Spherical Functions Associated With the Three Dimensional Sphere

In this paper, we determine all irreducible spherical functions \Phi of any K -type associated to the pair (G,K)=(\SO(4),\SO(3)). This is accomplished by associating to \Phi a vector valued function H=H(u) of a real variable u, which is analytic at u=0 and whose components are solutions of two coupled systems of ordinary differential equations. By an appropriate conjugation involving Hahn polynomials we uncouple one of the systems. Then this is taken to an uncoupled system of hypergeometric equations, leading to a vector valued solution P=P(u) whose entries are Gegenbauer's polynomials. Afterward, we identify those simultaneous solutions and use the representation theory of \SO(4) to characterize all irreducible spherical functions. The functions P=P(u) corresponding to the irreducible spherical functions of a fixed K-type \pi_\ell are appropriately packaged into a sequence of matrix valued polynomials (P_w)_{w\ge0} of size (\ell+1)\times(\ell+1). Finally we proved that \widetilde P_w={P_0}^{-1}P_w is a sequence of matrix orthogonal polynomials with respect to a weight matrix W. Moreover we showed that W admits a second order symmetric hypergeometric operator \widetilde D and a first order symmetric differential operator \widetilde E.Comment: 49 pages, 2 figure

Spin Calogero Particles and Bispectral Solutions of the Matrix KP Hierarchy

Pairs of $n\times n$ matrices whose commutator differ from the identity by a matrix of rank $r$ are used to construct bispectral differential operators with $r\times r$ matrix coefficients satisfying the Lax equations of the Matrix KP hierarchy. Moreover, the bispectral involution on these operators has dynamical significance for the spin Calogero particles system whose phase space such pairs represent. In the case $r=1$, this reproduces well-known results of Wilson and others from the 1990's relating (spinless) Calogero-Moser systems to the bispectrality of (scalar) differential operators. This new class of pairs $(L, \Lambda)$ of bispectral matrix differential operators is different than those previously studied in that $L$ acts from the left, but $\Lambda$ from the right on a common $r\times r$ eigenmatrix.Comment: 16 page

Jacobi Polynomials as su(2, 2) Unitary Irreducible Representation

Ver abstrac

Matrix interpretation of multiple orthogonality

In this work we give an interpretation of a (s(d + 1) + 1)-term recurrence relation in terms of type II multiple orthogonal polynomials.We rewrite this recurrence relation in matrix form and we obtain a three-term recurrence relation for vector polynomials with matrix coefficients. We present a matrix interpretation of the type II multi-orthogonality conditions.We state a Favard type theorem and the expression for the resolvent function associated to the vector of linear functionals. Finally a reinterpretation of the type II Hermite- Padé approximation in matrix form is given

Strongly magnetized pulsars: explosive events and evolution

Well before the radio discovery of pulsars offered the first observational confirmation for their existence (Hewish et al., 1968), it had been suggested that neutron stars might be endowed with very strong magnetic fields of $10^{10}$-$10^{14}$G (Hoyle et al., 1964; Pacini, 1967). It is because of their magnetic fields that these otherwise small ed inert, cooling dead stars emit radio pulses and shine in various part of the electromagnetic spectrum. But the presence of a strong magnetic field has more subtle and sometimes dramatic consequences: In the last decades of observations indeed, evidence mounted that it is likely the magnetic field that makes of an isolated neutron star what it is among the different observational manifestations in which they come. The contribution of the magnetic field to the energy budget of the neutron star can be comparable or even exceed the available kinetic energy. The most magnetised neutron stars in particular, the magnetars, exhibit an amazing assortment of explosive events, underlining the importance of their magnetic field in their lives. In this chapter we review the recent observational and theoretical achievements, which not only confirmed the importance of the magnetic field in the evolution of neutron stars, but also provide a promising unification scheme for the different observational manifestations in which they appear. We focus on the role of their magnetic field as an energy source behind their persistent emission, but also its critical role in explosive events.Comment: Review commissioned for publication in the White Book of "NewCompStar" European COST Action MP1304, 43 pages, 8 figure

A Prescription for Improving Drug Formulary Decision Making

Gordon Schiff and colleagues present a new tool and checklist to help formularies make decisions about drug inclusion and to guide rational drug use

Frequency of sequence mutations and variants for the BRCA1 and BRCA2 genes in a sample of Colombian women with suspected hereditary breast cancer syndrome: case series

Objetivo: describir variantes de secuencia en los genes BRCA1 y BRCA2 en una muestra de pacien­tes colombianas con historia personal o familiar de cáncer de mama sugestiva de riesgo genético. Materiales y métodos: serie de casos compuesta por 67 pacientes que fueron remitidas para estu­dio genético por sospecha de síndrome de cáncer de mama y ovario hereditario (HBOC). De los 67 casos, 42 (62,7%) cumplieron con los criterios de indicación médica de la National Comprehensive Cancer Network (NCCN) del 2013, y en ellos se realizó secuenciación completa de los genes BRCA1 y BRCA2. Se determinó la frecuencia de mutación, variantes de secuencia y significancia clínica de las variantes halladas con base en Breast Cancer Informa-tion Core (BIC). Resultados: se identificaron mutaciones para el gen BRCA1 en seis pacientes (14,3%), no se docu­mentó mutación para el gen BRCA2, además se detectaron 43 variantes genéticas en 27 pacientes (64,2% de 42 casos). De estas, 21 (48,8%) fueron identificadas en el gen BRCA1 y 22 (51,2%) en el gen BRCA2.Dentro de estas variantes, se identi­ficaron 5 mutaciones patogénicas solo en el gen BRCA1, de las cuales solo una había sido reportada previamente en Colombia. Conclusiones: este estudio identifica variantes genéticas patogénicas en el gen BRCA1no descritas en estudios previos en la población colombiana y otras conocidas en diferentes poblaciones; permi­tiendo de esta forma ampliar el conocimiento sobre las variantes en población colombiana de los genes BRCA1 y BRCA2. Sin embargo, se requieren más es­tudios con suficiente poder y calidad metodológica para poder estimar la frecuencia de mutaciones y de variantes de secuencia para estos genes en mujeres colombianas con sospecha de síndrome de cáncer de mama u ovario hereditario.Objective: To describe sequence variants in the BRCA1 and BRCA2 genes in a sample of Colombian patients with a personal or family histor y of breast cancer suggestive of genetic risk. Materials and methods: Case series consisting of 67 patients referred for genetic testing because of suspected hereditar y breast and ovarian cancer syndrome (HBOC). Of the 67 cases, 42 (62.7%) met the medical indication criteria of the 2013 National Comprehensive Cancer Network (NCCN) and they were subjected to the entire sequencing of the BRCA1 and BRCA2 genes. A determination was made of the frequency of sequence mutation, variants, and of the clinical significance of the variants found based on the Breast Cancer Information Core (BIC). Results: Mutations were identified for the BRCA 1 gene in six patients (14.3%), no mutation was documented for the BRCA 2 gene, and 43 genetic variants were found in 27 patients (64.2% of 42 cases). Of these, 21 (48.8%) were identified in the BRCA1 gene and 22 (51.2%) in the BRCA 2 gene. Among these variants, 5 pathogenic mutations were found only in the BRCA1 gene and, of those, only 1 had been reported previously in Colombia.Conclusions: This study identifies pathogenic genetic variants in the BRCA1 gene not described previously in the Colombian population, as well as others known in different populations. Therefore, it helps expand knowledge regarding the variants of the BRCA1 and BRCA2 genes in the Colom­bian population. However, additional studies are required with sufficient power and methodologi­cal quality to estimate the frequency of sequence mutations and variants for the BRCA1 and BRCA2 genes in Colombian women suspected of having the hereditar y breast or ovarian cancer syndrome

A study of a culturally focused psychiatric consultation service for Asian American and Latino American primary care patients with depression

<p>Abstract</p> <p>Background</p> <p>Ethnic minorities with depression are more likely to seek mental health care through primary care providers (PCPs) than mental health specialists. However, both provider and patient-specific challenges exist. PCP-specific challenges include unfamiliarity with depressive symptom profiles in diverse patient populations, limited time to address mental health, and limited referral options for mental health care. Patient-specific challenges include stigma around mental health issues and reluctance to seek mental health treatment. To address these issues, we implemented a multi-component intervention for Asian American and Latino American primary care patients with depression at Massachusetts General Hospital (MGH).</p> <p>Methods/Design</p> <p>We propose a randomized controlled trial to evaluate a culturally appropriate intervention to improve the diagnosis and treatment of depression in our target population. Our goals are to facilitate a) primary care providers' ability to provide appropriate, culturally informed care of depression, and b) patients' knowledge of and resources for receiving treatment for depression. Our two-year long intervention targets Asian American and Latino American adult (18 years of age or older) primary care patients at MGH screening positive for symptoms of depression. All eligible patients in the intervention arm of the study who screen positive will be offered a culturally focused psychiatric (CFP) consultation. Patients will meet with a study clinician and receive toolkits that include psychoeducational booklets, worksheets and community resources. Within two weeks of the initial consultation, patients will attend a follow-up visit with the CFP clinicians. Primary outcomes will determine the feasibility and cost associated with implementation of the service, and evaluate patient and provider satisfaction with the CFP service. Exploratory aims will describe the study population at screening, recruitment, and enrollment and identify which variables influenced patient participation in the program.</p> <p>Discussion</p> <p>The study involves an innovative yet practical intervention that builds on existing resources and strives to improve quality of care for depression for minorities. Additionally, it complements the current movement in psychiatry to enhance the treatment of depression in primary care settings. If found beneficial, the intervention will serve as a model for care of Asian American and Latino American patients.</p> <p>Trial Registration</p> <p>ClinicalTrials.gov: <a href="http://www.clinicaltrials.gov/ct2/show/NCT01239407">NCT01239407</a></p

Nutrient intakes and nutritional biomarkers in pregnant adolescents: a systematic review of studies in developed countries

Background: Babies born to adolescent mothers have been shown to have poorer outcomes compared to those born to adults. Nutritional status may have an important role to play in improving the health of pregnant adolescents; however there is a lack of evidence regarding the adequacy of adolescent diets during pregnancy. This systematic review aims to examine what is known about the nutritional status of adolescent pregnant women. Methods: A systematic search of the literature identified 21 studies which met the inclusion criteria for the review. Primary research papers using any methods were included where they were published in English between January 1995 and May 2015 and included measurements of nutrient intakes or biological markers of nutritional status in pregnant women aged 11-19 years. Individual study data was first summarised narratively before study means were pooled to give an estimate of nutritional status in the population. Results: The results show that individual studies reported intakes of energy, fibre and a number of key micronutrients which were below recommended levels. Biological markers of iron and selenium status also showed cause for concern. Pooled analysis of individual means as a percentage of UK Dietary Reference Intakes showed intakes of vitamin D (34.8 % CI 0-83.1) to be significantly below recommendations (p=0.05). Serum selenium levels were also found to be low (61.8 μg/L, CI 39-84). Conclusions: This review has identified a number of areas where the nutritional status of pregnant adolescents is sub-optimal, which may have implications for the health of adolescent mothers and their babies. It was not however possible to examine the impact of supplement use or socio-demographic characteristics which limits the interpretation these results. Further work is needed to establish the characteristics of those most at risk within this population, how this differs from adult pregnant women and the role of supplementation in achieving adequate nutrition