title: Contractions of 2D 2nd order quantum superintegrable systems and the Askey scheme for hypergeometric orthogonal polynomials

authors: Kalnins, Ernie G.

subjects: Askey scheme

abstract: We show explicitly that all 2nd order superintegrable systems in 2 dimensions are limiting cases of a single system: the generic 3-parameter potential on the 2-sphere, S9 in our listing. We extend the Wigner-Inönü method of Lie algebra contractions to contractions of quadratic algebras and show that all of the quadratic symmetry algebras of these systems are contractions of that of S9. Amazingly, all of the relevant contractions of these superintegrable systems on flat space and the sphere are uniquely induced by the well known Lie algebra contractions of e(2) and so(3). By contracting function space realizations of irreducible representations of the S9 algebra (which give the structure equations for Racah/Wilson polynomials) to the other superintegrable systems, and using Wigner's idea of ''saving'' a representation, we obtain the full Askey scheme of hypergeometric orthogonal polynomials. This relationship directly ties the polynomials and their structure equations to physical phenomena. It is more general because it applies to all special functions that arise from these systems via separation of variables, not just those of hypergeometric type, and it extends to higher dimensions.

text: Contractions of 2D 2nd order quantum superintegrable systems and the Askey scheme for hypergeometric orthogonal polynomials We show explicitly that all 2nd order superintegrable systems in 2 dimensions are limiting cases of a single system: the generic 3-parameter potential on the 2-sphere, S9 in our listing. We extend the Wigner-Inönü method of Lie algebra contractions to contractions of quadratic algebras and show that all of the quadratic symmetry algebras of these systems are contractions of that of S9. Amazingly, all of the relevant contractions of these superintegrable systems on flat space and the sphere are uniquely induced by the well known Lie algebra contractions of e(2) and so(3). By contracting function space realizations of irreducible representations of the S9 algebra (which give the structure equations for Racah/Wilson polynomials) to the other superintegrable systems, and using Wigner's idea of ''saving'' a representation, we obtain the full Askey scheme of hypergeometric orthogonal polynomials. This relationship directly ties the polynomials and their structure equations to physical phenomena. It is more general because it applies to all special functions that arise from these systems via separation of variables, not just those of hypergeometric type, and it extends to higher dimensions.

year: 2013

title: Detection of Toxoplasma Gondii in Fresh New Zealand Farmed Meat by the Polymerase Chain Reaction

authors: Anderson, Michael Andrew

subjects: Toxoplasma

abstract: Toxoplasma gondii is an obligate intracellular parasite that is estimated to infect one third of the world’s human population. Upon infection this parasite causes the disease toxoplasmosis which in most healthy humans is chronic and often asymptomatic. If infection occurs in a human host without a competent immune system such as an unborn baby or infant or someone suffering from AIDS, toxoplasmosis can lead to permanent disability or death. A growing amount of evidence indicates a statistical relationship between chronic infection in healthy adults and neurological disorders leading to behavioural and psychological problems.
   Toxoplasma gondii can be spread through contact with cat faeces. This was thought to be the main mode of human infection. Subsequent testing with murine and Felidae models has shown that the bradyzoite of Toxoplasma gondii within intracellular cysts in muscle and neural tissue are far more infectious than the oocyst morphology shed in cat faeces. This indicates that consumption of infected meat products may also play a major contributing role in the world’s high rate of toxoplasmosis infection.
   The chief aim of this study was to develop a sensitive PCR assay to detect the presence of Toxoplasma gondii in fresh raw meat products. Beef, chicken, lamb and pork mince were chosen as convenient forms of fresh raw meat as each pack available for purchase contains the meat from several animal’s tissues (increasing the likelihood of contamination) and it has been partially homogenised allowing for easier sampling and DNA extraction.
   Secondary aims of this study were to evaluate PCR primer sets targeting polymorphic regions to gain some understanding of what strains of Toxoplasma gondii are present in our meat and the prevalence in the local cat populations.
   To accomplish these aims positive and negative PCR controls were also developed using a live toxoplasmosis vaccine and DNA extracted from Zebrafish. DNA extraction techniques were developed to purify DNA from both muscle tissue and feline faecal samples and primer sets were selected from published literature as well as designed using NCBI primer BLAST.   
   Toxoplasma gondii specific DNA was detected in only one of the 25 meat samples purchased. This was achieved using a primer set targeting the P30 region of the SAG1 gene and confirmed by DNA sequencing.
   Using primer sets targeting polymorphic sites within the Toxoplasma gondii genome, sequencing and restriction enzyme digests it was shown that Toxoplasma gondii present in the feral Felis catus population in the raglan area is type II at the GRA6 and SAG3 loci. Amplification of polymorphic PCR targets from DNA extracted from meat samples could not be achieved.
   Non-specific amplification occurred with a majority of primer sets trialed with meat DNA extracts indicating improvements are needed in primer design for the purpose of PCR detection of Toxoplasma gondii in meat. Nested PCR increased specificity however resulted in contamination in several instances.

text: Detection of Toxoplasma Gondii in Fresh New Zealand Farmed Meat by the Polymerase Chain Reaction Toxoplasma gondii is an obligate intracellular parasite that is estimated to infect one third of the world’s human population. Upon infection this parasite causes the disease toxoplasmosis which in most healthy humans is chronic and often asymptomatic. If infection occurs in a human host without a competent immune system such as an unborn baby or infant or someone suffering from AIDS, toxoplasmosis can lead to permanent disability or death. A growing amount of evidence indicates a statistical relationship between chronic infection in healthy adults and neurological disorders leading to behavioural and psychological problems.
   Toxoplasma gondii can be spread through contact with cat faeces. This was thought to be the main mode of human infection. Subsequent testing with murine and Felidae models has shown that the bradyzoite of Toxoplasma gondii within intracellular cysts in muscle and neural tissue are far more infectious than the oocyst morphology shed in cat faeces. This indicates that consumption of infected meat products may also play a major contributing role in the world’s high rate of toxoplasmosis infection.
   The chief aim of this study was to develop a sensitive PCR assay to detect the presence of Toxoplasma gondii in fresh raw meat products. Beef, chicken, lamb and pork mince were chosen as convenient forms of fresh raw meat as each pack available for purchase contains the meat from several animal’s tissues (increasing the likelihood of contamination) and it has been partially homogenised allowing for easier sampling and DNA extraction.
   Secondary aims of this study were to evaluate PCR primer sets targeting polymorphic regions to gain some understanding of what strains of Toxoplasma gondii are present in our meat and the prevalence in the local cat populations.
   To accomplish these aims positive and negative PCR controls were also developed using a live toxoplasmosis vaccine and DNA extracted from Zebrafish. DNA extraction techniques were developed to purify DNA from both muscle tissue and feline faecal samples and primer sets were selected from published literature as well as designed using NCBI primer BLAST.   
   Toxoplasma gondii specific DNA was detected in only one of the 25 meat samples purchased. This was achieved using a primer set targeting the P30 region of the SAG1 gene and confirmed by DNA sequencing.
   Using primer sets targeting polymorphic sites within the Toxoplasma gondii genome, sequencing and restriction enzyme digests it was shown that Toxoplasma gondii present in the feral Felis catus population in the raglan area is type II at the GRA6 and SAG3 loci. Amplification of polymorphic PCR targets from DNA extracted from meat samples could not be achieved.
   Non-specific amplification occurred with a majority of primer sets trialed with meat DNA extracts indicating improvements are needed in primer design for the purpose of PCR detection of Toxoplasma gondii in meat. Nested PCR increased specificity however resulted in contamination in several instances.

year: 2015

title: Māori wards in Tauranga Moana and Aotearoa: Liminal local government democracy

authors: Des Forges, Sandra

subjects: Māori wards

abstract: This thesis focuses on Māori representation within the highly contested arena of local government democracy in Aotearoa New Zealand. Limitations of the current Eurocentric model of local government democracy are considered at various spatial scales. Legislative changes to enable councils to establish Māori wards were launched in the early 2000s. Māori wards are defined locations where those on the Māori electoral roll vote for Māori ward candidates, resulting in dedicated Māori representation at elected member level. Until 2021 when the legislation was amended to remove the ability for public referenda to challenge council decisions on establishing Māori wards, however, little change occurred. Since then, 35 councils have established Māori wards for the 2022 local body elections.
The research asks how, and in what ways, do Māori wards decolonise local government and encourage greater Māori representation? To explore this question, the empirical chapters are framed around three key aspects of liminality; the in-between positioning of Māori wards reflecting a time of change; this liminal space being a time where unease and discomfort is experienced by some as Indigenous disparity is addressed; and the threshold positioning of Māori wards as a place of opportunity and creativity, where new ideas and practices may be considered. Geographical concepts of (un)belonging, exclusion and deep colonising reveal challenges for Māori participation at the level of local government decision-making. 
The research uses an Indigenous methodological framework, Te Ara Tika, based on a framework of Kaupapa Māori, and developed specifically for non-Māori researchers. Māori wards have been widely debated in the media, particularly at the time of changes to the Māori ward legislation in 2021. Thematic analysis of 122 media representations of the Māori ward debate constitutes part of the empirical evidence. Fourteen individual interviews with local government representatives, including elected Council members from Tauranga Moana and members of Te Rangapū Mana Whenua o Tauranga Moana Partnership, were conducted. Additionally, participant observations took place at three public meetings on Māori wards.
The way the current form of local government representative democracy impacts Māori representation is identified. The research demonstrates how local government continues to act as a tool of colonialism by privileging Western worldviews, institutions, and systems. The research finds that Māori wards are liminal democratic options that are both decolonising and deep colonising. Evidence shows that the liminal space of Māori wards is an opportunity to consider options for a way forward to reimagine local government as a place of belonging underpinned by Te Tiriti o Waitangi and Te Ao Māori principles. 
The research builds on decolonisation literatures that seek to unsettle the hegemony of Eurocentric institutions and systems within colonised countries such as Aotearoa. Providing a critical spatial perspective on the intersection of democracy, colonisation and Indigeneity, this thesis advances decolonising geographical knowledges. In particular, this research advances debates about democratic processes, exposing ways in which colonially-based local authority democratic mechanisms contribute to under-representation issues. A reimagined local government allows current hegemonic approaches to be rethought and provides insights for a shift towards genuine decolonising processes.

text: Māori wards in Tauranga Moana and Aotearoa: Liminal local government democracy This thesis focuses on Māori representation within the highly contested arena of local government democracy in Aotearoa New Zealand. Limitations of the current Eurocentric model of local government democracy are considered at various spatial scales. Legislative changes to enable councils to establish Māori wards were launched in the early 2000s. Māori wards are defined locations where those on the Māori electoral roll vote for Māori ward candidates, resulting in dedicated Māori representation at elected member level. Until 2021 when the legislation was amended to remove the ability for public referenda to challenge council decisions on establishing Māori wards, however, little change occurred. Since then, 35 councils have established Māori wards for the 2022 local body elections.
The research asks how, and in what ways, do Māori wards decolonise local government and encourage greater Māori representation? To explore this question, the empirical chapters are framed around three key aspects of liminality; the in-between positioning of Māori wards reflecting a time of change; this liminal space being a time where unease and discomfort is experienced by some as Indigenous disparity is addressed; and the threshold positioning of Māori wards as a place of opportunity and creativity, where new ideas and practices may be considered. Geographical concepts of (un)belonging, exclusion and deep colonising reveal challenges for Māori participation at the level of local government decision-making. 
The research uses an Indigenous methodological framework, Te Ara Tika, based on a framework of Kaupapa Māori, and developed specifically for non-Māori researchers. Māori wards have been widely debated in the media, particularly at the time of changes to the Māori ward legislation in 2021. Thematic analysis of 122 media representations of the Māori ward debate constitutes part of the empirical evidence. Fourteen individual interviews with local government representatives, including elected Council members from Tauranga Moana and members of Te Rangapū Mana Whenua o Tauranga Moana Partnership, were conducted. Additionally, participant observations took place at three public meetings on Māori wards.
The way the current form of local government representative democracy impacts Māori representation is identified. The research demonstrates how local government continues to act as a tool of colonialism by privileging Western worldviews, institutions, and systems. The research finds that Māori wards are liminal democratic options that are both decolonising and deep colonising. Evidence shows that the liminal space of Māori wards is an opportunity to consider options for a way forward to reimagine local government as a place of belonging underpinned by Te Tiriti o Waitangi and Te Ao Māori principles. 
The research builds on decolonisation literatures that seek to unsettle the hegemony of Eurocentric institutions and systems within colonised countries such as Aotearoa. Providing a critical spatial perspective on the intersection of democracy, colonisation and Indigeneity, this thesis advances decolonising geographical knowledges. In particular, this research advances debates about democratic processes, exposing ways in which colonially-based local authority democratic mechanisms contribute to under-representation issues. A reimagined local government allows current hegemonic approaches to be rethought and provides insights for a shift towards genuine decolonising processes.

year: 2023