title: Component-by-component construction of good intermediate-rank lattice rules

authors: Kuo, Frances Y.

subjects: mathematics

abstract: It is known that the generating vector of a rank-1 lattice rule can be constructed component-by-component to achieve strong tractability error bounds in both weighted Korobov spaces and weighted Sobolev spaces. Since the weights for these spaces are nonincreasing, the first few variables are in a sense more important than the rest. We thus propose to copy the points of a rank-1 lattice rule a number of times in the first few dimensions to yield an intermediate-rank lattice rule. We show that the generating vector (and in weighted Sobolev spaces, the shift also) of an intermediate-rank lattice rule can also be constructed component-by-component to achieve strong tractability error bounds. In certain circumstances, these bounds are better than the corresponding bounds for rank-1 lattice rules.

text: Component-by-component construction of good intermediate-rank lattice rules It is known that the generating vector of a rank-1 lattice rule can be constructed component-by-component to achieve strong tractability error bounds in both weighted Korobov spaces and weighted Sobolev spaces. Since the weights for these spaces are nonincreasing, the first few variables are in a sense more important than the rest. We thus propose to copy the points of a rank-1 lattice rule a number of times in the first few dimensions to yield an intermediate-rank lattice rule. We show that the generating vector (and in weighted Sobolev spaces, the shift also) of an intermediate-rank lattice rule can also be constructed component-by-component to achieve strong tractability error bounds. In certain circumstances, these bounds are better than the corresponding bounds for rank-1 lattice rules.

year: 2003

title: Phytoplankton dynamics in Lake Tarawera

authors: Baldwin, Amanda Brigitte

subjects: Tarawera

abstract: This study examined the dynamics of phytoplankton populations in deep (maximum depth 84 m), monomictic, oligotrophic Lake Tarawera in the Rotorua lakes district of New Zealand.  Specifically, components of the annual phytoplankton assemblage; a summer deep chlorophyll maximum, a winter areal phytoplankton maximum and nitrogen fixation in ephemeral cyanobacterial surface blooms, are investigated.

Alternate hypotheses for the formation of the observed diatom deep chlorophyll maximum (DCM) in Lake Tarawera were tested.  (1) That growth rates of phytoplankton are higher in the metalimnion than in the epilimnion, perhaps supported by higher concentrations of nutrients in the metalimnion. (2) That the DCM is formed by phytoplankton becoming entrained in more turbulent water at the thermocline and persists while the depth of the thermocline remains above the euphotic depth. 

Lake water concentrations of total inorganic nitrogen and total phosphorus measured monthly over a year at 10 m depth intervals at a mid lake station, provided no evidence that the metalimnion had higher nutrient concentrations than those in the epilimnion.  The productivity of DCM phytoplankton and epilimnion phytoplankton (5 m) was measured c. monthly over the six months that the DCM was present with in situ 13C uptake incubations.  Productivity was consistently higher in 5 m incubations (c. 5  g C L-1 h-1) than in DCM incubations.  The growth of DCM phytoplankton did not appear to be limited by either nitrogen or phosphorus as in situ incubations, over four days, with single or combined additions of these nutrients did not significantly increase chlorophyll a concentrations.  The depth of the DCM was similar to the depth of the thermocline while the thermocline remained above the euphotic depth, but this relationship ceased as the thermocline deepened in autumn and a DCM was no longer discernable.  Light availability at the thermocline therefore appears to be a key factor in regulating the position and persistence of DCM phytoplankton.  Though other studies have demonstrated higher growth of DCM phytoplankton, these maybe incidental, as all DCM formed by negatively buoyant phytoplankton appear to coincide with the depth of the thermocline.

The seasonal areal maximum of chlorophyll a phytoplankton biomass occurred in winter in Lake Tarawera, following the onset of whole lake mixing. This increase was preceded by high (32  g C L-1 h-1) carbon uptakes in in situ 13C surface incubations and increase in total phosphorus concentrations in surface waters.  Lake mixing may redistribute nutrients throughout the water column, and may also alleviate light limitation.  This is because the euphotic depth (25 - 30 m) is approximately half the average lake depth (55 m), so during lake mixing phytoplankton cells are in the euphotic zone half of the time.  The simultaneous increase in nutrients and light is likely to support the observed higher phytoplankton productivity and biomass in winter. 
Though Lake Tarawera is oligotrophic, surface blooms of cyanobacteria, occur from time to time.  In situ incubations of phytoplankton with excess nutrients added, showed that nitrogen was the nutrient most limiting to phytoplankton growth, and ratios of TN:TP from lake water samples also indicated that nitrogen was more likely to be limiting than phosphorus.  Acetylene reduction assays, carried out, in situ, during three shoreline bloom events over a two year period confirmed the presence of nitrogen fixation.  Nitrogen fixation followed a daily pattern, with highest rates of 40 nmol (106 heterocysts) -1 hr-1 at midday.  Though ratios of TN:TP in surface water samples were lowest during winter mixing, surface blooms were only identified in late autumn, toward the end of the stratified period.  Some of the highest concentrations of inorganic nitrogen in surface waters coincided with the occurrence of nitrogen fixation and may have been a consequence of nitrogen leaking from heterocysts.  The overall contribution nitrogen fixation to the lake nutrient budget is highly uncertain, but preliminary estimates attribute between 0.04% and 8% of 'new' nitrogen inputs to nitrogen fixation in Lake Tarawera.

text: Phytoplankton dynamics in Lake Tarawera This study examined the dynamics of phytoplankton populations in deep (maximum depth 84 m), monomictic, oligotrophic Lake Tarawera in the Rotorua lakes district of New Zealand.  Specifically, components of the annual phytoplankton assemblage; a summer deep chlorophyll maximum, a winter areal phytoplankton maximum and nitrogen fixation in ephemeral cyanobacterial surface blooms, are investigated.

Alternate hypotheses for the formation of the observed diatom deep chlorophyll maximum (DCM) in Lake Tarawera were tested.  (1) That growth rates of phytoplankton are higher in the metalimnion than in the epilimnion, perhaps supported by higher concentrations of nutrients in the metalimnion. (2) That the DCM is formed by phytoplankton becoming entrained in more turbulent water at the thermocline and persists while the depth of the thermocline remains above the euphotic depth. 

Lake water concentrations of total inorganic nitrogen and total phosphorus measured monthly over a year at 10 m depth intervals at a mid lake station, provided no evidence that the metalimnion had higher nutrient concentrations than those in the epilimnion.  The productivity of DCM phytoplankton and epilimnion phytoplankton (5 m) was measured c. monthly over the six months that the DCM was present with in situ 13C uptake incubations.  Productivity was consistently higher in 5 m incubations (c. 5  g C L-1 h-1) than in DCM incubations.  The growth of DCM phytoplankton did not appear to be limited by either nitrogen or phosphorus as in situ incubations, over four days, with single or combined additions of these nutrients did not significantly increase chlorophyll a concentrations.  The depth of the DCM was similar to the depth of the thermocline while the thermocline remained above the euphotic depth, but this relationship ceased as the thermocline deepened in autumn and a DCM was no longer discernable.  Light availability at the thermocline therefore appears to be a key factor in regulating the position and persistence of DCM phytoplankton.  Though other studies have demonstrated higher growth of DCM phytoplankton, these maybe incidental, as all DCM formed by negatively buoyant phytoplankton appear to coincide with the depth of the thermocline.

The seasonal areal maximum of chlorophyll a phytoplankton biomass occurred in winter in Lake Tarawera, following the onset of whole lake mixing. This increase was preceded by high (32  g C L-1 h-1) carbon uptakes in in situ 13C surface incubations and increase in total phosphorus concentrations in surface waters.  Lake mixing may redistribute nutrients throughout the water column, and may also alleviate light limitation.  This is because the euphotic depth (25 - 30 m) is approximately half the average lake depth (55 m), so during lake mixing phytoplankton cells are in the euphotic zone half of the time.  The simultaneous increase in nutrients and light is likely to support the observed higher phytoplankton productivity and biomass in winter. 
Though Lake Tarawera is oligotrophic, surface blooms of cyanobacteria, occur from time to time.  In situ incubations of phytoplankton with excess nutrients added, showed that nitrogen was the nutrient most limiting to phytoplankton growth, and ratios of TN:TP from lake water samples also indicated that nitrogen was more likely to be limiting than phosphorus.  Acetylene reduction assays, carried out, in situ, during three shoreline bloom events over a two year period confirmed the presence of nitrogen fixation.  Nitrogen fixation followed a daily pattern, with highest rates of 40 nmol (106 heterocysts) -1 hr-1 at midday.  Though ratios of TN:TP in surface water samples were lowest during winter mixing, surface blooms were only identified in late autumn, toward the end of the stratified period.  Some of the highest concentrations of inorganic nitrogen in surface waters coincided with the occurrence of nitrogen fixation and may have been a consequence of nitrogen leaking from heterocysts.  The overall contribution nitrogen fixation to the lake nutrient budget is highly uncertain, but preliminary estimates attribute between 0.04% and 8% of 'new' nitrogen inputs to nitrogen fixation in Lake Tarawera.

year: 2009

title: He Māori, He Turi, He Turi, He Māori. Advancing the aspirations of Māori Deaf with their indigenous Connections: A case study

authors: Dunn, Katie Merepaea

subjects: Māori Deaf

abstract: Indigenous peoples consider their connection to whenua (land), whakapapa (genealogy), te reo (language) and tikanga (cultural values) to be an integral part of their worldview (Mead, 2003 & Barlow, 1991).

The identity struggle for indigenous minorities living within a colonised environment has been well documented (Bishop, 1995; Smith G, 1997; Smith L, 1999, & Walker, 2004). The controversies over land, customs, culture and language are major issues to understanding and maintaining one’s own cultural identity and, when considering the Deaf indigenous minorities, the task seems colossal.

When a Māori individual belongs to the hearing majority, the ability to find a place to stand, a connection to one’s turangawaewae (standing place), whakapapa, and marae (village) can be a personal struggle; however, this can often be overcome through a shared experience, through communication at a whānau (family), hapū (sub tribe) and iwi (tribe) level.  However, when the individual is part of a double minority such as the Māori Deaf community, the ability to engage and establish a relationship to enhance their connection to their turangawaewae, can become difficult due to the need to communicate in three different languages: English, Māori and Sign Language.  These language issues can create barriers for the Deaf, Māori and hearing communities at a whānau, hapū and iwi level.

This thesis examines a series of workshops created to advance the indigenous connections and understanding within the Māori Deaf community and Te Ao Māori (Māori worldview). It explores how the integration of the Deaf and hearing, indigenous Māori language and New Zealand Sign Language along with practical workshops can assist the aspirations of Māori Deaf within the advancement of Te Ao Māori and Te Reo Māori.  Within this thesis I will undertake a series of interviews with participants who are at the forefront of the Māori Deaf community. A suggestion of moving forward to address the needs of the Māori Deaf community within the desire to connect to their Māori language and customs is also offered within this thesis.

text: He Māori, He Turi, He Turi, He Māori. Advancing the aspirations of Māori Deaf with their indigenous Connections: A case study Indigenous peoples consider their connection to whenua (land), whakapapa (genealogy), te reo (language) and tikanga (cultural values) to be an integral part of their worldview (Mead, 2003 & Barlow, 1991).

The identity struggle for indigenous minorities living within a colonised environment has been well documented (Bishop, 1995; Smith G, 1997; Smith L, 1999, & Walker, 2004). The controversies over land, customs, culture and language are major issues to understanding and maintaining one’s own cultural identity and, when considering the Deaf indigenous minorities, the task seems colossal.

When a Māori individual belongs to the hearing majority, the ability to find a place to stand, a connection to one’s turangawaewae (standing place), whakapapa, and marae (village) can be a personal struggle; however, this can often be overcome through a shared experience, through communication at a whānau (family), hapū (sub tribe) and iwi (tribe) level.  However, when the individual is part of a double minority such as the Māori Deaf community, the ability to engage and establish a relationship to enhance their connection to their turangawaewae, can become difficult due to the need to communicate in three different languages: English, Māori and Sign Language.  These language issues can create barriers for the Deaf, Māori and hearing communities at a whānau, hapū and iwi level.

This thesis examines a series of workshops created to advance the indigenous connections and understanding within the Māori Deaf community and Te Ao Māori (Māori worldview). It explores how the integration of the Deaf and hearing, indigenous Māori language and New Zealand Sign Language along with practical workshops can assist the aspirations of Māori Deaf within the advancement of Te Ao Māori and Te Reo Māori.  Within this thesis I will undertake a series of interviews with participants who are at the forefront of the Māori Deaf community. A suggestion of moving forward to address the needs of the Māori Deaf community within the desire to connect to their Māori language and customs is also offered within this thesis.

year: 2012