title: Superintegrable systems in Darboux spaces

authors: Kalnins, Ernie G.

subjects: Mathematics

abstract: Almost all research on superintegrable potentials concerns spaces of constant curvature. In this paper we find by exhaustive calculation, all superintegrable potentials in the four Darboux spaces of revolution that have at least two integrals of motion quadratic in the momenta, in addition to the Hamiltonian. These are two-dimensional spaces of nonconstant curvature. It turns out that all of these potentials are equivalent to superintegrable potentials in complex Euclidean 2-space or on the complex 2-sphere, via "coupling constant metamorphosis" (or equivalently, via Stäckel multiplier transformations). We present a table of the results.

text: Superintegrable systems in Darboux spaces Almost all research on superintegrable potentials concerns spaces of constant curvature. In this paper we find by exhaustive calculation, all superintegrable potentials in the four Darboux spaces of revolution that have at least two integrals of motion quadratic in the momenta, in addition to the Hamiltonian. These are two-dimensional spaces of nonconstant curvature. It turns out that all of these potentials are equivalent to superintegrable potentials in complex Euclidean 2-space or on the complex 2-sphere, via "coupling constant metamorphosis" (or equivalently, via Stäckel multiplier transformations). We present a table of the results.

year: 2003-12

title: Boosting trees for cost-sensitive classifications

authors: Ting, Kai Ming

subjects: computer science

abstract: This paper explores two boosting techniques for cost-sensitive tree classification in the situation where misclassification costs change very often. Ideally, one would like to have only one induction, and use the induced model for different misclassification costs. Thus, it demands robustness of the induced model against cost changes. Combining multiple trees gives robust predictions against this change. We demonstrate that ordinary boosting combined with the minimum expected cost criterion to select the prediction class is a good solution under this situation. We also introduce a variant of the ordinary boosting procedure which utilizes the cost information during training. We show that the proposed technique performs better than the ordinary boosting in terms of misclassification cost. However, this technique requires to induce a set of new trees every time the cost changes. Our empirical investigation also reveals some interesting behavior of boosting decision trees for cost-sensitive classification.

text: Boosting trees for cost-sensitive classifications This paper explores two boosting techniques for cost-sensitive tree classification in the situation where misclassification costs change very often. Ideally, one would like to have only one induction, and use the induced model for different misclassification costs. Thus, it demands robustness of the induced model against cost changes. Combining multiple trees gives robust predictions against this change. We demonstrate that ordinary boosting combined with the minimum expected cost criterion to select the prediction class is a good solution under this situation. We also introduce a variant of the ordinary boosting procedure which utilizes the cost information during training. We show that the proposed technique performs better than the ordinary boosting in terms of misclassification cost. However, this technique requires to induce a set of new trees every time the cost changes. Our empirical investigation also reveals some interesting behavior of boosting decision trees for cost-sensitive classification.

year: 1998-01

title: Covering tangata whenua in Aotearoa: a big data exploration of print media and Māori

authors: Phillips, Justin B.

abstract: A large body of academic research documents harmful media coverage of indigenous populations across the globe. New Zealand is no exception. Aotearoa’s indigenous people, Māori, share similar damaging experiences, leading one major NZ media company to publish an apology for their historically poor depiction of tangata whenua. This paper adds to that wealth of evidence using the automated methods of machine learning to examine coverage of Māori in NZ print media. Across roughly 800,000 sentences–spanning over two decades of coverage–this research investigates print media discourses involving Māori at a mass scale while demonstrating the applicability of such tools for further research. The results replicate a collection of existing findings at large-N scale, further documenting problematic discussions of violence, political representation, and culture, among several other concerns. The novel approach also hints at complex, obscure relationships embedded within problematic language in Aotearoa’s print media, identifying notions of division - both implied and otherwise - along with notable instances of resistance.

text: Covering tangata whenua in Aotearoa: a big data exploration of print media and Māori A large body of academic research documents harmful media coverage of indigenous populations across the globe. New Zealand is no exception. Aotearoa’s indigenous people, Māori, share similar damaging experiences, leading one major NZ media company to publish an apology for their historically poor depiction of tangata whenua. This paper adds to that wealth of evidence using the automated methods of machine learning to examine coverage of Māori in NZ print media. Across roughly 800,000 sentences–spanning over two decades of coverage–this research investigates print media discourses involving Māori at a mass scale while demonstrating the applicability of such tools for further research. The results replicate a collection of existing findings at large-N scale, further documenting problematic discussions of violence, political representation, and culture, among several other concerns. The novel approach also hints at complex, obscure relationships embedded within problematic language in Aotearoa’s print media, identifying notions of division - both implied and otherwise - along with notable instances of resistance.

year: 2022