Clifford Fibrations and Possible Kinematics

Following Herranz and Santander [Herranz F.J., Santander M., Mem. Real Acad. Cienc. Exact. Fis. Natur. Madrid 32 (1998), 59-84, physics/9702030] we will construct homogeneous spaces based on possible kinematical algebras and groups [Bacry H., Levy-Leblond J.-M., J. Math. Phys. 9 (1967), 1605-1614] and their contractions for 2-dimensional spacetimes. Our construction is different in that it is based on a generalized Clifford fibration: Following Penrose [Penrose R., Alfred A. Knopf, Inc., New York, 2005] we will call our fibration a Clifford fibration and not a Hopf fibration, as our fibration is a geometrical construction. The simple algebraic properties of the fibration describe the geometrical properties of the kinematical algebras and groups as well as the spacetimes that are derived from them. We develop an algebraic framework that handles all possible kinematic algebras save one, the static algebra

Clifford Algebras and Possible Kinematics

We review Bacry and Lévy-Leblond's work on possible kinematics as applied to 2-dimensional spacetimes, as well as the nine types of 2-dimensional Cayley-Klein geometries, illustrating how the Cayley-Klein geometries give homogeneous spacetimes for all but one of the kinematical groups. We then construct a two-parameter family of Clifford algebras that give a unified framework for representing both the Lie algebras as well as the kinematical groups, showing that these groups are true rotation groups. In addition we give conformal models for these spacetimes

Duality properties of indicatrices of knots

The bridge index and superbridge index of a knot are important invariants in knot theory. We define the bridge map of a knot conformation, which is closely related to these two invariants, and interpret it in terms of the tangent indicatrix of the knot conformation. Using the concepts of dual and derivative curves of spherical curves as introduced by Arnold, we show that the graph of the bridge map is the union of the binormal indicatrix, its antipodal curve, and some number of great circles. Similarly, we define the inflection map of a knot conformation, interpret it in terms of the binormal indicatrix, and express its graph in terms of the tangent indicatrix. This duality relationship is also studied for another dual pair of curves, the normal and Darboux indicatrices of a knot conformation. The analogous concepts are defined and results are derived for stick knots.Comment: 22 pages, 9 figure

Product type and the risk of inhibitor development in nonsevere haemophilia A patients: a case‒control study

Inhibitor development is a major complication of treatment with factor VIII concentrates in nonsevere haemophilia A. It has been suggested that plasma-derived factor VIII (FVIII) concentrates elicit fewer inhibitors than recombinant FVIII concentrates, but studies in severe haemophilia A patients have shown conflicting results. We designed a case‒control study to investigate the clinical and genetic risk factors for inhibitor development in nonsevere haemophilia A patients. We investigated whether the type of FVIII concentrate was associated with inhibitor development in nonsevere haemophilia A patients. This nested case‒control study includes 75 inhibitor patients and 223 controls, from a source population of the INSIGHT study, including all nonsevere haemophilia A patients (FVIII:C 2–40%) that were treated with FVIII concentrates in 33 European and one Australian centre. Cases and controls were matched for date of birth and cumulative number of exposure days (CED) to FVIII concentrate. A conditional logistic regression model was used to calculate unadjusted and adjusted odds ratios. No increased risk for inhibitor development was found for any type of FVIII concentrate; either when comparing recombinant FVIII concentrates to plasma-derived FVIII concentrates (adjusted odds ratio 0·96, 95% confidence interval (CI) 0·36–2·52) or for specific types of FVIII concentrates

A supergene determines highly divergent male reproductive morphs in the ruff

Three strikingly different alternative male mating morphs (aggressive 'independents', semicooperative 'satellites' and female-mimic 'faeders') coexist as a balanced polymorphism in the ruff, Philomachus pugnax, a lek-breeding wading bird1, 2, 3. Major differences in body size, ornamentation, and aggressive and mating behaviors are inherited as an autosomal polymorphism4, 5. We show that development into satellites and faeders is determined by a supergene6, 7, 8 consisting of divergent alternative, dominant and non-recombining haplotypes of an inversion on chromosome 11, which contains 125 predicted genes. Independents are homozygous for the ancestral sequence. One breakpoint of the inversion disrupts the essential CENP-N gene (encoding centromere protein N), and pedigree analysis confirms the lethality of homozygosity for the inversion. We describe new differences in behavior, testis size and steroid metabolism among morphs and identify polymorphic genes within the inversion that are likely to contribute to the differences among morphs in reproductive traits

Role of Aquaporin Water Channels in Airway Fluid Transport, Humidification, and Surface Liquid Hydration

Several aquaporin-type water channels are expressed in mammalian airways and lung: AQP1 in microvascular endothelia, AQP3 in upper airway epithelia, AQP4 in upper and lower airway epithelia, and AQP5 in alveolar epithelia. Novel quantitative methods were developed to compare airway fluid transport–related functions in wild-type mice and knockout mice deficient in these aquaporins. Lower airway humidification, measured from the moisture content of expired air during mechanical ventilation with dry air through a tracheotomy, was 54–56% efficient in wild-type mice, and reduced by only 3–4% in AQP1/AQP5 or AQP3/AQP4 double knockout mice. Upper airway humidification, measured from the moisture gained by dry air passed through the upper airways in mice breathing through a tracheotomy, decreased from 91 to 50% with increasing ventilation from 20 to 220 ml/min, and reduced by 3–5% in AQP3/AQP4 knockout mice. The depth and salt concentration of the airway surface liquid in trachea was measured in vivo using fluorescent probes and confocal and ratio imaging microscopy. Airway surface liquid depth was 45 ± 5 μm and [Na+] was 115 ± 4 mM in wild-type mice, and not significantly different in AQP3/AQP4 knockout mice. Osmotic water permeability in upper airways, measured by an in vivo instillation/sample method, was reduced by ∼40% by AQP3/AQP4 deletion. In doing these measurements, we discovered a novel amiloride-sensitive isosmolar fluid absorption process in upper airways (13% in 5 min) that was not affected by aquaporin deletion. These results establish the fluid transporting properties of mouse airways, and indicate that aquaporins play at most a minor role in airway humidification, ASL hydration, and isosmolar fluid absorption

Treatment-related risk factors for inhibitor development in non-severe hemophilia A after 50 cumulative exposure days: a case-control study

Background Non-severe hemophilia A patients have a life-long inhibitor risk. Yet, no studies have analyzed risk factors for inhibitor development after 50 factor VIII (FVIII) exposure days (EDs). Objectives This case-control study investigated treatment-related risk factors for inhibitor development in non-severe hemophilia A and assessed whether these risk factors were different for early versus late inhibitor development. Patients/Methods Non-severe hemophilia A patients (FVIII:C 2%-40%) were selected from the INSIGHT study. Inhibitor-positive patients were defined as early (50EDs) cases and matched to 1-4 inhibitor-negative controls by year of birth, cumulative number of EDs, and center/country. We investigated treatment intensity during the last 10 EDs prior to inhibitor development. Intensive treatment was defined as: surgery, peak treatment (10 consecutive EDs), and high mean FVIII dose (>45 IU/kg/ED). Odds ratios (OR) were calculated by logistic regression. Results Of 2709 patients, we analyzed 63 early and 26 late cases and 195 and 71 respectively matched controls. Peak treatment was associated with early and late inhibitor risk (crude OR 1.8, 95% confidence interval [CI] 1.0-3.4; 4.0, 95%CI 1.1-14.3). This association was slightly less pronounced after adjustment for mean FVIII dose. High mean FVIII dose was also associated with early and late inhibitor risk (crude OR 2.8, 95%CI 1.5-5.1; 4.5, 95%CI 1.2-16.6). Surgery increased inhibitor risk for early cases. This was less pronounced for late cases. Conclusions Our findings suggest that intensive FVIII treatment remains a risk factor for inhibitor development in non-severe hemophilia A after more than 50 EDs. Therefore, persistent caution is required throughout the life-time treatment course.Clinical epidemiolog

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

Search for gravitational waves from Scorpius X-1 in the second Advanced LIGO observing run with an improved hidden Markov model

We present results from a semicoherent search for continuous gravitational waves from the low-mass x-ray binary Scorpius X-1, using a hidden Markov model (HMM) to track spin wandering. This search improves on previous HMM-based searches of LIGO data by using an improved frequency domain matched filter, the J-statistic, and by analyzing data from Advanced LIGO's second observing run. In the frequency range searched, from 60 to 650 Hz, we find no evidence of gravitational radiation. At 194.6 Hz, the most sensitive search frequency, we report an upper limit on gravitational wave strain (at 95% confidence) of h095%=3.47×10-25 when marginalizing over source inclination angle. This is the most sensitive search for Scorpius X-1, to date, that is specifically designed to be robust in the presence of spin wandering. © 2019 American Physical Society

Search for Gravitational Waves Associated with Gamma-Ray Bursts Detected by Fermi and Swift during the LIGO-Virgo Run O3b

We search for gravitational-wave signals associated with gamma-ray bursts (GRBs) detected by the Fermi and Swift satellites during the second half of the third observing run of Advanced LIGO and Advanced Virgo (2019 November 1 15:00 UTC-2020 March 27 17:00 UTC). We conduct two independent searches: A generic gravitational-wave transients search to analyze 86 GRBs and an analysis to target binary mergers with at least one neutron star as short GRB progenitors for 17 events. We find no significant evidence for gravitational-wave signals associated with any of these GRBs. A weighted binomial test of the combined results finds no evidence for subthreshold gravitational-wave signals associated with this GRB ensemble either. We use several source types and signal morphologies during the searches, resulting in lower bounds on the estimated distance to each GRB. Finally, we constrain the population of low-luminosity short GRBs using results from the first to the third observing runs of Advanced LIGO and Advanced Virgo. The resulting population is in accordance with the local binary neutron star merger rate. © 2022. The Author(s). Published by the American Astronomical Society