title: Good lattice rules with a composite number of points based on the product weighted star discrepancy

authors: Joe, Stephen

subjects: mathematics

abstract: Rank-1 lattice rules based on a weighted star discrepancy with weights of a product form have been previously constructed under the assumption that the number of points is prime. Here, we extend these results to the non-prime case. We show that if the weights are summable, there exist lattice rules whose weighted star discrepancy is O(n−1+δ), for any δ > 0, with the implied constant independent of the dimension and the number of lattice points, but dependent on δ and the weights. Then we show that the generating vector of such a rule can be constructed using a component-by-component (CBC) technique. The cost of the CBC construction is analysed in the final part of the paper.

text: Good lattice rules with a composite number of points based on the product weighted star discrepancy Rank-1 lattice rules based on a weighted star discrepancy with weights of a product form have been previously constructed under the assumption that the number of points is prime. Here, we extend these results to the non-prime case. We show that if the weights are summable, there exist lattice rules whose weighted star discrepancy is O(n−1+δ), for any δ > 0, with the implied constant independent of the dimension and the number of lattice points, but dependent on δ and the weights. Then we show that the generating vector of such a rule can be constructed using a component-by-component (CBC) technique. The cost of the CBC construction is analysed in the final part of the paper.

year: 2008

title: Blind deconvolution of depth-of-field limited full-field lidar data by determination of focal parameters

authors: Godbaz, John Peter

subjects: lidar

abstract: We present a new two-stage method for parametric spatially variant blind deconvolution of full-field Amplitude Modulated Continuous Wave lidar image pairs taken at different aperture settings subject to limited depth of field. A Maximum Likelihood based focal parameter determination algorithm uses range information to reblur the image taken with a smaller aperture size to match the large aperture image. This allows estimation of focal parameters without prior calibration of the optical setup and produces blur estimates which have better spatial resolution and less noise than previous depth from defocus (DFD) blur measurement algorithms. We compare blur estimates from the focal parameter determination method to those from Pentland's DFD method, Subbarao's S-Transform method and estimates from range data/the sampled point spread function. In a second stage the estimated focal parameters are applied to deconvolution of total integrated intensity lidar images improving depth of field. We give an example of application to complex domain lidar images and discuss the trade-off between recovered amplitude texture and sharp range estimates.

text: Blind deconvolution of depth-of-field limited full-field lidar data by determination of focal parameters We present a new two-stage method for parametric spatially variant blind deconvolution of full-field Amplitude Modulated Continuous Wave lidar image pairs taken at different aperture settings subject to limited depth of field. A Maximum Likelihood based focal parameter determination algorithm uses range information to reblur the image taken with a smaller aperture size to match the large aperture image. This allows estimation of focal parameters without prior calibration of the optical setup and produces blur estimates which have better spatial resolution and less noise than previous depth from defocus (DFD) blur measurement algorithms. We compare blur estimates from the focal parameter determination method to those from Pentland's DFD method, Subbarao's S-Transform method and estimates from range data/the sampled point spread function. In a second stage the estimated focal parameters are applied to deconvolution of total integrated intensity lidar images improving depth of field. We give an example of application to complex domain lidar images and discuss the trade-off between recovered amplitude texture and sharp range estimates.

year: 2010

title: Kotahi anō te tupuna o te tangata Māori, ko Ranginui e tū nei, ko Papatūānuku e takato nei. Colonisation through Christianity

authors: Wallace, Ritane

subjects: Christianity

abstract: This thesis will look at the role that Christianity and the missionaries played in the colonisation of Māori during the 1800s. With discussion about the colonisation of Aotearoa, it is generally felt within the Christian community that the work of the missionaries and the Crown are separate and therefore the universal belief is that the missionaries are pardoned from the critique of their work here in Aotearoa. However, Christianity throughout history has always been a doorway for the British Empire to enter land that was not their own.
  
It is widely accepted from the viewpoint of Christianity that it holds a religious superiority over all Indigenous people and their religions dating back to Pope Alexander VI and the issuing of the Papal Bull “Inter Caetera” in 1493 to justify Christian European explorers’ claims on land and waterways they allegedly discovered. Christian hegemony shaped missionary views of the ‘other’ and justified the assimilation of Indigenous people into European Christianity. The negative effects of Christianity on Māori far outweigh the positives as mission stations up and down Aotearoa contributed heavily to the loss of language, religion, and land, the three foundational pillars of Māori and other Indigenous peoples around the world.
   
The thesis seeks to hold the missionaries and Christianity to account for its contribution to the colonisation and religious assimilation of Māori into a foreign and unrelated belief system.

text: Kotahi anō te tupuna o te tangata Māori, ko Ranginui e tū nei, ko Papatūānuku e takato nei. Colonisation through Christianity This thesis will look at the role that Christianity and the missionaries played in the colonisation of Māori during the 1800s. With discussion about the colonisation of Aotearoa, it is generally felt within the Christian community that the work of the missionaries and the Crown are separate and therefore the universal belief is that the missionaries are pardoned from the critique of their work here in Aotearoa. However, Christianity throughout history has always been a doorway for the British Empire to enter land that was not their own.
  
It is widely accepted from the viewpoint of Christianity that it holds a religious superiority over all Indigenous people and their religions dating back to Pope Alexander VI and the issuing of the Papal Bull “Inter Caetera” in 1493 to justify Christian European explorers’ claims on land and waterways they allegedly discovered. Christian hegemony shaped missionary views of the ‘other’ and justified the assimilation of Indigenous people into European Christianity. The negative effects of Christianity on Māori far outweigh the positives as mission stations up and down Aotearoa contributed heavily to the loss of language, religion, and land, the three foundational pillars of Māori and other Indigenous peoples around the world.
   
The thesis seeks to hold the missionaries and Christianity to account for its contribution to the colonisation and religious assimilation of Māori into a foreign and unrelated belief system.

year: 2021