title: Bôcher and Abstract Contractions of 2nd Order Quadratic Algebras

authors: Escobar Ruiz, Mauricio A.

subjects: Science & Technology

abstract: Quadratic algebras are generalizations of Lie algebras which include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical and quantum mechanics. Distinct superintegrable systems and their quadratic algebras can be related by geometric contractions, induced by Bôcher contractions of the conformal Lie algebra ${\mathfrak{so}}(4,\mathbb {C})$ to itself. In this paper we give a precise definition of Bôcher contractions and show how they can be classified. They subsume well known contractions of ${\mathfrak{e}}(2,\mathbb {C})$ and ${\mathfrak{so}}(3,\mathbb {C})$ and have important physical and geometric meanings, such as the derivation of the Askey scheme for obtaining all hypergeometric orthogonal polynomials as limits of Racah/Wilson polynomials. We also classify abstract nondegenerate quadratic algebras in terms of an invariant that we call a canonical form. We describe an algorithm for finding the canonical form of such algebras. We calculate explicitly all canonical forms arising from quadratic algebras of 2D nondegenerate superintegrable systems on constant curvature spaces and Darboux spaces. We further discuss contraction of quadratic algebras, focusing on those coming from superintegrable systems.

text: Bôcher and Abstract Contractions of 2nd Order Quadratic Algebras Quadratic algebras are generalizations of Lie algebras which include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical and quantum mechanics. Distinct superintegrable systems and their quadratic algebras can be related by geometric contractions, induced by Bôcher contractions of the conformal Lie algebra ${\mathfrak{so}}(4,\mathbb {C})$ to itself. In this paper we give a precise definition of Bôcher contractions and show how they can be classified. They subsume well known contractions of ${\mathfrak{e}}(2,\mathbb {C})$ and ${\mathfrak{so}}(3,\mathbb {C})$ and have important physical and geometric meanings, such as the derivation of the Askey scheme for obtaining all hypergeometric orthogonal polynomials as limits of Racah/Wilson polynomials. We also classify abstract nondegenerate quadratic algebras in terms of an invariant that we call a canonical form. We describe an algorithm for finding the canonical form of such algebras. We calculate explicitly all canonical forms arising from quadratic algebras of 2D nondegenerate superintegrable systems on constant curvature spaces and Darboux spaces. We further discuss contraction of quadratic algebras, focusing on those coming from superintegrable systems.

year: 2017

title: Workload categorization for hazardous industries: the semantic modelling of multi-modal physiological data

authors: König, Jemma Lynette

subjects: complex event processing

abstract: The forestry industry is one of the most hazardous industries in New Zealand, and the physical and cognitive fatigue of forestry workers has been shown to contribute to this. Physical and cognitive fatigue can be exacerbated by prolonged physical and cognitive workload. As such, we propose that the identification and mitigation of fatigue factors could reduce the risk of incidents and injuries in hazardous work environments. This paper introduces a semantic model for workload categorization. The model takes as input a set of multi-modal physiological measurements and uses parallel processing, complex event processing, and rule-based modeling to categorize a series of workloads (resting, cognitive workload, and physical workload). The model has undergone a set of evaluations, including categorization accuracy and performance. The model has been tested under three scenarios: when a participant is resting and refraining from any physically or mentally demanding tasks; when a participant is undertaking a cognitively intensive task; and when a participant is walking, jogging, and running. The study has been conducted with participants between the ages of 22 and 39 and has shown an average accuracy of 89% for resting workload, 76% for cognitive workload, and 97% for physical workload. Finally, in this paper, we discuss the application and extension of this model to predict fatigue in hazardous industries. The work described in this paper contributes to a larger research project centered on investigating technology uses in hazardous work environments.

text: Workload categorization for hazardous industries: the semantic modelling of multi-modal physiological data The forestry industry is one of the most hazardous industries in New Zealand, and the physical and cognitive fatigue of forestry workers has been shown to contribute to this. Physical and cognitive fatigue can be exacerbated by prolonged physical and cognitive workload. As such, we propose that the identification and mitigation of fatigue factors could reduce the risk of incidents and injuries in hazardous work environments. This paper introduces a semantic model for workload categorization. The model takes as input a set of multi-modal physiological measurements and uses parallel processing, complex event processing, and rule-based modeling to categorize a series of workloads (resting, cognitive workload, and physical workload). The model has undergone a set of evaluations, including categorization accuracy and performance. The model has been tested under three scenarios: when a participant is resting and refraining from any physically or mentally demanding tasks; when a participant is undertaking a cognitively intensive task; and when a participant is walking, jogging, and running. The study has been conducted with participants between the ages of 22 and 39 and has shown an average accuracy of 89% for resting workload, 76% for cognitive workload, and 97% for physical workload. Finally, in this paper, we discuss the application and extension of this model to predict fatigue in hazardous industries. The work described in this paper contributes to a larger research project centered on investigating technology uses in hazardous work environments.

year: 2022-04

title: Te Whiuwhiu o te Hau Maori Counselling Certificate Programme: Agency placements and supervision. Summary of and evaluation

authors: Moeke-Pickering, Taima Materangatira

subjects: counselling

abstract: Three major characteristics in determining a potentially successful practicum were identified. Firstly, the importance of determining early on whether an agency can expose the student to the necessary counselling experience that enables students to meet the requirements of the course. Secondly, the importance of exposing students to information that enable them to efficiently achieve practicum placement goals. Thirdly, the need to utilise both reflective and skills based assessment to assess the development of counselling skills, as well as the completion of tasks and duties that are required of students. Further information was gleaned about the research participants' perspectives on supervision procedures, practicum contracts, benefits of having a practicum placement and suggested training areas for the proposed TWH supervision module.

text: Te Whiuwhiu o te Hau Maori Counselling Certificate Programme: Agency placements and supervision. Summary of and evaluation Three major characteristics in determining a potentially successful practicum were identified. Firstly, the importance of determining early on whether an agency can expose the student to the necessary counselling experience that enables students to meet the requirements of the course. Secondly, the importance of exposing students to information that enable them to efficiently achieve practicum placement goals. Thirdly, the need to utilise both reflective and skills based assessment to assess the development of counselling skills, as well as the completion of tasks and duties that are required of students. Further information was gleaned about the research participants' perspectives on supervision procedures, practicum contracts, benefits of having a practicum placement and suggested training areas for the proposed TWH supervision module.

year: 1995-01-01