Automatic closure of invariant linear manifolds for operator algebras

Kadison's transitivity theorem implies that, for irreducible representations of C*-algebras, every invariant linear manifold is closed. It is known that CSL algebras have this propery if, and only if, the lattice is hyperatomic (every projection is generated by a finite number of atoms). We show several other conditions are equivalent, including the conditon that every invariant linear manifold is singly generated. We show that two families of norm closed operator algebras have this property. First, let L be a CSL and suppose A is a norm closed algebra which is weakly dense in Alg L and is a bimodule over the (not necessarily closed) algebra generated by the atoms of L. If L is hyperatomic and the compression of A to each atom of L is a C*-algebra, then every linear manifold invariant under A is closed. Secondly, if A is the image of a strongly maximal triangular AF algebra under a multiplicity free nest representation, where the nest has order type -N, then every linear manifold invariant under A is closed and is singly generated.Comment: AMS-LaTeX, 15 pages, minor revision

Cartan Triples

We introduce the class of Cartan triples as a generalization of the notion of a Cartan MASA in a von Neumann algebra. We obtain a one-to-one correspondence between Cartan triples and certain Clifford extensions of inverse semigroups. Moreover, there is a spectral theorem describing bimodules in terms of their support sets in the fundamental inverse semigroup and, as a corollary, an extension of Aoi's theorem to this setting. This context contains that of Fulman's generalization of Cartan MASAs and we discuss his generalization in an appendix.Comment: 37 page

CARTAN TRIPLES

We introduce the class of Cartan triples as a generalization of the notion of a Car- tan MASA in a von Neumann algebra. We obtain a one-to-one correspondence between Cartan triples and certain Clifford extensions of inverse semigroups. Moreover, there is a spectral theorem describing bimodules in terms of their support sets in the fundamental inverse semigroup and, as a corollary, an extension of Aoi’s theorem to this setting. This context contains that of Fulman’s generalization of Cartan MASAs and we discuss his generalization in an appendix

The Hunt for Exomoons with Kepler (HEK): IV. A Search for Moons around Eight M-Dwarfs

With their smaller radii and high cosmic abundance, transiting planets around cool stars hold a unique appeal. As part of our on-going project to measure the occurrence rate of extrasolar moons, we here present results from a survey focussing on eight Kepler planetary candidates associated with M-dwarfs. Using photodynamical modeling and Bayesian multimodal nested sampling, we find no compelling evidence for an exomoon in these eight systems. Upper limits on the presence of such bodies probe down to $\sim0.4M_{\oplus}$ in the best case. For KOI-314, we are able to confirm the planetary nature of two out of the three known transiting candidates using transit timing variations. Of particular interest is KOI-314c, which is found to have a mass of $1.0_{-0.3}^{+0.4}M_{\oplus}$, making it the lowest mass transiting planet discovered to date. With a radius of $1.61_{-0.15}^{+0.16}R_{\oplus}$, this Earth-mass world is likely enveloped by a significant gaseous envelope comprising $\geq17_{-13}^{+12}$% of the planet by radius. We find evidence to support the planetary nature of KOI-784 too via transit timing, but we advocate further observations to verify the signals. In both systems, we infer that the inner planet has a higher density than the outer world, which may be indicative of photo-evaporation. These results highlight both the ability of Kepler to search for sub-Earth mass moons and the exciting ancillary science which often results from such efforts.Comment: 15 pages, 13 figures, 6 tables. Accepted in Ap

The Hunt for Exomoons with Kepler (HEK): II. Analysis of Seven Viable Satellite-Hosting Planet Candidates

From the list of 2321 transiting planet candidates announced by the Kepler Mission, we select seven targets with favorable properties for the capacity to dynamically maintain an exomoon and present a detectable signal. These seven candidates were identified through our automatic target selection (TSA) algorithm and target selection prioritization (TSP) filtering, whereby we excluded systems exhibiting significant time-correlated noise and focussed on those with a single transiting planet candidate of radius less than 6 Earth radii. We find no compelling evidence for an exomoon around any of the seven KOIs but constrain the satellite-to-planet mass ratios for each. For four of the seven KOIs, we estimate a 95% upper quantile of M_S/M_P<0.04, which given the radii of the candidates, likely probes down to sub-Earth masses. We also derive precise transit times and durations for each candidate and find no evidence for dynamical variations in any of the KOIs. With just a few systems analyzed thus far in the in-going HEK project, projections on eta-moon would be premature, but a high frequency of large moons around Super-Earths/Mini-Neptunes would appear to be incommensurable with our results so far.Comment: 32 pages, 11 figures, 23 tables, Accepted to Ap

The Hunt for Exomoons with Kepler (HEK): III. The First Search for an Exomoon around a Habitable-Zone Planet

Kepler-22b is the first transiting planet to have been detected in the habitable-zone of its host star. At 2.4 Earth radii, Kepler-22b is too large to be considered an Earth-analog, but should the planet host a moon large enough to maintain an atmosphere, then the Kepler-22 system may yet possess a telluric world. Aside from being within the habitable-zone, the target is attractive due to the availability of previously measured precise radial velocities and low intrinsic photometric noise, which has also enabled asteroseismology studies of the star. For these reasons, Kepler-22b was selected as a target-of-opportunity by the 'Hunt for Exomoons with Kepler' (HEK) project. In this work, we conduct a photodynamical search for an exomoon around Kepler-22b leveraging the transits, radial velocities and asteroseismology plus several new tools developed by the HEK project to improve exomoon searches. We find no evidence for an exomoon around the planet and exclude moons of mass >0.5 Earth masses to 95% confidence. By signal injection and blind retrieval, we demonstrate that an Earth-like moon is easily detected for this planet even when the time-correlated noise of the data set is taken into account. We provide updated parameters for the planet Kepler-22b including a revised mass of <53 Earth masses to 95% confidence and an eccentricity of 0.13(-0.13)(+0.36) by exploiting Single-body Asterodensity Profiling (SAP). Finally, we show that Kepler-22b has a >95% probability of being within the empirical habitable-zone but a <5% probability of being within the conservative habitable-zone.Comment: 19 pages, 11 figures, 7 tables. Accepted in ApJ. Planet-moon transit animations available at https://www.cfa.harvard.edu/~dkipping/kepler22.htm

Abdominal functional electrical stimulation to assist ventilator weaning in acute tetraplegia: a cohort study

Background Severe impairment of the major respiratory muscles resulting from tetraplegia reduces respiratory function, causing many people with tetraplegia to require mechanical ventilation during the acute stage of injury. Abdominal Functional Electrical Stimulation (AFES) can improve respiratory function in non-ventilated patients with sub-acute and chronic tetraplegia. The aim of this study was to investigate the clinical feasibility of using an AFES training program to improve respiratory function and assist ventilator weaning in acute tetraplegia.&lt;p&gt;&lt;/p&gt; Methods AFES was applied for between 20 and 40 minutes per day, five times per week on four alternate weeks, with 10 acute ventilator dependent tetraplegic participants. Each participant was matched retrospectively with a ventilator dependent tetraplegic control, based on injury level, age and sex. Tidal Volume (VT) and Vital Capacity (VC) were measured weekly, with weaning progress compared to the controls.&lt;p&gt;&lt;/p&gt; Results Compliance to training sessions was 96.7%. Stimulated VT was significantly greater than unstimulated VT. VT and VC increased throughout the study, with mean VC increasing significantly (VT: 6.2 mL/kg to 7.8 mL/kg VC: 12.6 mL/kg to 18.7 mL/kg). Intervention participants weaned from mechanical ventilation on average 11 (sd: ± 23) days faster than their matched controls.&lt;p&gt;&lt;/p&gt; Conclusion The results of this study indicate that AFES is a clinically feasible technique for acute ventilator dependent tetraplegic patients and that this intervention may improve respiratory function and enable faster weaning from mechanical ventilation.&lt;p&gt;&lt;/p&gt

Case-control study of arsenic in drinking water and lung cancer in California and Nevada.

Millions of people are exposed to arsenic in drinking water, which at high concentrations is known to cause lung cancer in humans. At lower concentrations, the risks are unknown. We enrolled 196 lung cancer cases and 359 controls matched on age and gender from western Nevada and Kings County, California in 2002-2005. After adjusting for age, sex, education, smoking and occupational exposures, odds ratios for arsenic concentrations ≥85 µg/L (median = 110 µg/L, mean = 173 µg/L, maximum = 1,460 µg/L) more than 40 years before enrollment were 1.39 (95% CI = 0.55-3.53) in all subjects and 1.61 (95% CI = 0.59-4.38) in smokers. Although odds ratios were greater than 1.0, these increases may have been due to chance given the small number of subjects exposed more than 40 years before enrollment. This study, designed before research in Chile suggested arsenic-related cancer latencies of 40 years or more, illustrates the enormous sample sizes needed to identify arsenic-related health effects in low-exposure countries with mobile populations like the U.S. Nonetheless, our findings suggest that concentrations near 100 µg/L are not associated with markedly high relative risks