title: Constructive approaches to quasi-Monte Carlo methods for multiple integration

authors: Kuo, Frances Y.

abstract: Recently, quasi-Monte Carlo methods have been successfully used for approximating multiple integrals in hundreds of dimensions in mathematical finance, and were significantly more efficient than Monte Carlo methods.
To understand the apparent success of quasi-Monte Carlo methods for multiple integration, one popular approach is to study worst-case error bounds in weighted function spaces in which the importance of the variables is moderated by some sequences of weights. Ideally, a family of quasi-Monte Carlo methods in some weighted function space should be strongly tractable. Strong tractability means that the minimal number of quadrature points n needed to reduce the initial error by a factor of ε is bounded by a polynomial in ε⁻¹ independently of the dimension d. Several recent publications show the existence of lattice rules that satisfy the strong tractability error bounds in weighted Korobov spaces of periodic integrands and weighted Sobolev spaces of non-periodic integrands. However, those results were non-constructive and thus give no clues as to how to actually construct these lattice rules.
In this thesis, we focus on the construction of quasi-Monte Carlo methods that are strongly tractable. We develop and justify algorithms for the construction of lattice rules that achieve strong tractability error bounds in weighted Korobov and Sobolev spaces. The parameters characterizing these lattice rules are found ‘component-by-component’: the (d + 1)-th components are obtained by successive 1-dimensional searches, with the previous d components kept unchanged. The cost of these algorithms vary from O(nd²) to O(n³d²) operations. With currently available technology, they allow construction of rules easily with values of n up to several million and dimensions d up to several hundred.

text: Constructive approaches to quasi-Monte Carlo methods for multiple integration Recently, quasi-Monte Carlo methods have been successfully used for approximating multiple integrals in hundreds of dimensions in mathematical finance, and were significantly more efficient than Monte Carlo methods.
To understand the apparent success of quasi-Monte Carlo methods for multiple integration, one popular approach is to study worst-case error bounds in weighted function spaces in which the importance of the variables is moderated by some sequences of weights. Ideally, a family of quasi-Monte Carlo methods in some weighted function space should be strongly tractable. Strong tractability means that the minimal number of quadrature points n needed to reduce the initial error by a factor of ε is bounded by a polynomial in ε⁻¹ independently of the dimension d. Several recent publications show the existence of lattice rules that satisfy the strong tractability error bounds in weighted Korobov spaces of periodic integrands and weighted Sobolev spaces of non-periodic integrands. However, those results were non-constructive and thus give no clues as to how to actually construct these lattice rules.
In this thesis, we focus on the construction of quasi-Monte Carlo methods that are strongly tractable. We develop and justify algorithms for the construction of lattice rules that achieve strong tractability error bounds in weighted Korobov and Sobolev spaces. The parameters characterizing these lattice rules are found ‘component-by-component’: the (d + 1)-th components are obtained by successive 1-dimensional searches, with the previous d components kept unchanged. The cost of these algorithms vary from O(nd²) to O(n³d²) operations. With currently available technology, they allow construction of rules easily with values of n up to several million and dimensions d up to several hundred.

year: 2002

title: Electrolytic purification of water

authors: Mathieson, Grant Alexander

subjects: Electrolytic

abstract: This thesis develops the concept of an in situ electrolytic processor, a machine with electrochemical functions that purifies aqueous fluids at the point of production, whether from a bore water supply or effluent from a tannery. Where the contaminants in an effluent are useful they are separated in a specialised electrolyser for re-use in the process that produced the original effluent. The value in doing this exceeds the cost of electrolytic processing for tannery effluent. The functions of an electrolytic purifier were resolved into: flotation by bubbles, flocculation by corrosion of aluminium anodes, electrowinning by cathodic plating, disinfection, oxidation-reduction and pH modification. Improved understanding of the control of these functions has led to the ability to design better electrolysers because the functions were combined in a form that was appropriate to the required purification process. A link between extra-faradic corrosion of an aluminium anode and pH modification is postulated.

Electrochemical principles were used as the basis for development of real processor models. These models were tested using bore water, cooling tower fluid, virus contaminated water, laundry water, municipal waste water, landfill leachate and pulp mill effluent.

The most effective model, designed during the course of the project and described as the Flume, incorporated a novel corroding anode composed of thin pieces of aluminium, water flow in a cathodic flume, and a cheap water-porous membrane to separate the electrolyte into anolyte and catholyte. The novel anode was designed to improve clearance of corrosion products by maintaining a fast flow speed in proximity to the zone of anodic corrosion. The Flume model was used in an extensive test at a tannery. Greater than 90% of chromium in tannery effluent was removed by a combination of electroflocculation and electroflotation, at a lower cost than by treatment using standard chemical flocculent, using a side-stream Flume processor at a tannery. A smaller scale Flume model was used to test mechanisms of treatment in the laboratory using synthetic tannery effluent.

When treating alkaline effluent, the separating membrane in the Flume model enabled production of alkali at the cathode and production of acid at the anode. This was used for pH modification of effluent and, where the majority of the flow was anolyte, was able to produce a catholyte of pH greater than 13 from a wide range of inflow pH. The caustic catholyte is a valuable by-product of the electrolytic processing, especially when the upstream processes require net input of alkali (as is the case at a tannery or kraft pulp mill) and more generally because downstream biological treatment processes benefit from receiving neutralised effluent.

The degree of pH moderation of the whole outflow compared to the inflow was found to be controllable by adjustment of cell voltage. This effect enables treatment of effluent with variable pH.

Optimisation of an electrolyser for energy recovery, by both reduction of electrode over-potentials and electrolyte resistance, was incorporated in the full-scale designs. Based on a feasible cell voltage of 5 V, 20% recovery of the energy input is expected.

text: Electrolytic purification of water This thesis develops the concept of an in situ electrolytic processor, a machine with electrochemical functions that purifies aqueous fluids at the point of production, whether from a bore water supply or effluent from a tannery. Where the contaminants in an effluent are useful they are separated in a specialised electrolyser for re-use in the process that produced the original effluent. The value in doing this exceeds the cost of electrolytic processing for tannery effluent. The functions of an electrolytic purifier were resolved into: flotation by bubbles, flocculation by corrosion of aluminium anodes, electrowinning by cathodic plating, disinfection, oxidation-reduction and pH modification. Improved understanding of the control of these functions has led to the ability to design better electrolysers because the functions were combined in a form that was appropriate to the required purification process. A link between extra-faradic corrosion of an aluminium anode and pH modification is postulated.

Electrochemical principles were used as the basis for development of real processor models. These models were tested using bore water, cooling tower fluid, virus contaminated water, laundry water, municipal waste water, landfill leachate and pulp mill effluent.

The most effective model, designed during the course of the project and described as the Flume, incorporated a novel corroding anode composed of thin pieces of aluminium, water flow in a cathodic flume, and a cheap water-porous membrane to separate the electrolyte into anolyte and catholyte. The novel anode was designed to improve clearance of corrosion products by maintaining a fast flow speed in proximity to the zone of anodic corrosion. The Flume model was used in an extensive test at a tannery. Greater than 90% of chromium in tannery effluent was removed by a combination of electroflocculation and electroflotation, at a lower cost than by treatment using standard chemical flocculent, using a side-stream Flume processor at a tannery. A smaller scale Flume model was used to test mechanisms of treatment in the laboratory using synthetic tannery effluent.

When treating alkaline effluent, the separating membrane in the Flume model enabled production of alkali at the cathode and production of acid at the anode. This was used for pH modification of effluent and, where the majority of the flow was anolyte, was able to produce a catholyte of pH greater than 13 from a wide range of inflow pH. The caustic catholyte is a valuable by-product of the electrolytic processing, especially when the upstream processes require net input of alkali (as is the case at a tannery or kraft pulp mill) and more generally because downstream biological treatment processes benefit from receiving neutralised effluent.

The degree of pH moderation of the whole outflow compared to the inflow was found to be controllable by adjustment of cell voltage. This effect enables treatment of effluent with variable pH.

Optimisation of an electrolyser for energy recovery, by both reduction of electrode over-potentials and electrolyte resistance, was incorporated in the full-scale designs. Based on a feasible cell voltage of 5 V, 20% recovery of the energy input is expected.

year: 2006

title: Institutional Racism and the Dynamics of Privilege in Public Health

authors: Came, Heather

subjects: Institutional racism

abstract: Institutional racism, a pattern of differential access to material resources and power determined by race, advantages one sector of the population while disadvantaging another. Such racism is not only about conspicuous acts of violence but can be carried in the hold of mono-cultural perspectives. Overt state violation of principles contributes to the backdrop against which much less overt yet insidious violations occur. New Zealand health policy is one such mono-cultural domain. It is dominated by western bio-medical discourses that preclude and under-value Māori,  the indigenous peoples of this land, in the conceptualisation, structure, content, and processes of health policies, despite Te Tiriti o Waitangi  guarantees to protect Māori interests.

Since the 1980s, the Department of Health has committed to honouring the Treaty of Waitangi as the founding document of Māori-settler relationships and governance arrangements. Subsequent Waitangi Tribunal reports, produced by an independent Commission of Inquiry have documented the often-illegal actions of successive governments advancing the interests of Pākehā  at the expense of Māori. Institutional controls have not prevented inequities between Māori and non-Māori across a plethora of social and economic indicators.

Activist scholars work to expose and transform perceived inequities. My research interest lies in how Crown Ministers and officials within the public health sector practice institutional racism and privilege and how it can be transformed. Through dialogue with Māori working within the health sector, fuelled by critical analysis and strategic advice from a research whānau (family) of Māori health leaders and a Pākehā Tiriti worker, and embracing the traditions of feminist and critical race theory  I provide evidence of racism that can invoke strong emotional reactions. More disturbing is its normalisation to nigh imperceptibility within ones personal and professional life. The exposure of racism as a socially created phenomenon is a strength of the research presented here. 

My action orientation is my ethical response. Honouring Te Tiriti o Waitangi is a pathway to transforming racism. Such change is likely to be resisted by the Pākehā majority. This anticipated resistance is not a credible reason to weaken responsibility for such necessary change. Transforming institutional racism needs to be driven by senior managers, professional bodies, unions, and by communities. Policies, practices and leadership that enable institutional racism need to be systematically eliminated from the health sector. Crown officials must be supported to strengthen their professional accountabilities and to embrace ethical bicultural practice. Greater transparency could enable more effective monitoring of Crown behaviour and support transformed practice.

text: Institutional Racism and the Dynamics of Privilege in Public Health Institutional racism, a pattern of differential access to material resources and power determined by race, advantages one sector of the population while disadvantaging another. Such racism is not only about conspicuous acts of violence but can be carried in the hold of mono-cultural perspectives. Overt state violation of principles contributes to the backdrop against which much less overt yet insidious violations occur. New Zealand health policy is one such mono-cultural domain. It is dominated by western bio-medical discourses that preclude and under-value Māori,  the indigenous peoples of this land, in the conceptualisation, structure, content, and processes of health policies, despite Te Tiriti o Waitangi  guarantees to protect Māori interests.

Since the 1980s, the Department of Health has committed to honouring the Treaty of Waitangi as the founding document of Māori-settler relationships and governance arrangements. Subsequent Waitangi Tribunal reports, produced by an independent Commission of Inquiry have documented the often-illegal actions of successive governments advancing the interests of Pākehā  at the expense of Māori. Institutional controls have not prevented inequities between Māori and non-Māori across a plethora of social and economic indicators.

Activist scholars work to expose and transform perceived inequities. My research interest lies in how Crown Ministers and officials within the public health sector practice institutional racism and privilege and how it can be transformed. Through dialogue with Māori working within the health sector, fuelled by critical analysis and strategic advice from a research whānau (family) of Māori health leaders and a Pākehā Tiriti worker, and embracing the traditions of feminist and critical race theory  I provide evidence of racism that can invoke strong emotional reactions. More disturbing is its normalisation to nigh imperceptibility within ones personal and professional life. The exposure of racism as a socially created phenomenon is a strength of the research presented here. 

My action orientation is my ethical response. Honouring Te Tiriti o Waitangi is a pathway to transforming racism. Such change is likely to be resisted by the Pākehā majority. This anticipated resistance is not a credible reason to weaken responsibility for such necessary change. Transforming institutional racism needs to be driven by senior managers, professional bodies, unions, and by communities. Policies, practices and leadership that enable institutional racism need to be systematically eliminated from the health sector. Crown officials must be supported to strengthen their professional accountabilities and to embrace ethical bicultural practice. Greater transparency could enable more effective monitoring of Crown behaviour and support transformed practice.

year: 2012