Soft matrix models and Chern-Simons partition functions

We study the properties of matrix models with soft confining potentials. Their precise mathematical characterization is that their weight function is not determined by its moments. We mainly rely on simple considerations based on orthogonal polynomials and the moment problem. In addition, some of these models are equivalent, by a simple mapping, to matrix models that appear in Chern-Simons theory. The models can be solved with q deformed orthogonal polynomials (Stieltjes-Wigert polynomials), and the deformation parameter turns out to be the usual $q$ parameter in Chern-Simons theory. In this way, we give a matrix model computation of the Chern-Simons partition function on $S^{3}$ and show that there are infinitely many matrix models with this partition function.Comment: 13 pages, 3 figure

The q-harmonic oscillator and an analog of the Charlier polynomials

A model of a q-harmonic oscillator based on q-Charlier polynomials of Al-Salam and Carlitz is discussed. Simple explicit realization of q-creation and q-annihilation operators, q-coherent states and an analog of the Fourier transformation are found. A connection of the kernel of this transform with biorthogonal rational functions is observed

The smallest eigenvalue of Hankel matrices

Let H_N=(s_{n+m}),n,m\le N denote the Hankel matrix of moments of a positive measure with moments of any order. We study the large N behaviour of the smallest eigenvalue lambda_N of H_N. It is proved that lambda_N has exponential decay to zero for any measure with compact support. For general determinate moment problems the decay to 0 of lambda_N can be arbitrarily slow or arbitrarily fast. In the indeterminate case, where lambda_N is known to be bounded below by a positive constant, we prove that the limit of the n'th smallest eigenvalue of H_N for N tending to infinity tends rapidly to infinity with n. The special case of the Stieltjes-Wigert polynomials is discussed

Parents' views on care of their very premature babies in neonatal intensive care units: a qualitative study

Background The admission of a very premature infant to the neonatal intensive care unit (NICU) is often a difficult time for parents. This paper explores parents’ views and experiences of the care for their very premature baby on NICU. Methods Parents were eligible if they had a baby born before 32 weeks gestation and cared for in a NICU, and spoke English well. 32 mothers and 7 fathers were interviewed to explore their experiences of preterm birth. Although parents’ evaluation of care in the NICU was not the aim of these interviews, all parents spoke spontaneously and at length on this topic. Results were analysed using thematic analysis. Results Overall, parents were satisfied with the care on the neonatal unit. Three major themes determining satisfaction with neonatal care emerged: 1) parents’ involvement; including looking after their own baby, the challenges of expressing breast milk, and easy access to their baby; 2) staff competence and efficiency; including communication, experience and confidence, information and explanation; and 3) interpersonal relationships with staff; including sensitive and emotional support, reassurance and encouragement, feeling like an individual. Conclusions Determinants of positive experiences of care were generally consistent with previous research. Specifically, provision of information, support for parents and increasing their involvement in the care of their baby were highlighted by parents as important in their experience of care

Recommendations for Enhancing Psychosocial Support of NICU Parents through Staff Education and Support

Providing psychosocial support to parents whose infants are hospitalized in the neonatal intensive care unit (NICU) can improve parents’ functioning as well as their relationships with their babies. Yet, few NICUs offer staff education that teaches optimal methods of communication with parents in distress. Limited staff education in how to best provide psychosocial support to families is one factor that may render those who work in the NICU at risk for burnout, compassion fatigue and secondary traumatic stress syndrome. Staff who develop burnout may have further reduced ability to provide effective support to parents and babies. Recommendations for providing NICU staff with education and support are discussed. The goal is to deliver care that exemplifies the belief that providing psychosocial care and support to the family is equal in importance to providing medical care and developmental support to the baby

Using focused ethnography in paediatric settings to explore professionals' and parents' attitudes towards expertise in managing chronic kidney disease stage 3-5

© 2014 Nightingale et al.; licensee BioMed Central Ltd. Background: Interactions between parents and healthcare professionals are essential when parents of children with chronic conditions are learning to share expertise about clinical care, but limited evidence exists on how they actually interact. This paper discusses the use of focused ethnography in paediatric settings as an effective means of exploring attitudes towards expertise. Methods: The paper draws on repeated observations, interviews and field-notes involving the parents of six children with chronic kidney disease, and 28 healthcare professionals at two, tertiary, children's hospital-based units. Data were analysed using the Framework approach and the concepts of expertise and self-management. Results: Our study highlighted rewards and challenges associated with focused ethnography in this context. Rewards included the ability to gain a richer understanding of the complex phenomena of mutual acknowledgement of expertise that occurs during parent/ healthcare professional interactions. Challenges related to gaining informed consent and ensuring potential participants had an adequate understanding of the purpose of the study. Two dimensions of parental expertise around their child (personal and clinical) were evident in our data. Parents' and professionals' expertise about the child and their condition was acknowledged and exchanged as parents learnt to share clinical-care with the multi-disciplinary team. Healthcare professionals acknowledged parents' need to understand aspects of each of the eight disciplinary knowledge bases relating to their child' s management and recognised parents' expert knowledge of their child, found ways to mobilise this knowledge, and wove parents' expertise into the management plan. Parents spoke of the degree to which their own expert knowledge of their child complemented healthcare professionals' clinical knowledge. However, ambivalence around expertise was evident as both parents and healthcare professionals questioned what the expertise was, and who the expert was. Our discussion focuses on the ways healthcare professionals and parents share expertise around the child's condition as parents take on responsibility for home-based clinical care. Conclusions: Our findings point to focused ethnography being an effective way of capturing new insights into parent and professional interactions in a paediatric setting and mutual acknowledgement of expertise; these insights may help redress the reported limitations of previous, retrospective studies