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: The influence of fire on vegetation dynamics of a New Zealand restiad bog

authors: Wilson, Clara Renée

subjects: fire

abstract: New Zealand restiad bogs have a history of natural fire, yet little is known about their fire ecology compared to other frequently burnt ecosystems. Previous research has identified general vegetation recovery trends, but it remains unclear how certain species increase their dominance following fire and what the main environmental changes associated with burning are. To address these research gaps, this study focussed on three areas of varying last burn date (2017, 2005, and 1974) within Kopuatai Bog. 

Measures of vegetation dynamics, light availability, and nutrient concentrations (in peat and foliage) were compared between burnt and adjacent unburnt sites. At the 2017 burn site, post-fire flowering of the sedge species, Machaerina teretifolia and Schoenus brevifolius, was assessed. At the same site, near-surface temperature fluctuations were monitored for almost one year, and samples collected two weeks post-fire were used to test for immediate nutrient enrichment. The role of the peat seed bank was tested experimentally, by exposing peat to heat and/or smoke and assessing germination. 

Species capable of vegetative recovery dominated within the first two years post-fire. By 14 years, vegetation had largely recovered to pre-fire composition, although percent cover of Leptospermum scoparium, Machaerina teretifolia, Schoenus brevifolius, and Epacris pauciflora were higher on the burnt area. Leptospermum’s response can be explained by its well-documented serotinous capability. The increase in sedge species is attributed to their strong fire-stimulated flowering response, particularly in Machaerina, which averaged 30.4 flowering heads m-2 at the 2017 burn site. Epacris recovered from a rich peat seed bank, as demonstrated by the response in the germination experiment of 3143 seedlings m-2, on average. The effect of heat on germination was unclear. Further research, including improved heat treatments, is required to determine the effect of heat on seeds of restiad species, Empodisma robustum and Sporadanthus ferrugineus, which were relatively common in the control and smoke treatments. 

Fire resulted in immediate increases in peat total P, S, Ca, Mg, K, Na, Fe, Mn, Cu concentrations. These effects had declined by two years post-fire, although foliar nutrients suggest that plant-available nutrients may have still been elevated at this time. Peat total N was unaffected. Near-surface maximum and average air temperatures were found to be consistently higher on the burn, while minimum temperatures were seasonally variable. Fire caused an increase in light availability from 0.1-0.2% diffuse light availability under an intact Empodisma-dominated canopy to 19.5% 16 months post-fire – an effect which had subsided completely by 14 years post-fire. 

While nutrient enhancement, particularly in P, may temporarily enhance plant productivity, the most important driver of vegetation dynamics appears to be light. Fire opens up the canopy, providing an opportunity for seedlings to become established – an opportunity which Leptospermum, Epacris, and the sedge species take advantage of.

text: The influence of fire on vegetation dynamics of a New Zealand restiad bog New Zealand restiad bogs have a history of natural fire, yet little is known about their fire ecology compared to other frequently burnt ecosystems. Previous research has identified general vegetation recovery trends, but it remains unclear how certain species increase their dominance following fire and what the main environmental changes associated with burning are. To address these research gaps, this study focussed on three areas of varying last burn date (2017, 2005, and 1974) within Kopuatai Bog. 

Measures of vegetation dynamics, light availability, and nutrient concentrations (in peat and foliage) were compared between burnt and adjacent unburnt sites. At the 2017 burn site, post-fire flowering of the sedge species, Machaerina teretifolia and Schoenus brevifolius, was assessed. At the same site, near-surface temperature fluctuations were monitored for almost one year, and samples collected two weeks post-fire were used to test for immediate nutrient enrichment. The role of the peat seed bank was tested experimentally, by exposing peat to heat and/or smoke and assessing germination. 

Species capable of vegetative recovery dominated within the first two years post-fire. By 14 years, vegetation had largely recovered to pre-fire composition, although percent cover of Leptospermum scoparium, Machaerina teretifolia, Schoenus brevifolius, and Epacris pauciflora were higher on the burnt area. Leptospermum’s response can be explained by its well-documented serotinous capability. The increase in sedge species is attributed to their strong fire-stimulated flowering response, particularly in Machaerina, which averaged 30.4 flowering heads m-2 at the 2017 burn site. Epacris recovered from a rich peat seed bank, as demonstrated by the response in the germination experiment of 3143 seedlings m-2, on average. The effect of heat on germination was unclear. Further research, including improved heat treatments, is required to determine the effect of heat on seeds of restiad species, Empodisma robustum and Sporadanthus ferrugineus, which were relatively common in the control and smoke treatments. 

Fire resulted in immediate increases in peat total P, S, Ca, Mg, K, Na, Fe, Mn, Cu concentrations. These effects had declined by two years post-fire, although foliar nutrients suggest that plant-available nutrients may have still been elevated at this time. Peat total N was unaffected. Near-surface maximum and average air temperatures were found to be consistently higher on the burn, while minimum temperatures were seasonally variable. Fire caused an increase in light availability from 0.1-0.2% diffuse light availability under an intact Empodisma-dominated canopy to 19.5% 16 months post-fire – an effect which had subsided completely by 14 years post-fire. 

While nutrient enhancement, particularly in P, may temporarily enhance plant productivity, the most important driver of vegetation dynamics appears to be light. Fire opens up the canopy, providing an opportunity for seedlings to become established – an opportunity which Leptospermum, Epacris, and the sedge species take advantage of.

year: 2020

title: New Zealand’s indigenous forests – their status and drivers of change

authors: Allen, Robert

abstract: New Zealand’s remaining indigenous forests and shrublands are of immense cultural, environmental, and economic significance. A representative plot-based sample of these forests and shrublands has recently allowed an unbiased depiction of their composition
and structure. This is necessary for international reporting, performance assessment and management prioritisation. Their composition, structure, and function are driven by a diverse array of factors, many of which are complexly interrelated. The imprint of disturbances is pervasive and it is necessary to understand disturbances to interpret human-related impacts. For example, understanding impacts of exotic browsing mammals is only possible within a context of forest ecosystem development and tree demographic processes. There are now extensive areas of shrublands successional to forest, often composed of mixtures of indigenous and exotic species. These shrublands expand the pportunities for ecosystem services from, for example, carbon sequestration to water quality. An increasing area of indigenous forests and shrublands are managed for distinctive Māori aspirations that include sustainable use.

text: New Zealand’s indigenous forests – their status and drivers of change New Zealand’s remaining indigenous forests and shrublands are of immense cultural, environmental, and economic significance. A representative plot-based sample of these forests and shrublands has recently allowed an unbiased depiction of their composition
and structure. This is necessary for international reporting, performance assessment and management prioritisation. Their composition, structure, and function are driven by a diverse array of factors, many of which are complexly interrelated. The imprint of disturbances is pervasive and it is necessary to understand disturbances to interpret human-related impacts. For example, understanding impacts of exotic browsing mammals is only possible within a context of forest ecosystem development and tree demographic processes. There are now extensive areas of shrublands successional to forest, often composed of mixtures of indigenous and exotic species. These shrublands expand the pportunities for ecosystem services from, for example, carbon sequestration to water quality. An increasing area of indigenous forests and shrublands are managed for distinctive Māori aspirations that include sustainable use.

year: 2015