Variational approach to a class of nonlinear oscillators with several limit cycles

We study limit cycles of nonlinear oscillators described by the equation $\ddot x + \nu F(\dot x) + x =0$. Depending on the nonlinearity this equation may exhibit different number of limit cycles. We show that limit cycles correspond to relative extrema of a certain functional. Analytical results in the limits $\nu ->0$ and $\nu -> \infty$ are in agreement with previously known criteria. For intermediate $\nu$ numerical determination of the limit cycles can be obtained.Comment: 12 pages, 3 figure

Herschel/HIFI measurements of the ortho/para ratio in water towards Sagittarius B2(M) and W31C

We present Herschel/HIFI observations of the fundamental rotational transitions of ortho- and para-H16 2 O and H18 2 O in absorption towards Sagittarius B2(M) and W31C. The ortho/para ratio in water in the foreground clouds on the line of sight towards these bright continuum sources is generally consistent with the statistical high-temperature ratio of 3, within the observational uncertainties. However, somewhat unexpectedly, we derive a low ortho/para ratio of 2.35±0.35, corresponding to a spin temperature of ∼27 K, towards Sagittarius B2(M) at velocities of the expanding molecular ring. Water molecules in this region appear to have formed with, or relaxed to, an ortho/para ratio close to the value corresponding to the local temperature of the gas and dust

The impact of the metabotropic glutamate receptor and other gene family interaction networks on autism

Although multiple reports show that defective genetic networks underlie the aetiology of autism, few have translated into pharmacotherapeutic opportunities. Since drugs compete with endogenous small molecules for protein binding, many successful drugs target large gene families with multiple drug binding sites. Here we search for defective gene family interaction networks (GFINs) in 6,742 patients with the ASDs relative to 12,544 neurologically normal controls, to find potentially druggable genetic targets. We find significant enrichment of structural defects (P≤2.40E-09, 1.8-fold enrichment) in the metabotropic glutamate receptor (GRM) GFIN, previously observed to impact attention deficit hyperactivity disorder (ADHD) and schizophrenia. Also, the MXD-MYC-MAX network of genes, previously implicated in cancer, is significantly enriched (P≤3.83E-23, 2.5-fold enrichment), as is the calmodulin 1 (CALM1) gene interaction network (P≤4.16E-04, 14.4-fold enrichment), which regulates voltage-independent calcium-activated action potentials at the neuronal synapse. We find that multiple defective gene family interactions underlie autism, presenting new translational opportunities to explore for therapeutic interventions

Intratracheal administration of endotoxin and cytokines: VIII. LPS induces E-selectin expression; anti-E-selectin and soluble E-selectin inhibit acute inflammation

E-selectin is an inducible endothelial adhesion molecule that binds neutrophils. E-selectin mRNA is not constitutively detectable in the lungs of rats. Intratracheal injection of LPS induces pulmonary E-selectin mRNA expression at 2–4 h. Intratracheal injection of LPS followed at 2 and 4 h by intravenous injection of mouse F(ab′) 2 or F(ab′)) anti-E-selectin monoclonal antibody inhibits the emigration of neutrophils into the bronchoalveolar space at 6 h by 50–70%. TNF and IL-6 bioactivity are not decreased in bronchoalveolar lavage fluid after treatment with anti-E-selectin antibody as compared to controls, suggesting that the anti-E-selectin does not affect the magnitude of the LPS-initiated cytokine cascade. Intratracheal injection of LPS followed at 2 and 4 h by intravenous injection of soluble E-selectin inhibits neutrophilic emigration at 6 h by 64%, suggesting that endogenous soluble E-selectin shed from activated endothelium may play a role in the endogenous down-regulation of acute inflammation. E-selectin-mediated adhesion of neutrophils to endothelium appears crucial to the full development of the acute inflammation response.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44513/1/10753_2005_Article_BF01534436.pd

All-sky search for long-duration gravitational wave transients with initial LIGO

We present the results of a search for long-duration gravitational wave transients in two sets of data collected by the LIGO Hanford and LIGO Livingston detectors between November 5, 2005 and September 30, 2007, and July 7, 2009 and October 20, 2010, with a total observational time of 283.0 days and 132.9 days, respectively. The search targets gravitational wave transients of duration 10-500 s in a frequency band of 40-1000 Hz, with minimal assumptions about the signal waveform, polarization, source direction, or time of occurrence. All candidate triggers were consistent with the expected background; as a result we set 90% confidence upper limits on the rate of long-duration gravitational wave transients for different types of gravitational wave signals. For signals from black hole accretion disk instabilities, we set upper limits on the source rate density between 3.4×10-5 and 9.4×10-4 Mpc-3 yr-1 at 90% confidence. These are the first results from an all-sky search for unmodeled long-duration transient gravitational waves. © 2016 American Physical Society

All-sky search for long-duration gravitational wave transients with initial LIGO

We present the results of a search for long-duration gravitational wave transients in two sets of data collected by the LIGO Hanford and LIGO Livingston detectors between November 5, 2005 and September 30, 2007, and July 7, 2009 and October 20, 2010, with a total observational time of 283.0 days and 132.9 days, respectively. The search targets gravitational wave transients of duration 10-500 s in a frequency band of 40-1000 Hz, with minimal assumptions about the signal waveform, polarization, source direction, or time of occurrence. All candidate triggers were consistent with the expected background; as a result we set 90% confidence upper limits on the rate of long-duration gravitational wave transients for different types of gravitational wave signals. For signals from black hole accretion disk instabilities, we set upper limits on the source rate density between 3.4×10-5 and 9.4×10-4 Mpc-3 yr-1 at 90% confidence. These are the first results from an all-sky search for unmodeled long-duration transient gravitational waves. © 2016 American Physical Society

Search for Tensor, Vector, and Scalar Polarizations in the Stochastic Gravitational-Wave Background

The detection of gravitational waves with Advanced LIGO and Advanced Virgo has enabled novel tests of general relativity, including direct study of the polarization of gravitational waves. While general relativity allows for only two tensor gravitational-wave polarizations, general metric theories can additionally predict two vector and two scalar polarizations. The polarization of gravitational waves is encoded in the spectral shape of the stochastic gravitational-wave background, formed by the superposition of cosmological and individually unresolved astrophysical sources. Using data recorded by Advanced LIGO during its first observing run, we search for a stochastic background of generically polarized gravitational waves. We find no evidence for a background of any polarization, and place the first direct bounds on the contributions of vector and scalar polarizations to the stochastic background. Under log-uniform priors for the energy in each polarization, we limit the energy densities of tensor, vector, and scalar modes at 95% credibility to Ω0T<5.58×10-8, Ω0V<6.35×10-8, and Ω0S<1.08×10-7 at a reference frequency f0=25 Hz. © 2018 American Physical Society

On the progenitor of binary neutron star merger GW170817

On 2017 August 17 the merger of two compact objects with masses consistent with two neutron stars was discovered through gravitational-wave (GW170817), gamma-ray (GRB 170817A), and optical (SSS17a/AT 2017gfo) observations. The optical source was associated with the early-type galaxy NGC 4993 at a distance of just ∼40 Mpc, consistent with the gravitational-wave measurement, and the merger was localized to be at a projected distance of ∼2 kpc away from the galaxy's center. We use this minimal set of facts and the mass posteriors of the two neutron stars to derive the first constraints on the progenitor of GW170817 at the time of the second supernova (SN). We generate simulated progenitor populations and follow the three-dimensional kinematic evolution from binary neutron star (BNS) birth to the merger time, accounting for pre-SN galactic motion, for considerably different input distributions of the progenitor mass, pre-SN semimajor axis, and SN-kick velocity. Though not considerably tight, we find these constraints to be comparable to those for Galactic BNS progenitors. The derived constraints are very strongly influenced by the requirement of keeping the binary bound after the second SN and having the merger occur relatively close to the center of the galaxy. These constraints are insensitive to the galaxy's star formation history, provided the stellar populations are older than 1 Gyr

SARS-CoV-2-specific nasal IgA wanes 9 months after hospitalisation with COVID-19 and is not induced by subsequent vaccination

BACKGROUND: Most studies of immunity to SARS-CoV-2 focus on circulating antibody, giving limited insights into mucosal defences that prevent viral replication and onward transmission. We studied nasal and plasma antibody responses one year after hospitalisation for COVID-19, including a period when SARS-CoV-2 vaccination was introduced. METHODS: In this follow up study, plasma and nasosorption samples were prospectively collected from 446 adults hospitalised for COVID-19 between February 2020 and March 2021 via the ISARIC4C and PHOSP-COVID consortia. IgA and IgG responses to NP and S of ancestral SARS-CoV-2, Delta and Omicron (BA.1) variants were measured by electrochemiluminescence and compared with plasma neutralisation data. FINDINGS: Strong and consistent nasal anti-NP and anti-S IgA responses were demonstrated, which remained elevated for nine months (p < 0.0001). Nasal and plasma anti-S IgG remained elevated for at least 12 months (p < 0.0001) with plasma neutralising titres that were raised against all variants compared to controls (p < 0.0001). Of 323 with complete data, 307 were vaccinated between 6 and 12 months; coinciding with rises in nasal and plasma IgA and IgG anti-S titres for all SARS-CoV-2 variants, although the change in nasal IgA was minimal (1.46-fold change after 10 months, p = 0.011) and the median remained below the positive threshold determined by pre-pandemic controls. Samples 12 months after admission showed no association between nasal IgA and plasma IgG anti-S responses (R = 0.05, p = 0.18), indicating that nasal IgA responses are distinct from those in plasma and minimally boosted by vaccination. INTERPRETATION: The decline in nasal IgA responses 9 months after infection and minimal impact of subsequent vaccination may explain the lack of long-lasting nasal defence against reinfection and the limited effects of vaccination on transmission. These findings highlight the need to develop vaccines that enhance nasal immunity. FUNDING: This study has been supported by ISARIC4C and PHOSP-COVID consortia. ISARIC4C is supported by grants from the National Institute for Health and Care Research and the Medical Research Council. Liverpool Experimental Cancer Medicine Centre provided infrastructure support for this research. The PHOSP-COVD study is jointly funded by UK Research and Innovation and National Institute of Health and Care Research. The funders were not involved in the study design, interpretation of data or the writing of this manuscript