Vector coherent state theory of the generic representations of so(5) in an so(3) basis

For applications of group theory in quantum mechanics, one generally needs explicit matrix representations of the spectrum generating algebras that arise in bases that reduce the symmetry group of some Hamiltonian of interest. Here we use vector coherent state techniques to develop an algorithm for constructing the matrices for arbitrary finite-dimensional irreps of the SO(5) Lie algebra in an SO(3) basis. The SO(3) subgroup of SO(5) is defined by regarding SO(5) as linear transformations of the five-dimensional space of an SO(3) irrep of angular momentum two. A need for such irreps arises in the nuclear collective model of quadrupole vibrations and rotations. The algorithm has been implemented in MAPLE, and some tables of results are presented.Comment: 20 pages, uses multirow.sty, submitted to J. Math. Phy

Coherent state triplets and their inner products

It is shown that if H is a Hilbert space for a representation of a group G, then there are triplets of spaces F_H, H, F^H, in which F^H is a space of coherent state or vector coherent state wave functions and F_H is its dual relative to a conveniently defined measure. It is shown also that there is a sequence of maps F_H -> H -> F^H which facilitates the construction of the corresponding inner products. After completion if necessary, the F_H, H, and F^H, become isomorphic Hilbert spaces. It is shown that the inner product for H is often easier to evaluate in F_H than F^H. Thus, we obtain integral expressions for the inner products of coherent state and vector coherent state representations. These expressions are equivalent to the algebraic expressions of K-matrix theory, but they are frequently more efficient to apply. The construction is illustrated by many examples.Comment: 33 pages, RevTex (Latex2.09) This paper is withdrawn because it contained errors that are being correcte

Testing the Master Constraint Programme for Loop Quantum Gravity III. SL(2,R) Models

This is the third paper in our series of five in which we test the Master Constraint Programme for solving the Hamiltonian constraint in Loop Quantum Gravity. In this work we analyze models which, despite the fact that the phase space is finite dimensional, are much more complicated than in the second paper: These are systems with an SL(2,\Rl) gauge symmetry and the complications arise because non -- compact semisimple Lie groups are not amenable (have no finite translation invariant measure). This leads to severe obstacles in the refined algebraic quantization programme (group averaging) and we see a trace of that in the fact that the spectrum of the Master Constraint does not contain the point zero. However, the minimum of the spectrum is of order $\hbar^2$ which can be interpreted as a normal ordering constant arising from first class constraints (while second class systems lead to $\hbar$ normal ordering constants). The physical Hilbert space can then be be obtained after subtracting this normal ordering correction.Comment: 33 pages, no figure

A novel transflectance near infrared spectroscopy technique for monitoring hot melt extrusion

yesA transflectance near infra red (NIR) spectroscopy approach has been used to simultaneously measure drug and plasticiser content of polymer melts with varying opacity during hot melt extrusion. A high temperature reflectance NIR probe was mounted in the extruder die directly opposed to a highly reflective surface. Carbamazepine (CBZ) was used as a model drug, with polyvinyl pyrollidone-vinyl acetate co-polymer (PVP-VA) as a matrix and polyethylene glycol (PEG) as a plasticiser. The opacity of the molten extrudate varied from transparent at low CBZ loading to opaque at high CBZ loading. Particulate amorphous API and voids formed around these particles were found to cause the opacity. The extrusion process was monitored in real time using transflectance NIR; calibration and validation runs were performed using a wide range of drug and plasticiser loadings. Once calibrated, the technique was used to simultaneously track drug and plasticiser content during applied step changes in feedstock material. Rheological and thermal characterisations were used to help understand the morphology of extruded material. The study has shown that it is possible to use a single NIR spectroscopy technique to monitor opaque and transparent melts during HME, and to simultaneously monitor two distinct components within a formulation

IMI-Management and Investigation of High Myopia in Infants and Young Children

The purpose of this study was to evaluate the epidemiology, etiology, clinical assessment, investigation, management, and visual consequences of high myopia (≤−6 diopters [D]) in infants and young children

Long-term outcomes of stereotactic body radiation therapy (SBRT) with fiducial tracking for inoperable stage I non-small cell lung cancer (NSCLC)

BACKGROUND: Stereotactic body radiation therapy (SBRT) for stage I non-small cell lung cancer (NSCLC) is considered standard of care in the medically inoperable patient population. Multiple methods of SBRT delivery exist including fiducial-based tumor tracking, which allows for smaller treatment margins and avoidance of patient immobilization devices. We explore the long-term clinical outcomes of this novel fiducial-based SBRT method. METHODS: In this single institutional retrospective review, we detail the outcomes of medically inoperable pathologically confirmed stage I NSCLC. Patients were treated with the Cyberknife SBRT system using a planning target volume (PTV) defined as a 5-mm expansion from gross tumor volume (GTV) without creation of an internal target volume (ITV). Dose was delivered in three or five equal fractions of 10 to 20 Gy. Pretreatment and posttreatment pulmonary function test (PFT) changes and evidence of late radiological rib fractures were analyzed for the majority of patients. Actuarial local control, locoregional control, distant control, and overall survival were calculated using the Kaplan-Meier method. RESULTS: Sixty-one patients with a median age of 75 years were available for analysis. The majority (80 %) of patients were deemed to be medically inoperable due to underlying pulmonary dysfunction. Eleven patients (18 %) developed symptomatic pneumothoraces secondary to fiducial placement under CT guidance, which precipitously dropped to 0 % following transition to bronchoscopic fiducial placement. The 2-year rib fracture risk was 21.4 % with a median time to rib fracture of 2.9 years. PFTs averaged over all patients and parameters demonstrated small absolute declines, 5.7 % averaged PFT decline, at approximately 1 year of follow-up, but only the diffusing capacity of lung for carbon monoxide (DL(CO)) demonstrated a statistically significant decline (10.29 vs. 9.01 mL/min/mmHg, p = 0.01). Five-year local control, locoregional control, and overall survival were 87.6, 71.8, and 39.3 %, respectively. CONCLUSIONS: Despite reduced treatment margins and lack of patient immobilization, SBRT with fiducial-based tumor tracking achieves clinically comparable long-term outcomes to other linac-based SBRT approaches

Multiplicity-free theorems of the restrictions of unitary highest weight modules with respect to reductive symmetric pairs

The complex analytic methods have found a wide range of applications in the study of multiplicity-free representations. This article discusses, in particular, its applications to the question of restricting highest weight modules with respect to reductive symmetric pairs. We present a number of multiplicity-free branching theorems that include the multiplicity-free property of some of known results such as the Clebsh--Gordan--Pieri formula for tensor products, the Plancherel theorem for Hermitian symmetric spaces (also for line bundle cases), the Hua--Kostant--Schmid $K$-type formula, and the canonical representations in the sense of Vershik--Gelfand--Graev. Our method works in a uniform manner for both finite and infinite dimensional cases, for both discrete and continuous spectra, and for both classical and exceptional cases

Secondary 12-Month Ocular Outcomes of a Phase 1 Dosing Study of Bevacizumab for Retinopathy of Prematurity

Importance Lower bevacizumab dosages are being used for type 1 retinopathy of prematurity, but there are limited data on long-term ocular outcomes with lower doses. Objective To evaluate ocular outcomes at 12 months’ corrected age for eyes that received a dose of 0.625 mg, 0.25 mg, 0.125 mg, 0.063 mg, or 0.031 mg of bevacizumab for type 1 retinopathy of prematurity. Design, Setting, and Participants This prospective cohort study used a masked, multicenter, phase 1 dose de-escalation study design and was conducted from April 2016 to October 2017. Study eyes were treated with a dose of 0.25, 0.125, 0.063, or 0.031 mg of bevacizumab; fellow eyes were treated with a dosage 1 level higher than the study eye. Additional treatment after 4 weeks was at investigator discretion. Data analysis occurred from November 2018 to March 2019. Interventions Intravitreous bevacizumab injections of 0.625 mg to 0.031 mg. Main Outcomes and Measures Visual fixation, amblyopia, alignment, nystagmus, cycloplegic refraction, and ocular examinations were assessed at 12 months’ corrected age as preplanned secondary outcomes. The primary outcome 4 weeks after treatment and secondary outcomes after 6 months’ corrected age have been previously reported. Results Forty-six of 61 infants (75%) had a 12-month follow-up examination (46 study eyes and 43 fellow eyes; median [interquartile range] birth weight, 650 [590-760] g). Of 87 eyes with a cycloplegic refraction, 12 (14% [95% CI, 7%-27%]) had myopia of more than −5.00 D spherical equivalent; 2 (2%; [95% CI, 0%-8%]) had hyperopia greater than 5.00 D spherical equivalent; and 5 infants (11% [95% CI, 4%-24%]) had anisometropia greater than 1.50 D spherical equivalent. Abnormalities of the cornea, lens, or anterior segment were reported in 1 eye (1% [95% CI, 0%-6%]), 3 eyes (3% [95% CI, 1%-10%]), and 3 eyes (3% [95% CI, 1%-10%]), respectively. Optic nerve atrophy was identified in 11 eyes (13% [95% CI, 6%-26%]), and 1 eye (1% [95% CI, 0%-6%]) had total retinal detachment. Strabismus was reported in 13 infants (30% [95% CI, 17%-45%]), manifest nystagmus in 7 infants (15% [95% CI, 6%-29%]), and amblyopia in 3 infants (7% [95% CI, 1%-18%]). Overall, 98% of infants had central fixation in each eye (44 of 45 eyes). Conclusions and Relevance In this study of low-dose bevacizumab, the secondary outcomes of high myopia, strabismus, retinal detachment, nystagmus, and other ocular abnormalities at 1 year were consistent with rates reported in other studies with higher dosages

Pathophysiological classification of chronic rhinosinusitis

BACKGROUND: Recent consensus statements demonstrate the breadth of the chronic rhinosinusitis (CRS) differential diagnosis. However, the classification and mechanisms of different CRS phenotypes remains problematic. METHOD: Statistical patterns of subjective and objective findings were assessed by retrospective chart review. RESULTS: CRS patients were readily divided into those with (50/99) and without (49/99) polyposis. Aspirin sensitivity was limited to 17/50 polyp subjects. They had peripheral blood eosinophilia and small airways obstruction. Allergy skin tests were positive in 71% of the remaining polyp subjects. IgE was<10 IU/ml in 8/38 polyp and 20/45 nonpolyp subjects (p = 0.015, Fisher's Exact test). CT scans of the CRS without polyp group showed sinus mucosal thickening (probable glandular hypertrophy) in 28/49, and nasal osteomeatal disease in 21/49. Immunoglobulin isotype deficiencies were more prevalent in nonpolyp than polyp subjects (p < 0.05). CONCLUSION: CRS subjects were retrospectively classified in to 4 categories using the algorithm of (1) polyp vs. nonpolyp disease, (2) aspirin sensitivity in polyposis, and (3) sinus mucosal thickening vs. nasal osteomeatal disease (CT scan extent of disease) for nonpolypoid subjects. We propose that the pathogenic mechanisms responsible for polyposis, aspirin sensitivity, humoral immunodeficiency, glandular hypertrophy, eosinophilia and atopy are primary mechanisms underlying these CRS phenotypes. The influence of microbial disease and other factors remain to be examined in this framework. We predict that future clinical studies and treatment decisions will be more logical when these interactive disease mechanisms are used to stratify CRS patients