title: Theoretical electroencephalogram stationary spectrum for a white-noise-driven cortex: Evidence for a general anesthetic-induced phase transition

authors: Steyn-Ross, Moira L.

subjects: electroencephalogram

abstract: We present a model for the dynamics of a cerebral cortex in which inputs to neuronal assemblies are treated as random Gaussian fluctuations about a mean value. We incorporate the effect of general anesthetic agents on the cortex as a modulation of the inhibitory neurotransmitter rate constant. Stochastic differential equations are derived for the state variable he, the average excitatory soma potential, coherent fluctuations of which are believed to be the source of scalp-measured electroencephalogram (EEG) signals. Using this stochastic approach we derive a stationary (long-time limit) fluctuation spectrum for he. The model predicts that there will be three distinct stationary (equilibrium) regimes for cortical activity. In region I (“coma”), corresponding to a strong inhibitory anesthetic effect, he is single valued, large, and negative, so that neuronal firing rates are suppressed. In region II for a zero or small anesthetic effect, he can take on three values, two of which are stable; we label the stable solutions as “active” (enhanced firing) and “quiescent” (suppressed firing). For region III, corresponding to negative anesthetic (i.e., analeptic) effect, he again becomes single valued, but is now small and negative, resulting in strongly elevated firing rates (“seizure”). If we identify region II as associated with the conscious state of the cortex, then the model predicts that there will be a rapid transit between the active-conscious and comatose unconscious states at a critical value of anesthetic concentration, suggesting the existence of phase transitions in the cortex. The low-frequency spectral power in the he signal should increase strongly during the initial stage of anesthesia induction, before collapsing to much lower values after the transition into comatose-unconsciousness. These qualitative predictions are consistent with clinical measurements by Bührer et al. [Anaesthesiology 77, 226 (1992)], MacIver et al. [ibid. 84, 1411 (1996)], and Kuizenga et al. [Br. J. Anaesthesia 80, 725 (1998)]. This strong increase in EEG spectral power in the vicinity of the critical point is similar to the divergences observed during thermodynamic phase transitions. We show that the divergence in low-frequency power in our model is a natural consequence of the existence of turning points in the trajectory of stationary states for the cortex.

text: Theoretical electroencephalogram stationary spectrum for a white-noise-driven cortex: Evidence for a general anesthetic-induced phase transition We present a model for the dynamics of a cerebral cortex in which inputs to neuronal assemblies are treated as random Gaussian fluctuations about a mean value. We incorporate the effect of general anesthetic agents on the cortex as a modulation of the inhibitory neurotransmitter rate constant. Stochastic differential equations are derived for the state variable he, the average excitatory soma potential, coherent fluctuations of which are believed to be the source of scalp-measured electroencephalogram (EEG) signals. Using this stochastic approach we derive a stationary (long-time limit) fluctuation spectrum for he. The model predicts that there will be three distinct stationary (equilibrium) regimes for cortical activity. In region I (“coma”), corresponding to a strong inhibitory anesthetic effect, he is single valued, large, and negative, so that neuronal firing rates are suppressed. In region II for a zero or small anesthetic effect, he can take on three values, two of which are stable; we label the stable solutions as “active” (enhanced firing) and “quiescent” (suppressed firing). For region III, corresponding to negative anesthetic (i.e., analeptic) effect, he again becomes single valued, but is now small and negative, resulting in strongly elevated firing rates (“seizure”). If we identify region II as associated with the conscious state of the cortex, then the model predicts that there will be a rapid transit between the active-conscious and comatose unconscious states at a critical value of anesthetic concentration, suggesting the existence of phase transitions in the cortex. The low-frequency spectral power in the he signal should increase strongly during the initial stage of anesthesia induction, before collapsing to much lower values after the transition into comatose-unconsciousness. These qualitative predictions are consistent with clinical measurements by Bührer et al. [Anaesthesiology 77, 226 (1992)], MacIver et al. [ibid. 84, 1411 (1996)], and Kuizenga et al. [Br. J. Anaesthesia 80, 725 (1998)]. This strong increase in EEG spectral power in the vicinity of the critical point is similar to the divergences observed during thermodynamic phase transitions. We show that the divergence in low-frequency power in our model is a natural consequence of the existence of turning points in the trajectory of stationary states for the cortex.

year: 1999

title: Prioritising ecological restoration sites and strategies in Hamilton City, New Zealand

authors: Rogers, Hannah Catherine

subjects: Urban ecological restoration

abstract: Urban ecological restoration faces distinct challenges due to the highly modified biophysical conditions that characterise cities. To overcome these difficulties and assist in decision-making, ecological principles should underpin comprehensive analyses at both the landscape and site-specific scale. With increasing recognition of the role that the environment plays in social and economic prosperity, there are a growing number of strategies focused on increasing native habitat in urban centres. This thesis presents three integrated studies in support of Hamilton City Council’s goal under the Nature in the City Strategy to increase indigenous vegetation cover from about 1.8% to a minimum of 10% by 2050. Landform and ecological unit representativeness analyses in the city reveal the extent of under-represented environments, but it also presents opportunities to improve this criterion rapidly. Then, a multicriteria ecological prioritisation tool specifically developed for Hamilton City identified the most ecologically intact sites that could support the selection of potential gully and reserve restoration sites following the Nature in the City Strategy. Finally, at the site-specific scale, assessments of the vegetation composition and structure of three kahikatea forest remnants determined appropriate restoration strategies that may guide restoration projects in other cities.

Landform and ecological unit areas in Hamilton City that would need to be restored to meet ecological representativeness thresholds under the 10% goal are presented. The peatlands, alluvial plains and hills landform and their respective ecological units are severely under-represented, while the gullies are sufficiently represented. However, gullies tend to contain more micro-environments and diversity than the other landforms, so restoring them may provide greater biodiversity rewards. Compared to previous representativeness studies of Hamilton City, this assessment provides more refined information available on a geographic information system (GIS) and highlights opportunities for its rapid improvement. For example, adequately representing some of the most under-represented ecological units, such as peat domes, would require the least restoration effort by extent (14 hectares (ha)). While improving representativeness could enhance the city’s pool of indigenous species, this study demonstrated that it should not be used alone to prioritise restoration sites in highly modified urban environments. Rather, representativeness could be included in a wider range of criteria and more appropriately employed for regional or national strategies.

About 198 ha of Hamilton City is dominated by native vegetation, requiring the restoration of 886 ha or approximately 32 ha annually from 2023 to achieve the 10% goal by 2050. A prioritisation tool specifically developed for the city comprising eight ecological criteria identified 873 gully and reserve sites with the most intact ecological integrity that satisfy this area. These sites were allocated into five prioritisation categories to support the adoption of a staged approach for this city-wide restoration project. Sites that received high ecological scores included sections within Hamilton Gardens, Hammond Park, Minogue Park, Kirikiriroa gully, the major riverside gully and Mangaonua gully. Most high-ranking sites were found in the city’s east, although restoring sites on both sides of Hamilton City would enhance ecological connectivity on a regional scale. As the city expands, restoring large undeveloped areas would likely require fewer resources than restoring many dispersed isolated patches. Similarly, restoring whole systems, such as the high-ranking Kirikiriroa gully, is suggested to provide greater biodiversity rewards. Further application of this tool could incorporate social, economic and cultural criteria for a more holistic prioritisation of sites. 

The condition of kahikatea (Dacrycarpus dacrydioides, white pine) forest remnants at Totara Park, Hillcrest Park and Grove Park was examined and compared with Te Papanui (Claudelands Bush/Jubilee Park) as the reference site to identify restoration strategies. Age structure analyses found that Hillcrest Park comprises the oldest kahikatea population with an average age of 82 years, followed by Grove Park (70 years), Te Papanui (60 years) and Totara Park (32 years). The Kahikatea Green Wheel, life form and epiphyte analyses highlighted the importance of Totara Park’s high water table and sheltered conditions. While Te Papanui was found to support the most native vascular plants (64 species), Totara Park’s conditions have contributed to its greater species richness (41 species) than Hillcrest Park (15 species) and Grove Park (eight species). More native epiphytes were also identified at Totara Park (nine) than Te Papanui (six), Hillcrest Park (one) and Grove Park (none). Epiphytes absent from Te Papanui found at Totara Park may be due to the loss of the once abundant Dicksonia squarrosa (whekī), a prominent host. Differences between the native vascular plants found at Te Papanui and the case studies signal gaps in characteristic species of kahikatea forest that could be filled by relevant planting at each site. While Totara Park’s remnant requires a careful manipulation restoration strategy to gradually remove troublesome plants without disturbing its locally rare native flora, the ecological integrity of Hillcrest Park and Grove Park could improve most from buffer, ground cover and shrub tier plantings.

text: Prioritising ecological restoration sites and strategies in Hamilton City, New Zealand Urban ecological restoration faces distinct challenges due to the highly modified biophysical conditions that characterise cities. To overcome these difficulties and assist in decision-making, ecological principles should underpin comprehensive analyses at both the landscape and site-specific scale. With increasing recognition of the role that the environment plays in social and economic prosperity, there are a growing number of strategies focused on increasing native habitat in urban centres. This thesis presents three integrated studies in support of Hamilton City Council’s goal under the Nature in the City Strategy to increase indigenous vegetation cover from about 1.8% to a minimum of 10% by 2050. Landform and ecological unit representativeness analyses in the city reveal the extent of under-represented environments, but it also presents opportunities to improve this criterion rapidly. Then, a multicriteria ecological prioritisation tool specifically developed for Hamilton City identified the most ecologically intact sites that could support the selection of potential gully and reserve restoration sites following the Nature in the City Strategy. Finally, at the site-specific scale, assessments of the vegetation composition and structure of three kahikatea forest remnants determined appropriate restoration strategies that may guide restoration projects in other cities.

Landform and ecological unit areas in Hamilton City that would need to be restored to meet ecological representativeness thresholds under the 10% goal are presented. The peatlands, alluvial plains and hills landform and their respective ecological units are severely under-represented, while the gullies are sufficiently represented. However, gullies tend to contain more micro-environments and diversity than the other landforms, so restoring them may provide greater biodiversity rewards. Compared to previous representativeness studies of Hamilton City, this assessment provides more refined information available on a geographic information system (GIS) and highlights opportunities for its rapid improvement. For example, adequately representing some of the most under-represented ecological units, such as peat domes, would require the least restoration effort by extent (14 hectares (ha)). While improving representativeness could enhance the city’s pool of indigenous species, this study demonstrated that it should not be used alone to prioritise restoration sites in highly modified urban environments. Rather, representativeness could be included in a wider range of criteria and more appropriately employed for regional or national strategies.

About 198 ha of Hamilton City is dominated by native vegetation, requiring the restoration of 886 ha or approximately 32 ha annually from 2023 to achieve the 10% goal by 2050. A prioritisation tool specifically developed for the city comprising eight ecological criteria identified 873 gully and reserve sites with the most intact ecological integrity that satisfy this area. These sites were allocated into five prioritisation categories to support the adoption of a staged approach for this city-wide restoration project. Sites that received high ecological scores included sections within Hamilton Gardens, Hammond Park, Minogue Park, Kirikiriroa gully, the major riverside gully and Mangaonua gully. Most high-ranking sites were found in the city’s east, although restoring sites on both sides of Hamilton City would enhance ecological connectivity on a regional scale. As the city expands, restoring large undeveloped areas would likely require fewer resources than restoring many dispersed isolated patches. Similarly, restoring whole systems, such as the high-ranking Kirikiriroa gully, is suggested to provide greater biodiversity rewards. Further application of this tool could incorporate social, economic and cultural criteria for a more holistic prioritisation of sites. 

The condition of kahikatea (Dacrycarpus dacrydioides, white pine) forest remnants at Totara Park, Hillcrest Park and Grove Park was examined and compared with Te Papanui (Claudelands Bush/Jubilee Park) as the reference site to identify restoration strategies. Age structure analyses found that Hillcrest Park comprises the oldest kahikatea population with an average age of 82 years, followed by Grove Park (70 years), Te Papanui (60 years) and Totara Park (32 years). The Kahikatea Green Wheel, life form and epiphyte analyses highlighted the importance of Totara Park’s high water table and sheltered conditions. While Te Papanui was found to support the most native vascular plants (64 species), Totara Park’s conditions have contributed to its greater species richness (41 species) than Hillcrest Park (15 species) and Grove Park (eight species). More native epiphytes were also identified at Totara Park (nine) than Te Papanui (six), Hillcrest Park (one) and Grove Park (none). Epiphytes absent from Te Papanui found at Totara Park may be due to the loss of the once abundant Dicksonia squarrosa (whekī), a prominent host. Differences between the native vascular plants found at Te Papanui and the case studies signal gaps in characteristic species of kahikatea forest that could be filled by relevant planting at each site. While Totara Park’s remnant requires a careful manipulation restoration strategy to gradually remove troublesome plants without disturbing its locally rare native flora, the ecological integrity of Hillcrest Park and Grove Park could improve most from buffer, ground cover and shrub tier plantings.

year: 2022

title: Aro mai aro atu: Raising Māori-medium students' academic oral language proficiency

authors: Shandley, Rosina Mary

subjects: Māori-medium

abstract: From the early 1860s, colonial governments worked systematically to eradicate the language and culture of the indigenous people of Aotearoa / New Zealand, and, by the late 1960s, the death of the Māori language was being predicted by leading linguists. Māori leaders responded in the 1980s with language regeneration initiatives that included the birth of Māori-medium education. Today, this uniquely indigenous education system is a significant site of language learning for new generations of Māori children. In Māori-medium education, children are nurtured, educated, and loved as Māori, and they are more likely to attain educational qualifications than their Māori peers who attend English-medium schools. 

The success of Māori-medium education is achieved in the face of a raft of ongoing challenges that teachers and students confront on a daily basis. Years of language marginalisation, including the disruption to intergenerational transfer, mean Māori-medium students are required to learn the curriculum through their second and less-developed language. They have limited opportunities to hear or use the Māori language outside of the school, and this places huge pressure on teachers who are often their most significant language models. The challenge is compounded by the limited education that has been made available to teachers in relation to second-language pedagogies specifically designed for Māori-medium classrooms. The resulting situation is that Māori-medium teachers are often left struggling to find ways that they can develop students’ Māori language proficiency at the same time as their curriculum achievement so that one is not sacrificed for the other. 

This study designed and trialled pedagogies to support Māori-medium students to develop their academic oral language proficiency at the same time as their curriculum achievement. It was a mixed methods study grounded in a kaupapa Māori approach, and involved three teachers and 24 students across three separate Māori-medium schools. An Anga Putanga Ako (Curriculum Outcomes Matrix) was developed to support the students to understand what they needed to learn to progress through the writing curriculum. Teachers then learnt to share explicit learning outcomes from the Anga Putanga Ako with students before lessons and to allow them time to discuss their achievement of those outcomes in pairs at the conclusion of those lessons. Linguistic scaffolds were developed to support students’ learning conversations, including the self and peer assessment of the learning outcomes, and decisions about their curriculum achievement levels and next learning steps.

The quantitative and qualitative results of the study revealed that the confluence of the self and peer assessment practices, supported by the Anga Putanga Ako and linguistic scaffolds, improved the students’ academic oral language and accelerated their reading and writing achievement significantly beyond what is usually expected in a Māori-medium classroom in 14 weeks. The study also found that, through implementing the self and peer assessment pedagogies, teachers were able to identify ways they could develop their students’ academic language and curriculum achievement simultaneously and how these approaches could be applied across the curriculum.

It was clear from the research results that pedagogies that support second-language development and curriculum learning, such as the self and peer assessment pedagogies demonstrated in this study, need to be explicitly taught with consistency across initial and in-service teacher education programmes. This development is necessary to help ensure Māori-medium students are supported with the thinking and linguistic skills needed to contribute to the creation of new knowledge, to support or challenge the current social order as they see fit, and to continue to transfer the Māori language to new generations of mokopuna.

text: Aro mai aro atu: Raising Māori-medium students' academic oral language proficiency From the early 1860s, colonial governments worked systematically to eradicate the language and culture of the indigenous people of Aotearoa / New Zealand, and, by the late 1960s, the death of the Māori language was being predicted by leading linguists. Māori leaders responded in the 1980s with language regeneration initiatives that included the birth of Māori-medium education. Today, this uniquely indigenous education system is a significant site of language learning for new generations of Māori children. In Māori-medium education, children are nurtured, educated, and loved as Māori, and they are more likely to attain educational qualifications than their Māori peers who attend English-medium schools. 

The success of Māori-medium education is achieved in the face of a raft of ongoing challenges that teachers and students confront on a daily basis. Years of language marginalisation, including the disruption to intergenerational transfer, mean Māori-medium students are required to learn the curriculum through their second and less-developed language. They have limited opportunities to hear or use the Māori language outside of the school, and this places huge pressure on teachers who are often their most significant language models. The challenge is compounded by the limited education that has been made available to teachers in relation to second-language pedagogies specifically designed for Māori-medium classrooms. The resulting situation is that Māori-medium teachers are often left struggling to find ways that they can develop students’ Māori language proficiency at the same time as their curriculum achievement so that one is not sacrificed for the other. 

This study designed and trialled pedagogies to support Māori-medium students to develop their academic oral language proficiency at the same time as their curriculum achievement. It was a mixed methods study grounded in a kaupapa Māori approach, and involved three teachers and 24 students across three separate Māori-medium schools. An Anga Putanga Ako (Curriculum Outcomes Matrix) was developed to support the students to understand what they needed to learn to progress through the writing curriculum. Teachers then learnt to share explicit learning outcomes from the Anga Putanga Ako with students before lessons and to allow them time to discuss their achievement of those outcomes in pairs at the conclusion of those lessons. Linguistic scaffolds were developed to support students’ learning conversations, including the self and peer assessment of the learning outcomes, and decisions about their curriculum achievement levels and next learning steps.

The quantitative and qualitative results of the study revealed that the confluence of the self and peer assessment practices, supported by the Anga Putanga Ako and linguistic scaffolds, improved the students’ academic oral language and accelerated their reading and writing achievement significantly beyond what is usually expected in a Māori-medium classroom in 14 weeks. The study also found that, through implementing the self and peer assessment pedagogies, teachers were able to identify ways they could develop their students’ academic language and curriculum achievement simultaneously and how these approaches could be applied across the curriculum.

It was clear from the research results that pedagogies that support second-language development and curriculum learning, such as the self and peer assessment pedagogies demonstrated in this study, need to be explicitly taught with consistency across initial and in-service teacher education programmes. This development is necessary to help ensure Māori-medium students are supported with the thinking and linguistic skills needed to contribute to the creation of new knowledge, to support or challenge the current social order as they see fit, and to continue to transfer the Māori language to new generations of mokopuna.

year: 2022