title: Determination of the rank of an integration lattice

authors: Joe, Stephen

subjects: mathematics

abstract: The continuing and widespread use of lattice rules for high-dimensional numerical quadrature is driving the development of a rich and detailed theory. Part of this theory is devoted to computer searches for rules, appropriate to particular situations. 
In some applications, one is interested in obtaining the (lattice) rank of a lattice rule Q(Λ) directly from the elements of a generator matrix B (possibly in upper triangular lattice form) of the corresponding dual lattice Λ⊥. We treat this problem in detail, demonstrating the connections between this (lattice) rank and the conventional matrix rank deficiency of modulo p versions of B.

text: Determination of the rank of an integration lattice The continuing and widespread use of lattice rules for high-dimensional numerical quadrature is driving the development of a rich and detailed theory. Part of this theory is devoted to computer searches for rules, appropriate to particular situations. 
In some applications, one is interested in obtaining the (lattice) rank of a lattice rule Q(Λ) directly from the elements of a generator matrix B (possibly in upper triangular lattice form) of the corresponding dual lattice Λ⊥. We treat this problem in detail, demonstrating the connections between this (lattice) rank and the conventional matrix rank deficiency of modulo p versions of B.

year: 2006

title: Long-term changes in Zooplankton community composition in North Island lakes: What are the drivers of change?

authors: Taylor, Amber

abstract: Zooplankton are an important component of freshwater ecosystems, forming a trophic bridge between primary producers and higher trophic levels. They are highly responsive to changes in their environment and have therefore been recognised as a useful tool for monitoring and assessing aquatic ecosystem health. However, long-term studies of changes in zooplankton communities are rare globally. Long-term studies of zooplankton composition are even more scarce within New Zealand. Past researches on New Zealand zooplankton have primarily focused on the seasonal variation of zooplankton composition, rather than long-term temporal changes, and have been undertaken over time periods of two years or less.
This study utilised zooplankton compositional data from past research papers (1950-1990) conducted within North Island, New Zealand lakes and data from two 2021 sampling events, to investigate long-term temporal zooplankton community composition change. A historical dataset was constructed by conducting a desktop investigation of past studies that included zooplankton species lists. Further, zooplankton samples were collected in 2021 using vertical net hauls from nine lakes within the Bay of Plenty and Waikato regions, using zooplankton nets with three different mesh sizes (37 μm, 75 μm and 100 μm). Species lists from the historical and 2021 samples were statistically analysed to identify changes in zooplankton diversity and community composition through time. The samples from each of the three nets were also analysed independently of the historical samples, to determine the influence of mesh size on zooplankton composition and species richness estimates from semi-quantitative samples.
Three major changes in zooplankton communities were evident over time. Firstly, high frequencies of the Holarctic cladoceran Daphnia galeata were found in the samples collected in 2021 yet were absent in samples taken prior to 1990. This result is consistent with the reported invasion of this species into New Zealand lakes since the early 1990s. Secondly, the cyclopoid copepod Macrocyclops albidus was not observed within the 2021 samples yet has been frequently present in species lists from the historical literature. This species has also not been commonly identified in recent research papers. Their low frequencies within the 2021 samples also coincides with increases in the importance of the D. galeata and cyclopoid copepod Mesocyclops australiensis in the 2021 samples and recent literature relative to historical datasets. Finally, there was an increase in the occurrence of many rotifer taxa within the 2021 samples compared to the historical samples. Interestingly, these taxa were largely deemed as an uncommon constituent of the plankton within New Zealand waters in the 1950s to 1970s. The increased importance of rotifer species within recent samples appeared to be a product of underestimation due to improper mesh selection by past researchers.
Analysis of the semi-quantitative data of the three zooplankton nets with different mesh sizes indicated that zooplankton composition and species richness using the 75 μm net was more representative of that collected by the 35 μm samples than the 100 μm samples. This result indicates that a 75 μm net would be adequate when comparing zooplankton results within a 35 μm net among the studied lakes. Species richness within the two smaller meshed nets were higher than the 100 μm net, indicating a net with mesh size of 100 μm and greater would result in an underestimation of zooplankton community composition and species richness.

text: Long-term changes in Zooplankton community composition in North Island lakes: What are the drivers of change? Zooplankton are an important component of freshwater ecosystems, forming a trophic bridge between primary producers and higher trophic levels. They are highly responsive to changes in their environment and have therefore been recognised as a useful tool for monitoring and assessing aquatic ecosystem health. However, long-term studies of changes in zooplankton communities are rare globally. Long-term studies of zooplankton composition are even more scarce within New Zealand. Past researches on New Zealand zooplankton have primarily focused on the seasonal variation of zooplankton composition, rather than long-term temporal changes, and have been undertaken over time periods of two years or less.
This study utilised zooplankton compositional data from past research papers (1950-1990) conducted within North Island, New Zealand lakes and data from two 2021 sampling events, to investigate long-term temporal zooplankton community composition change. A historical dataset was constructed by conducting a desktop investigation of past studies that included zooplankton species lists. Further, zooplankton samples were collected in 2021 using vertical net hauls from nine lakes within the Bay of Plenty and Waikato regions, using zooplankton nets with three different mesh sizes (37 μm, 75 μm and 100 μm). Species lists from the historical and 2021 samples were statistically analysed to identify changes in zooplankton diversity and community composition through time. The samples from each of the three nets were also analysed independently of the historical samples, to determine the influence of mesh size on zooplankton composition and species richness estimates from semi-quantitative samples.
Three major changes in zooplankton communities were evident over time. Firstly, high frequencies of the Holarctic cladoceran Daphnia galeata were found in the samples collected in 2021 yet were absent in samples taken prior to 1990. This result is consistent with the reported invasion of this species into New Zealand lakes since the early 1990s. Secondly, the cyclopoid copepod Macrocyclops albidus was not observed within the 2021 samples yet has been frequently present in species lists from the historical literature. This species has also not been commonly identified in recent research papers. Their low frequencies within the 2021 samples also coincides with increases in the importance of the D. galeata and cyclopoid copepod Mesocyclops australiensis in the 2021 samples and recent literature relative to historical datasets. Finally, there was an increase in the occurrence of many rotifer taxa within the 2021 samples compared to the historical samples. Interestingly, these taxa were largely deemed as an uncommon constituent of the plankton within New Zealand waters in the 1950s to 1970s. The increased importance of rotifer species within recent samples appeared to be a product of underestimation due to improper mesh selection by past researchers.
Analysis of the semi-quantitative data of the three zooplankton nets with different mesh sizes indicated that zooplankton composition and species richness using the 75 μm net was more representative of that collected by the 35 μm samples than the 100 μm samples. This result indicates that a 75 μm net would be adequate when comparing zooplankton results within a 35 μm net among the studied lakes. Species richness within the two smaller meshed nets were higher than the 100 μm net, indicating a net with mesh size of 100 μm and greater would result in an underestimation of zooplankton community composition and species richness.

year: 2023

title: Time to Diagnosis and Persistence: The Two Major Determinants of Effective Tuberculosis Control

authors: Ruthe, Alaine Tess

subjects: tuberculosis

abstract: The greatest challenge confronting effective tuberculosis (TB) eradication is the time to diagnosis, and duration of treatment of chronically infected individuals which represent a pool of infection. In an attempt to help limit the spread of TB in New Zealand, a fast SNP based diagnostic test was developed, to quickly identify the highly transmissible and virulent endemic Rangipo strain. The role of VapBC toxin-antitoxin systems in M. tuberculosis has been the subject of great interest recently, due to their expanded number in the genome and links with virulence and the regulation of cell growth in response to environmental stress. Their ability to regulate growth under adverse conditions for presumed survival advantages possibly leading to dormancy or persistence, make them ideal candidates for the development of new M. tuberculosis treatments. To establish differential expression of vapC, and therefore identify possible pathways and functions of the VapBC proteins, RT-qPCR was used to assess the expression levels of vapB and vapC in M. smegmatis under conditions of stress. No consistant changes in vapC mRNA levels were observed, resulting in the hypothesis that it is not the transcriptional differences which are important in the regulation of VapC, but post-transcriptional factors. In order to investigate the function(s) of M. tuberculosis VapBCs, these VapBC proteins were expressed and purified in M. smegmatis, and the VapC toxin tested for RNase activity. The purification, expression, RNase testing and bioinformatic analysis of M. tuberculosis VapCs suggested that VapCRv2530c, VapCRv0065 and VapCRv0617 may all target the same recognition sequence, UA*GG. Bioinformatic analysis revealed an abundance of this target sequence in horizontal gene transfer and TA genes, raising the possibility that VapC toxins could be functioning as selfish elements, or initiating transcriptional regulation cascades when a rapid change in the proteomic response and metabolic state of the cell is required. It is intriguing that the three M. tuberculosis VapC proteins tested thus far appear to target the same recognition sequence, possibly suggesting that all 47 VapCs are RNases and are targeting the same sequence. Alternatively; VapCs may belong to sub-groups targeting different sequences, allowing M. tuberculosis to exude both gross and fine metabolic control; or, they may share the same target, but are regulated by different activators triggered in response to different environmental stimuli.

text: Time to Diagnosis and Persistence: The Two Major Determinants of Effective Tuberculosis Control The greatest challenge confronting effective tuberculosis (TB) eradication is the time to diagnosis, and duration of treatment of chronically infected individuals which represent a pool of infection. In an attempt to help limit the spread of TB in New Zealand, a fast SNP based diagnostic test was developed, to quickly identify the highly transmissible and virulent endemic Rangipo strain. The role of VapBC toxin-antitoxin systems in M. tuberculosis has been the subject of great interest recently, due to their expanded number in the genome and links with virulence and the regulation of cell growth in response to environmental stress. Their ability to regulate growth under adverse conditions for presumed survival advantages possibly leading to dormancy or persistence, make them ideal candidates for the development of new M. tuberculosis treatments. To establish differential expression of vapC, and therefore identify possible pathways and functions of the VapBC proteins, RT-qPCR was used to assess the expression levels of vapB and vapC in M. smegmatis under conditions of stress. No consistant changes in vapC mRNA levels were observed, resulting in the hypothesis that it is not the transcriptional differences which are important in the regulation of VapC, but post-transcriptional factors. In order to investigate the function(s) of M. tuberculosis VapBCs, these VapBC proteins were expressed and purified in M. smegmatis, and the VapC toxin tested for RNase activity. The purification, expression, RNase testing and bioinformatic analysis of M. tuberculosis VapCs suggested that VapCRv2530c, VapCRv0065 and VapCRv0617 may all target the same recognition sequence, UA*GG. Bioinformatic analysis revealed an abundance of this target sequence in horizontal gene transfer and TA genes, raising the possibility that VapC toxins could be functioning as selfish elements, or initiating transcriptional regulation cascades when a rapid change in the proteomic response and metabolic state of the cell is required. It is intriguing that the three M. tuberculosis VapC proteins tested thus far appear to target the same recognition sequence, possibly suggesting that all 47 VapCs are RNases and are targeting the same sequence. Alternatively; VapCs may belong to sub-groups targeting different sequences, allowing M. tuberculosis to exude both gross and fine metabolic control; or, they may share the same target, but are regulated by different activators triggered in response to different environmental stimuli.

year: 2015