Section Extension from Hyperbolic Geometry of Punctured Disk and Holomorphic Family of Flat Bundles

The construction of sections of bundles with prescribed jet values plays a fundamental role in problems of algebraic and complex geometry. When the jet values are prescribed on a positive dimensional subvariety, it is handled by theorems of Ohsawa-Takegoshi type which give extension of line bundle valued square-integrable top-degree holomorphic forms from the fiber at the origin of a family of complex manifolds over the open unit 1-disk when the curvature of the metric of line bundle is semipositive. We prove here an extension result when the curvature of the line bundle is only semipositive on each fiber with negativity on the total space assumed bounded from below and the connection of the metric locally bounded, if a square-integrable extension is known to be possible over a double point at the origin. It is a Hensel-lemma-type result analogous to Artin's application of the generalized implicit function theorem to the theory of obstruction in deformation theory. The motivation is the need in the abundance conjecture to construct pluricanonical sections from flatly twisted pluricanonical sections. We also give here a new approach to the original theorem of Ohsawa-Takegoshi by using the hyperbolic geometry of the punctured open unit 1-disk to reduce the original theorem of Ohsawa-Takegoshi to a simple application of the standard method of constructing holomorphic functions by solving the d-bar equation with cut-off functions and additional blowup weight functions

Unitarity potentials and neutron matter at the unitary limit

We study the equation of state of neutron matter using a family of unitarity potentials all of which are constructed to have infinite $^1S_0$ scattering lengths $a_s$. For such system, a quantity of much interest is the ratio $\xi=E_0/E_0^{free}$ where $E_0$ is the true ground-state energy of the system, and $E_0^{free}$ is that for the non-interacting system. In the limit of $a_s\to \pm \infty$, often referred to as the unitary limit, this ratio is expected to approach a universal constant, namely $\xi\sim 0.44(1)$. In the present work we calculate this ratio $\xi$ using a family of hard-core square-well potentials whose $a_s$ can be exactly obtained, thus enabling us to have many potentials of different ranges and strengths, all with infinite $a_s$. We have also calculated $\xi$ using a unitarity CDBonn potential obtained by slightly scaling its meson parameters. The ratios $\xi$ given by these different unitarity potentials are all close to each other and also remarkably close to 0.44, suggesting that the above ratio $\xi$ is indifferent to the details of the underlying interactions as long as they have infinite scattering length. A sum-rule and scaling constraint for the renormalized low-momentum interaction in neutron matter at the unitary limit is discussed.Comment: 7.5 pages, 7 figure

Temporal evolution of short-lived penumbral microjets

Context. Penumbral microjets are elongated jet-like brightenings observed in the chromosphere above sunspot penumbrae. They are transient events that last from a few seconds to several minutes and are thought to originate from magnetic reconnection processes. Previous studies have mainly focused on their morphological and spectral characteristics, and more recently on their spectropolarimetric signals during the maximum brightness stage. Studies addressing the temporal evolution of PMJs have also been carried out, but they are based on spatial and spectral time variations only. Aims. Here we investigate the temporal evolution of the polarization signals produced by short-lived PMJs (lifetimes $<$ 2 minutes) to infer how the magnetic field vector evolves in the upper photosphere and mid-chromosphere. Methods. We use fast-cadence spectropolarimetric observations of the Ca II 854.2 nm line taken with the CRisp Imaging Spectropolarimeter at the Swedish 1-m Solar Telescope. The weak-field approximation (WFA) is used to estimate the strength and inclination of the magnetic field vector. Results. The WFA reveals larger magnetic field changes in the upper photosphere than in the chromosphere during the PMJ maximum brightness stage. In the photosphere, the magnetic field inclination and strength undergo a transient increase for most PMJs, but in 25$\%$ of the cases the field strength decreases during the brightening. In the chromosphere, the magnetic field tends to be slightly stronger during the PMJs. Conclusions. The propagation of compressive perturbation fronts followed by a rarefaction phase in the aftershock region may explain the observed behavior of the magnetic field vector. The fact that such behavior varies among the analyzed PMJs could be a consequence of the limited temporal resolution of the observations and the fast-evolving nature of the PMJs.Comment: Paper accepted for publication in section 9. The Sun and the Heliosphere of Astronomy and Astrophysics. 18 pages, 21 figure

Drug-Drug Interactions in Subjects Enrolled in SWOG Trials of Oral Chemotherapy

Background Patients with cancer are at increased risk of drug-drug interactions (DDI), which can increase treatment toxicity or decrease efficacy. It is especially important to thoroughly screen DDI in oncology clinical trial subjects to ensure trial subject safety and data accuracy. This study determined the prevalence of potential DDI involving oral anti-cancer trial agents in subjects enrolled in two SWOG clinical trials. Methods Completed SWOG clinical trials of commercially available agents with possible DDI that had complete concomitant medication information available at enrollment were included. Screening for DDI was conducted through three methods: protocol-guided screening, Lexicomp® screening, and pharmacist determination of clinical relevance. Descriptive statistics were calculated. Results SWOG trials S0711 (dasatinib, n = 83) and S0528 (everolimus/lapatinib, n = 84) were included. Subjects received an average of 6.6 medications (standard deviation = 4.9, range 0–29) at enrollment. Based on the clinical trial protocols, at enrollment 18.6% (31/167) of subjects had a DDI and 12.0% (20/167) had a DDI that violated a protocol exclusion criterion. According to Lexicomp®, 28.7% of subjects (48/167) had a DDI classified as moderate or worse, whereas pharmacist review indicated that 7.2% of subjects (12/167) had a clinically relevant interaction. The majority of clinically relevant DDI identified were due to the coadministration of acid suppression therapies with dasatinib (83.3%, 10/12). Conclusions The high DDI prevalence in subjects enrolled on SWOG clinical trials, including a high prevalence that violate trial exclusion criteria, support the need for improved processes for DDI screening to ensure trial subject safety and trial data accuracy

Relationship between African-American Race and Delirium in the Intensive Care Unit

Objective Delirium is a highly prevalent syndrome of acute brain dysfunction among critically ill patients that has been linked to multiple risk factors such as age, pre-existing cognitive impairment, and use of sedatives; but to date the relationship between race and delirium is unclear. We conducted this study to identify whether African-American race is a risk factor for developing ICU delirium. Design A prospective cohort study. Setting Medical and Surgical ICUs of a university affiliated, safety-net hospital in Indianapolis, Indiana. Patients 2087 consecutive admissions with 1008 African-Americans admitted to the ICU services from May 2009 to August 2012. Interventions None Measurements and Main Results Incident delirium defined as first positive Confusion Assessment Method for the ICU (CAM-ICU) result after an initial negative CAM-ICU; and prevalent delirium defined as positive CAM-ICU on first CAM-ICU assessment. The overall incident delirium rate in African-Americans was 8.7% compared to 10.4% in Caucasians (P: 0.26). The prevalent delirium rate was 14% in both African-Americans and Caucasians (P: 0.95). Significant age and race interactions were detected for incident delirium (P: 0.02), but not for prevalent delirium (P: 0.3). The hazard ratio for incident delirium for African-Americans in the 18–49 years age group compared to Caucasians of similar age was 0.4 (0.1– 0.9). The hazard and odds ratios for incident and prevalent delirium in other groups were not different. Conclusions African-American race does not confer any additional risk for developing incident or prevalent delirium in the ICU. Instead younger African-Americans tend to have lower rates of incident delirium compared to similar age Caucasians

Exponent Bounds for a Family of Abelian Difference Sets

Which groups G contain difference sets with the parameters (v, k, λ)= (q3 + 2q2 , q2 + q, q), where q is a power of a prime p? Constructions of K. Takeuchi, R.L. McFarland, and J.F. Dillon together yield difference sets with these parameters if G contains an elementary abelian group of order q2 in its center. A result of R.J. Turyn implies that if G is abelian and p is self-conjugate modulo the exponent of G, then a necessary condition for existence is that the exponent of the Sylow p-subgroup of G be at most 2q when p = 2 and at most q if p is an odd prime. In this paper we lower these exponent bounds when q ≠ p by showing that a difference set cannot exist for the bounding exponent values of 2q and q. Thus if there exists an abelian (96, 20, 4)-difference set, then the exponent of the Sylow 2-subgroup is at most 4. We also obtain some nonexistence results for a more general family of (v, k, λ)-parameter values