title: The use of negative penalty functions in linear systems of equations

authors: Askes, Harm

subjects: constraint

abstract: Contrary to what is commonly thought, it is possible to obtain convergent results with negative (rather than positive) penalty functions. This has been shown and proven on various occasions for vibration analysis, but in this contribution it will also be shown and proven for systems of linear equations subjected to one or more constraints. As a key ingredient in the developed arguments, a pseudo-force is identified as the derivative of the constrained degree of freedom with respect to the inverse of the penalty parameter. Since this pseudo-force can be proven to be constant for large absolute values of the penalty parameter, it follows that the exact solution is bounded by the results obtained with negative and positive penalty parameters. The mathematical proofs are presented and two examples are shown to illustrate the principles.

text: The use of negative penalty functions in linear systems of equations Contrary to what is commonly thought, it is possible to obtain convergent results with negative (rather than positive) penalty functions. This has been shown and proven on various occasions for vibration analysis, but in this contribution it will also be shown and proven for systems of linear equations subjected to one or more constraints. As a key ingredient in the developed arguments, a pseudo-force is identified as the derivative of the constrained degree of freedom with respect to the inverse of the penalty parameter. Since this pseudo-force can be proven to be constant for large absolute values of the penalty parameter, it follows that the exact solution is bounded by the results obtained with negative and positive penalty parameters. The mathematical proofs are presented and two examples are shown to illustrate the principles.

year: 2006

title: Colonial geographies of settlement: Vegetation, towns, disease and well-being in Aotearoa/New Zealand, 1830s-1930s

authors: Beattie, James John

subjects: environment

abstract: A Fruitful new area of environmental history research can be undertaken on the relationship between plants and health in colonial societies. By using New Zealand as a case study, I demonstrate the strength of settler beliefs in the connections between existing environments, environmental transformation, and their own health. I attempt to reconnect the historiographies of medical and environmental history by arguing that urban settlements- as much as rural areas – were important sites for debates about environmental change and human health. I adopt a broad perspective in order to sketch out the contours of a new field, demonstrating the complicated connections between health, aesthetic appreciation, medicine and garden history. Furthermore, I argue that many environmental-health ideas associated with miasmic theories became incorporated into the microbial ‘revolution’ taking place from the late nineteenth century. Finally, I note that a close study of settler environmental-health ideas reveals a far more ambiguous- a far more anxious – history of European engagement with temperate colonies than the existing historiography on the topic posits. Rather than wholly confident and arrogant agent of environmental exploitation, it reveals that great anxieties about health existed side-by-side with confidence in the environmentally transformative potential of colonisation.

text: Colonial geographies of settlement: Vegetation, towns, disease and well-being in Aotearoa/New Zealand, 1830s-1930s A Fruitful new area of environmental history research can be undertaken on the relationship between plants and health in colonial societies. By using New Zealand as a case study, I demonstrate the strength of settler beliefs in the connections between existing environments, environmental transformation, and their own health. I attempt to reconnect the historiographies of medical and environmental history by arguing that urban settlements- as much as rural areas – were important sites for debates about environmental change and human health. I adopt a broad perspective in order to sketch out the contours of a new field, demonstrating the complicated connections between health, aesthetic appreciation, medicine and garden history. Furthermore, I argue that many environmental-health ideas associated with miasmic theories became incorporated into the microbial ‘revolution’ taking place from the late nineteenth century. Finally, I note that a close study of settler environmental-health ideas reveals a far more ambiguous- a far more anxious – history of European engagement with temperate colonies than the existing historiography on the topic posits. Rather than wholly confident and arrogant agent of environmental exploitation, it reveals that great anxieties about health existed side-by-side with confidence in the environmentally transformative potential of colonisation.

year: 2008

title: He whiringa aroha: A mokopuna and a pare in the peabody essex museum

authors: Murray, Moana

abstract: Taonga, Māori ancestral treasures, embody the mana and knowledge of Māori ancestors. He Whiringa Aroha is one such treasure: a carved pare that affirms the mana of wāhine in the colonial archives, but whose whakapapa has been obscured. This thesis uses the name ‘He Whiringa Aroha’ and the te reo Māori pronoun ‘ia’ to refer to ‘E5501’, which is located in the 1806 Richardson collection in the Peabody Essex Museum. As He Whiringa Aroha travelled from Aotearoa New Zealand to Massachusetts, United States, ia became entangled in historical narratives that disembodied the taonga from hapū and iwi Māori. Taonga were not only physically removed from Aotearoa, but taonga and Māori creative practices were named, gendered, and displayed by colonisers. American sailors collected and displayed He Whiringa Aroha as an exotic ‘curiosity’ to showcase their triumph over Pacific waters. Yet, He Whiringa Aroha is a power portal—a potent braid to the past, the future, and to those Māori ways of being that defy the limiting archival language of colonialism. How do we relate to taonga Māori that have been fragmented by the colonial archive? What are alternatives to restory and reclaim taonga that remain in overseas museums? 

Using a creative methodology grounded in Mana Wahine and pūrākau, this thesis weaves a whiri (braid) of aroha (reverence) that attempts to restore he hononga mokopuna–the connection between taonga and their descendants. Through poetry, a decolonial map, interviews with ringatoi (Māori creatives), and archival research, I explore how the histories of taonga can be reclaimed in Māori worldviews. Interviews with pūkenga and tohunga toi reveal Māori understandings of taonga as expressions of toi, defying western taxonomies of ‘art’ and ‘curio’. Furthermore, archival research into the East India Marine Society and Peabody Essex Museum unmasks the American sailors and their provenance practices that
have marginalised Māori, and in particular, wāhine Māori. Finally, I use pūrākau of atua wāhine, Mana Wahine and takatāpui scholarship to restory and rename He Whiringa Aroha. This archival storytelling raises new ethical questions about ownership and kaitiakitanga (guardianship), which pose interventions for existing conversations about the place of taonga Māori in overseas museum collections. Reclaiming the histories of ancestors in museums is more than decolonizing colonial archives; on the contrary, restorying taonga is an act of Indigenous resurgence. This Masters research opens new possibilities to reclaiming takatāpui narratives and the mana of wahine in museum archives.

text: He whiringa aroha: A mokopuna and a pare in the peabody essex museum Taonga, Māori ancestral treasures, embody the mana and knowledge of Māori ancestors. He Whiringa Aroha is one such treasure: a carved pare that affirms the mana of wāhine in the colonial archives, but whose whakapapa has been obscured. This thesis uses the name ‘He Whiringa Aroha’ and the te reo Māori pronoun ‘ia’ to refer to ‘E5501’, which is located in the 1806 Richardson collection in the Peabody Essex Museum. As He Whiringa Aroha travelled from Aotearoa New Zealand to Massachusetts, United States, ia became entangled in historical narratives that disembodied the taonga from hapū and iwi Māori. Taonga were not only physically removed from Aotearoa, but taonga and Māori creative practices were named, gendered, and displayed by colonisers. American sailors collected and displayed He Whiringa Aroha as an exotic ‘curiosity’ to showcase their triumph over Pacific waters. Yet, He Whiringa Aroha is a power portal—a potent braid to the past, the future, and to those Māori ways of being that defy the limiting archival language of colonialism. How do we relate to taonga Māori that have been fragmented by the colonial archive? What are alternatives to restory and reclaim taonga that remain in overseas museums? 

Using a creative methodology grounded in Mana Wahine and pūrākau, this thesis weaves a whiri (braid) of aroha (reverence) that attempts to restore he hononga mokopuna–the connection between taonga and their descendants. Through poetry, a decolonial map, interviews with ringatoi (Māori creatives), and archival research, I explore how the histories of taonga can be reclaimed in Māori worldviews. Interviews with pūkenga and tohunga toi reveal Māori understandings of taonga as expressions of toi, defying western taxonomies of ‘art’ and ‘curio’. Furthermore, archival research into the East India Marine Society and Peabody Essex Museum unmasks the American sailors and their provenance practices that
have marginalised Māori, and in particular, wāhine Māori. Finally, I use pūrākau of atua wāhine, Mana Wahine and takatāpui scholarship to restory and rename He Whiringa Aroha. This archival storytelling raises new ethical questions about ownership and kaitiakitanga (guardianship), which pose interventions for existing conversations about the place of taonga Māori in overseas museum collections. Reclaiming the histories of ancestors in museums is more than decolonizing colonial archives; on the contrary, restorying taonga is an act of Indigenous resurgence. This Masters research opens new possibilities to reclaiming takatāpui narratives and the mana of wahine in museum archives.

year: 2024