is important for both primed and naive adaptation, and that RecB is needed for naïve adaptation. Purified Cas1-Cas2 protein shows specificity for binding to and nicking forked DNA within single strand gaps, and collapsing forks into DNA duplexes. The data suggest that different genome stability systems interact with primed or naïve adaptation when responding to blocked or collapsed invader DNA replication. In this model, RecG and Cas3 proteins respond to invader DNA replication forks that are blocked by Cascade interference, enabling DNA capture. RecBCD targets DNA ends at collapsed forks, enabling DNA capture without interference. DNA polymerase I is proposed to fill DNA gaps during spacer integration

Assessment of healthcare worker protocol deviations and self-contamination during personal protective equipment donning and doffing

OBJECTIVETo evaluate healthcare worker (HCW) risk of self-contamination when donning and doffing personal protective equipment (PPE) using fluorescence and MS2 bacteriophage.DESIGNProspective pilot study.SETTINGTertiary-care hospital.PARTICIPANTSA total of 36 HCWs were included in this study: 18 donned/doffed contact precaution (CP) PPE and 18 donned/doffed Ebola virus disease (EVD) PPE.INTERVENTIONSHCWs donned PPE according to standard protocols. Fluorescent liquid and MS2 bacteriophage were applied to HCWs. HCWs then doffed their PPE. After doffing, HCWs were scanned for fluorescence and swabbed for MS2. MS2 detection was performed using reverse transcriptase PCR. The donning and doffing processes were videotaped, and protocol deviations were recorded.RESULTSOverall, 27% of EVD PPE HCWs and 50% of CP PPE HCWs made ≥1 protocol deviation while donning, and 100% of EVD PPE HCWs and 67% of CP PPE HCWs made ≥1 protocol deviation while doffing (P=.02). The median number of doffing protocol deviations among EVD PPE HCWs was 4, versus 1 among CP PPE HCWs. Also, 15 EVD PPE protocol deviations were committed by doffing assistants and/or trained observers. Fluorescence was detected on 8 EVD PPE HCWs (44%) and 5 CP PPE HCWs (28%), most commonly on hands. MS2 was recovered from 2 EVD PPE HCWs (11%) and 3 CP PPE HCWs (17%).CONCLUSIONSProtocol deviations were common during both EVD and CP PPE doffing, and some deviations during EVD PPE doffing were committed by the HCW doffing assistant and/or the trained observer. Self-contamination was common. PPE donning/doffing are complex and deserve additional study.Infect Control Hosp Epidemiol 2017;38:1077–1083</jats:sec

Tourism and the smartphone app: capabilities, emerging practice and scope in the travel domain.

Based on its advanced computing capabilities and ubiquity, the smartphone has rapidly been adopted as a tourism travel tool.With a growing number of users and a wide varietyof applications emerging, the smartphone is fundamentally altering our current use and understanding of the transport network and tourism travel. Based on a review of smartphone apps, this article evaluates the current functionalities used in the domestic tourism travel domain and highlights where the next major developments lie. Then, at a more conceptual level, the article analyses how the smartphone mediates tourism travel and the role it might play in more collaborative and dynamic travel decisions to facilitate sustainable travel. Some emerging research challenges are discussed

A Field-Based Approach for Determining ATOFMS Instrument Sensitivities to Ammonium and Nitrate

Aerosol time-of-flight mass spectrometry (ATOFMS) instruments measure the size and chemical composition of individual particles in real-time. ATOFMS chemical composition measurements are difficult to quantify, largely because the instrument sensitivities to different chemical species in mixed ambient aerosols are unknown. In this paper, we develop a field-based approach for determining ATOFMS instrument sensitivities to ammonium and nitrate in size-segregated atmospheric aerosols, using tandem ATOFMS-impactor sampling. ATOFMS measurements are compared with collocated impactor measurements taken at Riverside, CA, in September 1996, August 1997, and October 1997. This is the first comparison of ion signal intensities from a single-particle instrument with quantitative measurements of atmospheric aerosol chemical composition. The comparison reveals that ATOFMS instrument sensitivities to both NH_4^+ and NO_3^- decline with increasing particle aerodynamic diameter over a 0.32−1.8 μm calibration range. The stability of this particle size dependence is tested over the broad range of fine particle concentrations (PM_(1.8) = 17.6 ± 2.0−127.8 ± 1.8 μg m^(-3)), ambient temperatures (23−35 °C), and relative humidity conditions (21−69%), encountered during the field experiments. This paper describes a potentially generalizable methodology for increasing the temporal and size resolution of atmospheric aerosol chemical composition measurements, using tandem ATOFMS-impactor sampling