title: Superintegrability and associated polynomial solutions: Euclidean space and the sphere in two dimensions

authors: Kalnins, Ernie G.

subjects: Mathematics

abstract: In this work we examine the basis functions for those classical and quantum mechanical systems in two dimensions which admit separation of variables in at least two coordinate systems. We do this for the corresponding systems defined in Euclidean space and on the two-dimensional sphere. We present all of these cases from a unified point of view. In particular, all of the special functions that arise via variable separation have their essential features expressed in terms of their zeros. The principal new results are the details of the polynomial bases for each of the nonsubgroup bases, not just the subgroup Cartesian and polar coordinate cases, and the details of the structure of the quadratic algebras. We also study the polynomial eigenfunctions in elliptic coordinates of the n-dimensional isotropic quantum oscillator.

text: Superintegrability and associated polynomial solutions: Euclidean space and the sphere in two dimensions In this work we examine the basis functions for those classical and quantum mechanical systems in two dimensions which admit separation of variables in at least two coordinate systems. We do this for the corresponding systems defined in Euclidean space and on the two-dimensional sphere. We present all of these cases from a unified point of view. In particular, all of the special functions that arise via variable separation have their essential features expressed in terms of their zeros. The principal new results are the details of the polynomial bases for each of the nonsubgroup bases, not just the subgroup Cartesian and polar coordinate cases, and the details of the structure of the quadratic algebras. We also study the polynomial eigenfunctions in elliptic coordinates of the n-dimensional isotropic quantum oscillator.

year: 1996-12

title: Fully supervised training of Gaussian radial basis function networks in WEKA

authors: Frank, Eibe

subjects: Machine learning

abstract: Radial basis function networks are a type of feedforward network with a long history in machine learning. In spite of this, there is relatively little literature on how to train them so that accurate predictions are obtained. A common strategy is to train the hidden layer of the network using k-means clustering and the output layer using supervised learning. However, Wettschereck and Dietterich found that supervised training of hidden layer parameters can improve predictive performance. They investigated learning center locations, local variances of the basis functions, and attribute weights, in a supervised manner.

This document discusses supervised training of Gaussian radial basis function networks in the WEKA machine learning software. More specifically, we discuss the RBFClassifier and RBFRegressor classes available as part of the RBFNetwork package for WEKA 3.7 and consider (a) learning of center locations and one global variance parameter, (b) learning of center locations and one local variance parameter per basis function, and (c) learning center locations with per-attribute local variance parameters. We also consider learning attribute weights jointly with other parameters.

text: Fully supervised training of Gaussian radial basis function networks in WEKA Radial basis function networks are a type of feedforward network with a long history in machine learning. In spite of this, there is relatively little literature on how to train them so that accurate predictions are obtained. A common strategy is to train the hidden layer of the network using k-means clustering and the output layer using supervised learning. However, Wettschereck and Dietterich found that supervised training of hidden layer parameters can improve predictive performance. They investigated learning center locations, local variances of the basis functions, and attribute weights, in a supervised manner.

This document discusses supervised training of Gaussian radial basis function networks in the WEKA machine learning software. More specifically, we discuss the RBFClassifier and RBFRegressor classes available as part of the RBFNetwork package for WEKA 3.7 and consider (a) learning of center locations and one global variance parameter, (b) learning of center locations and one local variance parameter per basis function, and (c) learning center locations with per-attribute local variance parameters. We also consider learning attribute weights jointly with other parameters.

year: 2014

title: Health equity and wellbeing among older people's caregivers in New Zealand during COVID-19: Protocol for a qualitative study.

authors: Burholt, Vanessa

subjects: Aged

abstract: BACKGROUND: Knowledge of the challenges unpaid caregivers faced providing care to older people during the COVID-19 pandemic is limited. Challenges may be especially pronounced for those experiencing inequitable access to health and social care. This participatory action research study, located in New Zealand, has four main objectives, (i) to understand the challenges and rewards associated with caregiving to older care recipients during the COVID-19 pandemic restrictions; (ii) to map and collate resources developed (or mobilised) by organisations during the pandemic; (iii) to co-produce policy recommendations, identify useful caregiver resources and practices, prioritise unmet needs (challenges); and, (iv) to use project results in knowledge translation, in order to improve caregivers access to resources, and raise the profile and recognition of caregivers contribution to society. METHODS AND ANALYSIS: Māori, Pacific and rural-dwelling caregivers to 30 older care-recipients, and 30 representatives from organisations supporting caregivers in New Zealand will be interviewed. Combining data from the interviews and caregivers letters (from an archive of older people's pandemic experiences), framework analysis will be used to examine the interrelated systems of the human ecological model and the impact on caregiving experiences during the pandemic. Resources that service providers had created or used for caregivers and older people will be collated and categorised. Through co-production with caregivers and community partners we will produce three short films describing caregivers' pandemic experiences; identify a suite of resources for caregivers to use in future events requiring self-isolation, and in everyday life; and generate ideas to address unresolved issues.

text: Health equity and wellbeing among older people's caregivers in New Zealand during COVID-19: Protocol for a qualitative study. BACKGROUND: Knowledge of the challenges unpaid caregivers faced providing care to older people during the COVID-19 pandemic is limited. Challenges may be especially pronounced for those experiencing inequitable access to health and social care. This participatory action research study, located in New Zealand, has four main objectives, (i) to understand the challenges and rewards associated with caregiving to older care recipients during the COVID-19 pandemic restrictions; (ii) to map and collate resources developed (or mobilised) by organisations during the pandemic; (iii) to co-produce policy recommendations, identify useful caregiver resources and practices, prioritise unmet needs (challenges); and, (iv) to use project results in knowledge translation, in order to improve caregivers access to resources, and raise the profile and recognition of caregivers contribution to society. METHODS AND ANALYSIS: Māori, Pacific and rural-dwelling caregivers to 30 older care-recipients, and 30 representatives from organisations supporting caregivers in New Zealand will be interviewed. Combining data from the interviews and caregivers letters (from an archive of older people's pandemic experiences), framework analysis will be used to examine the interrelated systems of the human ecological model and the impact on caregiving experiences during the pandemic. Resources that service providers had created or used for caregivers and older people will be collated and categorised. Through co-production with caregivers and community partners we will produce three short films describing caregivers' pandemic experiences; identify a suite of resources for caregivers to use in future events requiring self-isolation, and in everyday life; and generate ideas to address unresolved issues.

year: 2022