title: Identities in the Algebra of Partial Maps

authors: Jackson, Marcel

subjects: mathematics

abstract: We consider the identities of a variety of semigroup-related algebras modelling the algebra of partial maps. We show that the identities are intimately related to a weak semigroup deductive system and we show that the equational theory is decidable. We do this by giving a term rewriting system for the variety. We then show that this variety has many subvarieties whose equational theory interprets the full uniform word problem for semigroups and consequently are undecidable. As a corollary it is shown that the equational theory of Clifford semigroups whose natural order is a semilattice is undecidable.

text: Identities in the Algebra of Partial Maps We consider the identities of a variety of semigroup-related algebras modelling the algebra of partial maps. We show that the identities are intimately related to a weak semigroup deductive system and we show that the equational theory is decidable. We do this by giving a term rewriting system for the variety. We then show that this variety has many subvarieties whose equational theory interprets the full uniform word problem for semigroups and consequently are undecidable. As a corollary it is shown that the equational theory of Clifford semigroups whose natural order is a semilattice is undecidable.

year: 2006

title: The Diet and Nutritional Ecology of the Auckland Tree Wētā Hemideina thoracica

authors: Brown, Matthew

subjects: Wētā

abstract: Insects are the main consumers of primary production in many terrestrial ecosystems, they are involved in the upwards migration of energy to higher trophic levels, and are often extremely important in structuring their ecosystems. Despite the many important ways that insects influence their ecosystems, many of the most basic aspects of the functional ecology of many groups of insects have not been investigated, and a great deal remains to be learned about what roles they play in the structure and functioning of their ecosystems. This study focuses on the Auckland tree wētā Hemideina thoracica (Orthoptera: Anostostomatidae, White, 1842), the most widespread species of tree wētā in the North Island of New Zealand, and one of the least studied species in the genus Hemideina. 
Faecal fragment analysis revealed that the diet of a population of Hemideina thoracica from a mixed podocarp/broadleaf forest was composed primarily of the leaves, fruits, and seeds, of the native plants Prumnopitys taxifolia, Podocarpus totara, Dacrycarpus dacrydioides,  Kunzia ericoides,  Melicytus sp., Pennantia corymbosa, and Coprosma rotundifolia, but the consumption of other invertebrates was also common, and formed a smaller component of the overall diet. Hemideina thoracica were also shown to feed selectively while foraging. It was determined that some plants were eaten readily by the wētā when encountered, while other plants that were equally abundant were either not consumed, or were consumed far less than would be predicted by their availability. Performing a solvent extraction, using hexane, revealed that the concentration of lipids and oils in the leaves of preferred plant species was higher than in the leaves of non-preferred species, and Hemideina thoracica may preferentially consume plants that have high lipid concentrations in their leaves. It also appeared probable that they forage on the forest floor more frequently than has been previously recognised. 
	A nutritional analysis performed in captivity revealed that H. thoracica are capable of balancing their consumption of the macronutrients protein and carbohydrates to construct an optimal diet from one or more sub-optimal sources, and strongly regulate their consumption of protein. When presented with the opportunity to construct their own diet, they consumed significantly more carbohydrates than protein, and constructed a diet with a mean protein to carbohydrate ratio of 27:73. They digested carbohydrates more efficiently than protein, but converted the protein that they consumed into biomass with a very high level of conversion efficiency. These results supported the results of the fragment analysis by demonstrating that the natural, optimal diet of H. thoracica is most likely composed of carbohydrate rich foods, but they may also be naturally omnivorous, as they utilise protein very efficiently. 
	The third, and final experiment, investigated whether H. thoracica feed on fruit in a manner that may facilitate seed dispersal for native plants in the wild. This experiment involved feeding fruit from three different native plants, Coprosma repens, Cordyline australis, and Fuchsia procumbens to a group of 40 H. thoracica, and revealed that H. thoracica frequently consume the flesh of the berry from around the seed, without ingesting the seeds themselves. When the seeds were consumed, 100 % of them were destroyed by the wētās digestive process, even in the case of very small and numerous seeds, like those of F. procumbens. It is therefore highly unlikely that H. thoracica is a seed dispersing plant-mutualist, as the seeds are either left where the fruit had fallen, or are destroyed. 
	The combined results of these studies demonstrated that Hemideina thoracica is an omnivorous polyphage, and their wild diet is composed primarily of leaves, fruits, and seeds, and the concentration of lipids and oils in the leaves appears to be an important cue in determining the palatability of different species. They are also naturally omnivorous, and protein derived from eating other insects is a common component of their overall diet They have a well developed ability to balance their consumption of protein and carbohydrates, and self-select a carbohydrate rich diet in captivity. It is also extremely unlikely that that H. thoracica act as seed dispersers for native, fruit producing plants.

text: The Diet and Nutritional Ecology of the Auckland Tree Wētā Hemideina thoracica Insects are the main consumers of primary production in many terrestrial ecosystems, they are involved in the upwards migration of energy to higher trophic levels, and are often extremely important in structuring their ecosystems. Despite the many important ways that insects influence their ecosystems, many of the most basic aspects of the functional ecology of many groups of insects have not been investigated, and a great deal remains to be learned about what roles they play in the structure and functioning of their ecosystems. This study focuses on the Auckland tree wētā Hemideina thoracica (Orthoptera: Anostostomatidae, White, 1842), the most widespread species of tree wētā in the North Island of New Zealand, and one of the least studied species in the genus Hemideina. 
Faecal fragment analysis revealed that the diet of a population of Hemideina thoracica from a mixed podocarp/broadleaf forest was composed primarily of the leaves, fruits, and seeds, of the native plants Prumnopitys taxifolia, Podocarpus totara, Dacrycarpus dacrydioides,  Kunzia ericoides,  Melicytus sp., Pennantia corymbosa, and Coprosma rotundifolia, but the consumption of other invertebrates was also common, and formed a smaller component of the overall diet. Hemideina thoracica were also shown to feed selectively while foraging. It was determined that some plants were eaten readily by the wētā when encountered, while other plants that were equally abundant were either not consumed, or were consumed far less than would be predicted by their availability. Performing a solvent extraction, using hexane, revealed that the concentration of lipids and oils in the leaves of preferred plant species was higher than in the leaves of non-preferred species, and Hemideina thoracica may preferentially consume plants that have high lipid concentrations in their leaves. It also appeared probable that they forage on the forest floor more frequently than has been previously recognised. 
	A nutritional analysis performed in captivity revealed that H. thoracica are capable of balancing their consumption of the macronutrients protein and carbohydrates to construct an optimal diet from one or more sub-optimal sources, and strongly regulate their consumption of protein. When presented with the opportunity to construct their own diet, they consumed significantly more carbohydrates than protein, and constructed a diet with a mean protein to carbohydrate ratio of 27:73. They digested carbohydrates more efficiently than protein, but converted the protein that they consumed into biomass with a very high level of conversion efficiency. These results supported the results of the fragment analysis by demonstrating that the natural, optimal diet of H. thoracica is most likely composed of carbohydrate rich foods, but they may also be naturally omnivorous, as they utilise protein very efficiently. 
	The third, and final experiment, investigated whether H. thoracica feed on fruit in a manner that may facilitate seed dispersal for native plants in the wild. This experiment involved feeding fruit from three different native plants, Coprosma repens, Cordyline australis, and Fuchsia procumbens to a group of 40 H. thoracica, and revealed that H. thoracica frequently consume the flesh of the berry from around the seed, without ingesting the seeds themselves. When the seeds were consumed, 100 % of them were destroyed by the wētās digestive process, even in the case of very small and numerous seeds, like those of F. procumbens. It is therefore highly unlikely that H. thoracica is a seed dispersing plant-mutualist, as the seeds are either left where the fruit had fallen, or are destroyed. 
	The combined results of these studies demonstrated that Hemideina thoracica is an omnivorous polyphage, and their wild diet is composed primarily of leaves, fruits, and seeds, and the concentration of lipids and oils in the leaves appears to be an important cue in determining the palatability of different species. They are also naturally omnivorous, and protein derived from eating other insects is a common component of their overall diet They have a well developed ability to balance their consumption of protein and carbohydrates, and self-select a carbohydrate rich diet in captivity. It is also extremely unlikely that that H. thoracica act as seed dispersers for native, fruit producing plants.

year: 2013

title: Te karanga tūturu o maieke:  Ngāti Kuri women’s taiao geographies

authors: Ringham, Sandra Lee

subjects: Māori and Indigenous geographies

abstract: This research examines the relationships, identities and sense of belonging of Māori women of within the Ngāti Kuri iwi (tribe) and te taiao (the natural world, environment, nature, country) in Te Hiku o te Ika, Far North, Aotearoa New Zealand. It shows how Ngāti Kuri women and te taiao are embedded in - yet also resist - colonial and patriarchal discourses. 
The Kaupapa Māori and Mana Wahine theoretical framework decolonises and transforms the ways in which Māori women have been represented and marginalised. Pūrākau (storywork) as a theory and methodology ensures Ngāti Kuri women’s stories are told by them and for them. Indigenous relational geography is woven into the theoretical framework to further understand Indigenous relationships to place and diverse feelings of belonging and responsibility.
Whakawhiti kōrero (research conversations), wānanga (workshops) and tipi haere (mobile wānanga) were carried out with 19 Ngāti Kuri women. Approximately 40 people from the iwi and / or scientific communities contribute to the thesis through the initiatives of the Ngāti Kuri Relationship Working Group (NKRWG), the Auckland War Memorial Museum and other research partners and as conservationists. 
Findings are organised around three themes: identities; relationships; and a sense of belonging. The first theme introduces Ngāti Kuri women’s identities as leaders and drivers of change, disrupting and dismantling the intersection of patriarchal and colonial discourse. The pūrākau of Maieke, a founding ancestress of Ngāti Kuri, brings to light the reclamation and transformation of Māori women’s identities and geographies, as defined by participants. Pre-colonisation Ngāti Kuri women had the capacity and authority to become a governing force in the daily lives of the iwi. The second theme highlights colonial and patriarchal naming of our world. Ngāti Kuri women are reconfiguring relationships and representation through the scientific naming of taonga (culturally valuable objects and species). Values and principles of kaitiakitanga (inherited guardianship) and whakawhanaugatanga (relating well to others) guide the naming process. The third theme focuses on participants’ reflections and understandings of the ways in which they sense place and feelings of belonging. Participants’ engagement with te taiao - through singing, storying and sensing place – highlights the way te taiao re-centres and transforms Ngāti Kuri women’s relationships and experiences of belonging to iwi homelands.
Importantly, the thesis concludes with a discussion of the challenges, successes and actions of Ngāti Kuri women as they continue to strive for tino rangatiratanga (self-determination), social and environmental well-being. I conceptualise new geographies that account for, and celebrate, uniquely Ngāti Kuri understandings of identities, relationships and feelings of belonging. Finally, a short creative story ends the thesis in order to show the transformative power of Ngāti Kuri women’s te taiao experiences.

text: Te karanga tūturu o maieke:  Ngāti Kuri women’s taiao geographies This research examines the relationships, identities and sense of belonging of Māori women of within the Ngāti Kuri iwi (tribe) and te taiao (the natural world, environment, nature, country) in Te Hiku o te Ika, Far North, Aotearoa New Zealand. It shows how Ngāti Kuri women and te taiao are embedded in - yet also resist - colonial and patriarchal discourses. 
The Kaupapa Māori and Mana Wahine theoretical framework decolonises and transforms the ways in which Māori women have been represented and marginalised. Pūrākau (storywork) as a theory and methodology ensures Ngāti Kuri women’s stories are told by them and for them. Indigenous relational geography is woven into the theoretical framework to further understand Indigenous relationships to place and diverse feelings of belonging and responsibility.
Whakawhiti kōrero (research conversations), wānanga (workshops) and tipi haere (mobile wānanga) were carried out with 19 Ngāti Kuri women. Approximately 40 people from the iwi and / or scientific communities contribute to the thesis through the initiatives of the Ngāti Kuri Relationship Working Group (NKRWG), the Auckland War Memorial Museum and other research partners and as conservationists. 
Findings are organised around three themes: identities; relationships; and a sense of belonging. The first theme introduces Ngāti Kuri women’s identities as leaders and drivers of change, disrupting and dismantling the intersection of patriarchal and colonial discourse. The pūrākau of Maieke, a founding ancestress of Ngāti Kuri, brings to light the reclamation and transformation of Māori women’s identities and geographies, as defined by participants. Pre-colonisation Ngāti Kuri women had the capacity and authority to become a governing force in the daily lives of the iwi. The second theme highlights colonial and patriarchal naming of our world. Ngāti Kuri women are reconfiguring relationships and representation through the scientific naming of taonga (culturally valuable objects and species). Values and principles of kaitiakitanga (inherited guardianship) and whakawhanaugatanga (relating well to others) guide the naming process. The third theme focuses on participants’ reflections and understandings of the ways in which they sense place and feelings of belonging. Participants’ engagement with te taiao - through singing, storying and sensing place – highlights the way te taiao re-centres and transforms Ngāti Kuri women’s relationships and experiences of belonging to iwi homelands.
Importantly, the thesis concludes with a discussion of the challenges, successes and actions of Ngāti Kuri women as they continue to strive for tino rangatiratanga (self-determination), social and environmental well-being. I conceptualise new geographies that account for, and celebrate, uniquely Ngāti Kuri understandings of identities, relationships and feelings of belonging. Finally, a short creative story ends the thesis in order to show the transformative power of Ngāti Kuri women’s te taiao experiences.

year: 2022