Jack superpolynomials with negative fractional parameter: clustering properties and super-Virasoro ideals

The Jack polynomials P_\lambda^{(\alpha)} at \alpha=-(k+1)/(r-1) indexed by certain (k,r,N)-admissible partitions are known to span an ideal I^{(k,r)}_N of the space of symmetric functions in N variables. The ideal I^{(k,r)}_N is invariant under the action of certain differential operators which include half the Virasoro algebra. Moreover, the Jack polynomials in I^{(k,r)}_N admit clusters of size at most k: they vanish when k+1 of their variables are identified, and they do not vanish when only k of them are identified. We generalize most of these properties to superspace using orthogonal eigenfunctions of the supersymmetric extension of the trigonometric Calogero-Moser-Sutherland model known as Jack superpolynomials. In particular, we show that the Jack superpolynomials P_{\Lambda}^{(\alpha)} at \alpha=-(k+1)/(r-1) indexed by certain (k,r,N)-admissible superpartitions span an ideal {\mathcal I}^{(k,r)}_N of the space of symmetric polynomials in N commuting variables and N anticommuting variables. We prove that the ideal {\mathcal I}^{(k,r)}_N is stable with respect to the action of the negative-half of the super-Virasoro algebra. In addition, we show that the Jack superpolynomials in {\mathcal I}^{(k,r)}_N vanish when k+1 of their commuting variables are equal, and conjecture that they do not vanish when only k of them are identified. This allows us to conclude that the standard Jack polynomials with prescribed symmetry should satisfy similar clustering properties. Finally, we conjecture that the elements of {\mathcal I}^{(k,2)}_N provide a basis for the subspace of symmetric superpolynomials in N variables that vanish when k+1 commuting variables are set equal to each other.Comment: 36 pages; the main changes in v2 are : 1) in the introduction, we present exceptions to an often made statement concerning the clustering property of the ordinary Jack polynomials for (k,r,N)-admissible partitions (see Footnote 2); 2) Conjecture 14 is substantiated with the extensive computational evidence presented in the new appendix C; 3) the various tests supporting Conjecture 16 are reporte

Supersymmetric Many-particle Quantum Systems with Inverse-square Interactions

The development in the study of supersymmetric many-particle quantum systems with inverse-square interactions is reviewed. The main emphasis is on quantum systems with dynamical OSp(2|2) supersymmetry. Several results related to exactly solved supersymmetric rational Calogero model, including shape invariance, equivalence to a system of free superoscillators and non-uniqueness in the construction of the Hamiltonian, are presented in some detail. This review also includes a formulation of pseudo-hermitian supersymmetric quantum systems with a special emphasis on rational Calogero model. There are quite a few number of many-particle quantum systems with inverse-square interactions which are not exactly solved for a complete set of states in spite of the construction of infinitely many exact eigen functions and eigenvalues. The Calogero-Marchioro model with dynamical SU(1,1|2) supersymmetry and a quantum system related to short-range Dyson model belong to this class and certain aspects of these models are reviewed. Several other related and important developments are briefly summarized.Comment: LateX, 65 pages, Added Acknowledgment, Discussions and References, Version to appear in Jouranl of Physics A: Mathematical and Theoretical (Commissioned Topical Review Article

Response to Harcombe

The crux of Dr. Harcombe’s critique is her assertion that our study design was inappropriate for our research objective, which was to investigate whether maternal carbohydrate restriction before conception was associated with neural tube defects (NTDs) in the National Birth Defects Prevention Study (NBDPS), a population-based case-control study of birth defects (Desrosiers, Siega-Riz, Mosley, Meyer, & The National Birth Defects Prevention Study, 2018). In her Letter, Dr. Harcombe claims that our study is fundamentally flawed because “cases should have been women who restrict carbohydrates and the controls should have been women who don’t and the outcome measure should have been NTD-affected pregnancies.” Despite her confusing (mis)use of the terms case and control, what Dr. Harcombe appears to be describing is a cohort study

Biomass thermal conversion research at SERI

SERI's involvement in the thermochemical conversion of biomass to fuels and chemicals is reviewed. The scope and activities of the Biomass Thermal Conversion and Exploratory Branch are reviewed. The current status and future plans for three tasks are presented: (1) Pyrolysis Mechanisms; (2) High Pressure O/sub 2/ Gasifier; and (3) Gasification Test Facility

Quadrimodal Distribution of Death after Trauma: Predictors of Death in the Fourth Peak

Introduction: Patterns of death after trauma are changing due to diagnostic and treatment advances. We examined mortality in critically injured patients at risk of death after discharge. Methods: We reviewed all critically injured (Injury Severity Score≥25 AND death in Emergency Room , death within 24hrs, OR ICU admission\u3e24hrs) adults (age≥18) admitted to a Level 1 trauma center (01/01/2000-12/31/2010) and determined death post-discharge (Social Security Death Index) of patients discharged alive. We compared demographics, injury data, and critical care resource utilization between those who died during follow-up and survivors using univariate tests and Cox proportional hazards models. Results: Of 1,695 critically injured patients, 1135 (67%) were discharged alive. As of 05/1/2012, 977 (58%) index survivors were alive (median follow-up 62mos (IQR35,96)). Of 158 deaths post-discharge, 75 (47%) occurred within the first year. Patients who died post-discharge had longer hospital (24dys (IQR13,38) vs. 17dys (IQR10,27)) and ICU LOS (17dys (IQR6,29) vs. 8dys (IQR4,19)) and were more likely to undergo tracheostomies (36.1% vs. 15.6%, p16dys increased risk of death at one year (HR1.94 (1.22,3.06)) and by the end of follow-up (HR2.19 (1.58,3.04)) compared to shorter ICU stays. Conclusion: We propose the first year after discharge as the fourth peak of trauma related mortality. Duration of ICU LOS during index hospitalization is associated with post-discharge mortality

Response to Camacho

We appreciate Dr. Camacho’s interest in our article (Desrosiers, Siega-Riz, Mosley, Meyer, & National Birth Defects Prevention Study, 2018), and welcome the opportunity to respond. As Dr. Camacho emphasizes, the association between folic acid and neural tube defects (NTDs) is well established (Viswanathan et al., 2017). What is less certain are factors potentially related to folate insufficiency among women of reproductive age, and even more so, among women who meet the U.S. Preventative Health Task Force’s recommendation of 0.4–0.8 mg/day of supplemental folic acid (Tinker, Hamner, Qi, & Crider, 2015; US Preventive Services Task Force, 2017). Understanding the reasons for folate insufficiency could help prevent some cases of birth defects in the future and is thus a worthy research pursuit. One theory expressed in the literature is whether avoidance of carbohydrate-rich foods such as enriched grains (fortified with folic acid) and beans (high in natural folate) could lead to meaningful reductions in folate status, which could in turn lead to an increased risk for some women of having an NTD-affected pregnancy (Mills, 2017; Quinlivan & Gregory, 2007)

Microvascular response to transfusion in elective spine surgery

AIM: To investigate the microvascular (skeletal muscle tissue oxygenation; SmO2) response to transfusion in patients undergoing elective complex spine surgery. METHODS: After IRB approval and written informed consent, 20 patients aged 18 to 85 years of age undergoing \u3e 3 level anterior and posterior spine fusion surgery were enrolled in the study. Patients were followed throughout the operative procedure, and for 12 h postoperatively. In addition to standard American Society of Anesthesiologists monitors, invasive measurements including central venous pressure, continual analysis of stroke volume (SV), cardiac output (CO), cardiac index (CI), and stroke volume variability (SVV) was performed. To measure skeletal muscle oxygen saturation (SmO2) during the study period, a non-invasive adhesive skin sensor based on Near Infrared Spectroscopy was placed over the deltoid muscle for continuous recording of optical spectra. All administration of fluids and blood products followed standard procedures at the Hospital for Special Surgery, without deviation from usual standards of care at the discretion of the Attending Anesthesiologist based on individual patient comorbidities, hemodynamic status, and laboratory data. Time stamps were collected for administration of colloids and blood products, to allow for analysis of SmO2 immediately before, during, and after administration of these fluids, and to allow for analysis of hemodynamic data around the same time points. Hemodynamic and oxygenation variables were collected continuously throughout the surgery, including heart rate, blood pressure, mean arterial pressure, SV, CO, CI, SVV, and SmO2. Bivariate analyses were conducted to examine the potential associations between the outcome of interest, SmO2, and each hemodynamic parameter measured using Pearson\u27s correlation coefficient, both for the overall cohort and within-patients individually. The association between receipt of packed red blood cells and SmO2 was performed by running an interrupted time series model, with SmO2 as our outcome, controlling for the amount of time spent in surgery before and after receipt of PRBC and for the inherent correlation between observations. Our model was fit using PROC AUTOREG in SAS version 9.2. All other analyses were also conducted in SAS version 9.2 (SAS Institute Inc., Cary, NC, United States). RESULTS: Pearson correlation coefficients varied widely between SmO2 and each hemodynamic parameter examined. The strongest positive correlations existed between ScvO2 (P = 0.41) and SV (P = 0.31) and SmO2; the strongest negative correlations were seen between albumin (P = -0.43) and cell saver (P = -0.37) and SmO2. Correlations for other laboratory parameters studied were weak and only based on a few observations. In the final model we found a small, but significant increase in SmO2 at the time of PRBC administration by 1.29 units (P = 0.0002). SmO2 values did not change over time prior to PRBC administration (P = 0.6658) but following PRBC administration, SmO2 values declined significantly by 0.015 units (P \u3c 0.0001). CONCLUSION: Intra-operative measurement of SmO2 during large volume, yet controlled hemorrhage, does not show a statistically significant correlation with either invasive hemodynamic, or laboratory parameters in patients undergoing elective complex spine surgery

Nitrides as ammonia synthesis catalysts and as potential nitrogen transfer reagents

In this article, an overview of the application of selected metal nitrides as ammonia synthesis catalysts is presented. The potential development of some systems into nitrogen transfer reagents is also described