Root data with group actions

Suppose $k$ is a field, $G$ is a connected reductive algebraic $k$-group, $T$ is a maximal $k$-torus in $G$, and $\Gamma$ is a finite group that acts on $(G,T)$. From the above, one obtains a root datum $\Psi$ on which $\text{Gal}(k)\times\Gamma$ acts. Provided that $\Gamma$ preserves a positive system in $\Psi$, not necessarily invariant under $\text{Gal}(k)$, we construct an inverse to this process. That is, given a root datum on which $\text{Gal}(k)\times\Gamma$ acts appropriately, we show how to construct a pair $(G,T)$, on which $\Gamma$ acts as above. Although the pair $(G,T)$ and the action of $\Gamma$ are canonical only up to an equivalence relation, we construct a particular pair for which $G$ is $k$-quasisplit and $\Gamma$ fixes a $\text{Gal}(k)$-stable pinning of $G$. Using these choices, we can define a notion of taking "$\Gamma$-fixed points" at the level of equivalence classes, and this process is compatible with a general "restriction" process for root data with $\Gamma$-action.Comment: v2: one word inserted, one citation inserted, one reference updated, one misspelling correcte

A simultaneous generalization of independence and disjointness in boolean algebras

We give a definition of some classes of boolean algebras generalizing free boolean algebras; they satisfy a universal property that certain functions extend to homomorphisms. We give a combinatorial property of generating sets of these algebras, which we call n-independent. The properties of these classes (n-free and omega-free boolean algebras) are investigated. These include connections to hypergraph theory and cardinal invariants on these algebras. Related cardinal functions, $n$Ind, which is the supremum of the cardinalities of n-independent subsets; i_n, the minimum size of a maximal n-independent subset; and i_omega, the minimum size of an omega-independent subset, are introduced and investigated. The values of i_n and i_omega on P(omega)/fin are shown to be independent of ZFC.Comment: Sumbitted to Orde

Permanent Superhumps in V1974 Cyg

We present results of 32 nights of CCD photometry of V1974 Cygni, from the years 1994 and 1995. We verify the presence of two distinct periodicities in the light curve: 0.0812585 day~1.95 hours and 0.0849767 d~2.04 hr. We establish that the shorter periodicity is the orbital period of the underlying binary system. The longer period oscillates with an average value of |dot(P)| ~ 3x10^(7)--typical to permanent superhumps. The two periods obey the linear relation between the orbital and superhump periods that holds among members of the SU Ursae Majoris class of dwarf novae. A third periodicity of 0.083204 d~2.00 hr appeared in 1994 but not in 1995. It may be related to the recently discovered anti-superhump phenomenon. These results suggest a linkage between the classical nova V1974 Cyg and the SU UMa stars, and indicate the existence of an accretion disk and permanent superhumps in the system no later than 30 months after the nova outburst. From the precessing disk model of the superhump phenomenon we estimate that the mass ratio in the binary system is between 2.2 and 3.6. Combined with previous results this implies a white dwarf mass of 0.75-1.07 M sun.Comment: 11 pages, 10 eps. figures, Latex, accepted for publication in MNRA

Type Iax Supernovae

Type Iax supernovae (SN Iax), also called SN 2002cx-like supernovae, are the largest class of peculiar white dwarf (thermonuclear) supernovae, with over fifty members known. SN Iax have lower ejecta velocity and lower luminosities, and these parameters span a much wider range, than normal type Ia supernovae (SN Ia). SN Iax are spectroscopically similar to some SN Ia near maximum light, but are unique among all supernovae in their late-time spectra, which never become fully nebular. SN Iax overwhelmingly occur in late-type host galaxies, implying a relatively young population. The SN Iax 2012Z is the only white dwarf supernova for which a pre-explosion progenitor system has been detected. A variety of models have been proposed, but one leading scenario has emerged: a type Iax supernova may be a pure-deflagration explosion of a carbon-oxygen (or hybrid carbon-oxygen-neon) white dwarf, triggered by helium accretion to the Chandrasekhar mass, that does not necessarily fully disrupt the star.Comment: Author version of a chapter in the 'Handbook of Supernovae', edited by A. Alsabti and P. Murdin, Springer. 31 pages, 6 figure

Protocol for a mixed-methods exploratory investigation of care following intensive care discharge: the REFLECT study

© Author(s) 2019. Re-use permitted under CC BY. Published by BMJ.INTRODUCTION: A substantial number of patients discharged from intensive care units (ICUs) subsequently die without leaving hospital. It is unclear how many of these deaths are preventable. Ward-based management following discharge from ICU is an area that patients and healthcare staff are concerned about. The primary aim of REFLECT (Recovery Following Intensive Care Treatment) is to develop an intervention plan to reduce in-hospital mortality rates in patients who have been discharged from ICU. METHODS AND ANALYSIS: REFLECT is a multicentre mixed-methods exploratory study examining ward care delivery to adult patients discharged from ICU. The study will be made up of four substudies. Medical notes of patients who were discharged from ICU and subsequently died will be examined using a retrospective case records review (RCRR) technique. Patients and their relatives will be interviewed about their post-ICU care, including relatives of patients who died in hospital following ICU discharge. Staff involved in the care of patients post-ICU discharge will be interviewed about the care of this patient group. The medical records of patients who survived their post-ICU stay will also be reviewed using the RCRR technique. The analyses of the substudies will be both descriptive and use a modified grounded theory approach to identify emerging themes. The evidence generated in these four substudies will form the basis of the intervention development, which will take place through stakeholder and clinical expert meetings. ETHICS AND DISSEMINATION: Ethical approval has been obtained through the Wales Research and Ethics Committee 4 (17/WA/0107). We aim to disseminate the findings through international conferences, international peer-reviewed journals and social media. TRIAL REGISTRATION NUMBER: ISRCTN14658054.Peer reviewedFinal Published versio

Effects of food type, feeding frequency, and temperature on juvenile survival and growth of Marisa cornuarietis (Mollusca: Gastropoda)

The present experiments are part of a larger study designed to investigate the influence of husbandry parameters on the life history of the ramshorn snail, Marisa cornuarietis, in order to identify suitable husbandry conditions for maintaining multi-generation populations in the laboratory for use in ecotoxicological testing. In this paper we focus on the effects of a combination of food types and feeding frequencies (i.e., the frequency with which the snails were offered food) on juvenile growth and survival at different temperatures. Offspring produced in the laboratory by wild specimens of M. cornuarietis, from Puerto Rico, were used to test the effects of three types of food (lettuce, alginate with fish food, alginate with snail mix) fed at three frequencies (given ad libitum on 4/4, 2/4, or 1/4 d) on juvenile survival and growth. The 4-d feeding regimens were repeated four times, giving a total of 16 d for the experiments. The experiments were conducted at two temperatures (22° and 25°C) under a 12 h light:12 h dark photoperiod. Juvenile growth rates increased with increasing feeding frequency for all food types. The most rapid growth rates occurred in the high-frequency lettuce treatments and the slowest growth rates in the low-frequency lettuce and alginate with snail mix treatments. Juvenile snails grew faster at 25° than at 22°C, and mortality was about twice as high at the lower temperature. Growth rates were used to provide a rough estimate of time to maturity, which was determined to take about twice as long at 22° than at 25°C. The results showed that lettuce is the best food if supplied in abundance, but effects on growth are very dependent on feeding frequency and temperature. We conclude that 25°C is a more appropriate temperature for maintaining populations than 22°C, that lettuce provides a suitable food source, and that food should be supplied continuously for husbandry and toxicity testing of populations of M. cornuarietis

Hypnosis in the Criminal Case: Facts and Fallacies

Throughout the past century, criminal cases have been documented in which a party has sought to introduce into evidence information obtained through the process of hypnosis. The usefulness of the technique of hypnosis in various psychological the rapies has already been well established. The courts, however, have differed markedly in their decisions on the admissibility of hypnotic material into evidence. Consequently, no clear rationale or guidelines for admissibility have been established

A broadband metasurface Luneburg lens for microwave surface waves

This is the author accepted manuscript. The final version is available from AIP Publishing via the DOI in this recordA broadband planar microwave Luneburg lens made of a three-layer metasurface with hexagonal symmetry is presented. This metasurface supports a transverse-electric mode confined to the surface that presents very low dispersion and a stable mode index across a broad frequency band. This enables the lens to operate in the range of frequencies between 8 GHz and 19 GHz. The lens was manufactured using a lithographic technique with three 25 μm copper-coated Mylar sheets. The resulting device is only 75 μm thick, flexible, and light-weight.We acknowledge financial support from the Engineering and Physical Sciences Research Council (EPSRC) of the United Kingdom via the EPSRC Centre for Doctoral Training in Metamaterials (Grant No. EP/L015331/1). J.P.G. wishes to thank Flann Microwave Ltd (Bodmin, UK) for additional financial support of her studentshi

The acidic domain of the endothelial membrane protein GPIHBP1 stabilizes lipoprotein lipase activity by preventing unfolding of its catalytic domain.

GPIHBP1 is a glycolipid-anchored membrane protein of capillary endothelial cells that binds lipoprotein lipase (LPL) within the interstitial space and shuttles it to the capillary lumen. The LPL•GPIHBP1 complex is responsible for margination of triglyceride-rich lipoproteins along capillaries and their lipolytic processing. The current work conceptualizes a model for the GPIHBP1•LPL interaction based on biophysical measurements with hydrogen-deuterium exchange/mass spectrometry, surface plasmon resonance, and zero-length cross-linking. According to this model, GPIHBP1 comprises two functionally distinct domains: (1) an intrinsically disordered acidic N-terminal domain; and (2) a folded C-terminal domain that tethers GPIHBP1 to the cell membrane by glycosylphosphatidylinositol. We demonstrate that these domains serve different roles in regulating the kinetics of LPL binding. Importantly, the acidic domain stabilizes LPL catalytic activity by mitigating the global unfolding of LPL's catalytic domain. This study provides a conceptual framework for understanding intravascular lipolysis and GPIHBP1 and LPL mutations causing familial chylomicronemia

'The last channel': vision at the temporal margin of the field.

The human visual field, on the temporal side, extends to at least 90° from the line of sight. Using a two-alternative forced-choice procedure in which observers are asked to report the direction of motion of a Gabor patch, and taking precautions to exclude unconscious eye movements in the direction of the stimulus, we show that the limiting eccentricity of image-forming vision can be established with precision. There are large, but reliable, individual differences in the limiting eccentricity. The limiting eccentricity exhibits a dependence on log contrast; but it is not reduced when the modulation visible to the rods is attenuated, a result compatible with the histological evidence that the outermost part of the retina exhibits a high density of cones. Our working hypothesis is that only one type of neural channel is present in the far periphery of the retina, a channel that responds to temporally modulated stimuli of low spatial frequency and that is directionally selective.Evelyn Trus