title: Latin squares with no transversals

authors: Cavenagh, Nicholas J.

subjects: Science & Technology

abstract: Ak-plex in a latin square of ordernis a selection of kn entries that includes k representatives from each row and column and k occurrences of each symbol.  A 1-plex is also known as a transversal.
It is well known that if n is even then Bₙ,  the addition table for the integers modulo n,  possesses no transversals.  We show that there are a great many latin squares that are similar to Bₙ and have no transversal.  As a consequence, the number of species of transversal-free latin squares is shown to be at least nⁿ³⁼²⁽¹⁼²ᵒ⁽¹⁾ for even n→∞.
We also produce various constructions for latin squares that have no transversal but do have a k-plex for some odd k >1.  We prove a 2002 conjecture of the second author that for all even orders n >4 there is a latin square of order n that contains a 3-plex but no transversal.  We also show that for odd k and m≥2, there exists a latin square of order 2km with a k-plex but no k'-plex for odd k'< k.

text: Latin squares with no transversals Ak-plex in a latin square of ordernis a selection of kn entries that includes k representatives from each row and column and k occurrences of each symbol.  A 1-plex is also known as a transversal.
It is well known that if n is even then Bₙ,  the addition table for the integers modulo n,  possesses no transversals.  We show that there are a great many latin squares that are similar to Bₙ and have no transversal.  As a consequence, the number of species of transversal-free latin squares is shown to be at least nⁿ³⁼²⁽¹⁼²ᵒ⁽¹⁾ for even n→∞.
We also produce various constructions for latin squares that have no transversal but do have a k-plex for some odd k >1.  We prove a 2002 conjecture of the second author that for all even orders n >4 there is a latin square of order n that contains a 3-plex but no transversal.  We also show that for odd k and m≥2, there exists a latin square of order 2km with a k-plex but no k'-plex for odd k'< k.

year: 2017

title: Dogs' scent detection performance with rapidly changing targets

authors: Chia, Maria Shue Ying

abstract: Scent detection dogs trained to detect one target scent are sometimes needed to detect a different target. Recent studies have demonstrated that scent detection animals can be trained to detect multiple scents simultaneously. However, in some cases, it may be problematic if the dogs indicate on previous targets. Therefore, it would be useful to know how quickly they can learn to detect new target scents, and not to indicate on previously trained target scents. The aim of this study was to evaluate dogs’ ability to learn to detect new target scents while simultaneously rejecting all previously trained target scents. Firstly, five pet dogs were trained to detect a training scent (amyl acetate) using an automated apparatus. The dogs were then required to detect a four new target scents within four phases. Target scents were treated as non-target scents in all subsequent phases; indications on previously trained target scents were not reinforced. Non-target scents in each phase consisted of three randomly selected chemicals that were presented in a randomised rotation. The dogs were required to complete a phase with one target and meet the criteria of more than 80% for correct indication and correct rejection responses, without performing an indication response more than once on the previous target scent for four out of five sessions. The results of the experiment demonstrated that (1) the dogs were able to successfully discriminate between the specified target scent and all non-target scents within each phase; (2) the persistence of indication behaviour on previously trained target scents decreased more rapidly with each phase; and (3) there was a re-emergence of indication responses when each previously trained target scent was presented after extinction conditions. In summary, the present study demonstrates that dogs can be retrained to indicate on new targets and reject previous targets. The learning processes associated with the dogs learning to indicate on new targets, and learning not to indicate on previous target scents must both be considered. These results have significant practical implications and it is hoped that the they will improve our ability to employ individual scent-detection animals to find multiple targets.

text: Dogs' scent detection performance with rapidly changing targets Scent detection dogs trained to detect one target scent are sometimes needed to detect a different target. Recent studies have demonstrated that scent detection animals can be trained to detect multiple scents simultaneously. However, in some cases, it may be problematic if the dogs indicate on previous targets. Therefore, it would be useful to know how quickly they can learn to detect new target scents, and not to indicate on previously trained target scents. The aim of this study was to evaluate dogs’ ability to learn to detect new target scents while simultaneously rejecting all previously trained target scents. Firstly, five pet dogs were trained to detect a training scent (amyl acetate) using an automated apparatus. The dogs were then required to detect a four new target scents within four phases. Target scents were treated as non-target scents in all subsequent phases; indications on previously trained target scents were not reinforced. Non-target scents in each phase consisted of three randomly selected chemicals that were presented in a randomised rotation. The dogs were required to complete a phase with one target and meet the criteria of more than 80% for correct indication and correct rejection responses, without performing an indication response more than once on the previous target scent for four out of five sessions. The results of the experiment demonstrated that (1) the dogs were able to successfully discriminate between the specified target scent and all non-target scents within each phase; (2) the persistence of indication behaviour on previously trained target scents decreased more rapidly with each phase; and (3) there was a re-emergence of indication responses when each previously trained target scent was presented after extinction conditions. In summary, the present study demonstrates that dogs can be retrained to indicate on new targets and reject previous targets. The learning processes associated with the dogs learning to indicate on new targets, and learning not to indicate on previous target scents must both be considered. These results have significant practical implications and it is hoped that the they will improve our ability to employ individual scent-detection animals to find multiple targets.

year: 2020

title: Redefining taonga: The Treaty Principles Bill and its potential impact on the status of te reo Māori

authors: Carter, Wayne Ngahuka

abstract: This thesis explores the potential impact of Aotearoa New Zealand’s proposed Treaty Principles Bill on the recognition and protection of te reo Māori (Māori language) as a taonga under the Treaty of Waitangi. This research examines the redefinition of fundamental Treaty principles as outlined in the bill, specifically addressing important questions concerning how the transition from partnership, protection and participation towards a focus in equal rights might influence both the legal standing and the cultural status of te reo Māori. With a quantitative methodology approach, this study draws from a range of sources, including legislative policies, political documents, historical records, and academic analysis, to evaluate the impacts and risks this bill could impose. A comparative analysis study with international examples of indigenous language protection provides broader insights into the potential effects on Māori language revitalisation efforts and te reo Māori and its status under the 2016 Māori Language Act. Early findings indicate that the Treaty Principles Bill has ignited considerable debate throughout Aotearoa New Zealand, emphasising tensions between traditional interpretations of the Treaty of Waitangi and framework proposed by the Act Party. Māori rights advocates and public debates express worries that the bill could diminish current protection and reduce advancements achieved for te reo Māori as a taonga. Critics argue that redefining these principles might fracture Māori-Crown relationships, possibly weakening differences and impacting New Zealand’s governance and national identity. This debate emphasises the challenging task of restoring New Zealand’s colonial past with its modern goals for fairness and equality. As Parliament reviews this legislation, it is confronted with a crucial decision that will influence the future direction of Aotearoa New Zealand.

text: Redefining taonga: The Treaty Principles Bill and its potential impact on the status of te reo Māori This thesis explores the potential impact of Aotearoa New Zealand’s proposed Treaty Principles Bill on the recognition and protection of te reo Māori (Māori language) as a taonga under the Treaty of Waitangi. This research examines the redefinition of fundamental Treaty principles as outlined in the bill, specifically addressing important questions concerning how the transition from partnership, protection and participation towards a focus in equal rights might influence both the legal standing and the cultural status of te reo Māori. With a quantitative methodology approach, this study draws from a range of sources, including legislative policies, political documents, historical records, and academic analysis, to evaluate the impacts and risks this bill could impose. A comparative analysis study with international examples of indigenous language protection provides broader insights into the potential effects on Māori language revitalisation efforts and te reo Māori and its status under the 2016 Māori Language Act. Early findings indicate that the Treaty Principles Bill has ignited considerable debate throughout Aotearoa New Zealand, emphasising tensions between traditional interpretations of the Treaty of Waitangi and framework proposed by the Act Party. Māori rights advocates and public debates express worries that the bill could diminish current protection and reduce advancements achieved for te reo Māori as a taonga. Critics argue that redefining these principles might fracture Māori-Crown relationships, possibly weakening differences and impacting New Zealand’s governance and national identity. This debate emphasises the challenging task of restoring New Zealand’s colonial past with its modern goals for fairness and equality. As Parliament reviews this legislation, it is confronted with a crucial decision that will influence the future direction of Aotearoa New Zealand.

year: 2025