title: Induced subarrays of Latin squares without repeated symbols

authors: Abel, R. Julian R.

subjects: Latin square

abstract: We show that for any Latin square L of order 2m, we can partition the rows and columns of L into pairs so that at most (m+3)/2 of the 2x2 subarrays induced contain a repeated symbol. We conjecture that any Latin square of order 2m (where m ≥ 2, with exactly five transposition class exceptions of order 6) has such a partition so that every 2x2 subarray induced contains no repeated symbol. We verify this conjecture by computer when m ≤ 4.

text: Induced subarrays of Latin squares without repeated symbols We show that for any Latin square L of order 2m, we can partition the rows and columns of L into pairs so that at most (m+3)/2 of the 2x2 subarrays induced contain a repeated symbol. We conjecture that any Latin square of order 2m (where m ≥ 2, with exactly five transposition class exceptions of order 6) has such a partition so that every 2x2 subarray induced contains no repeated symbol. We verify this conjecture by computer when m ≤ 4.

year: 2013

title: Meaningful Witnessing in the United States, India & New Zealand: The Possibility Space for Digital Video Within Human Rights, Protest Movements and Activist Practices

authors: Lenzner, Benjamin

subjects: digital video

abstract: This dissertation examines the emergence of digital video practices rooted in human rights, social justice issues and protest movements through a number of select case studies in the United States, India and New Zealand. This project analyzes and critiques the formation of digital video practices through the lens of Manuel DeLanda’s interpretation of assemblage theory. Examining interactions between crucial elements present in a possibility space that aid in the cultivation and assembling of budding forms of digital video, this study considers the implications in the relationships between both material and expressive qualities of these assemblings. The central argument of this thesis asserts that digital video practices centered on human rights, social justice and protest movements require adaptable linkages between supportive structures, creative capacities and digital video technologies in order to produce sustainable and creative digital video practices buttressed by documentary agendas that fuel their dynamic evolution.

My research seeks to engage with the complexities of agency and technology and examines their significance in different contexts by providing a constructive outlet for practitioners to share the process behind their methods in order to offer insight into their creative workflow. Digital video technologies are proliferating at a rapid pace, yet very few video practices have formed that suggest linkages to documentary traditions. One can bear witness, yet to traverse video documentation in order to create a rhetorical argument of meaningful witnessing is a complex process that requires more than easy access to mobile video tools connected to the Internet. The case studies analyzed in these three democratic nations support the argument threaded throughout the project; digital video practices have the potential to thrive, albeit in pockets where formal or informal support systems are present and through assemblages where digital video technologies are constantly being adapted and an investment in human capital is paramount to the privileging of digital video tools or online platforms. Case studies that focus on individual practices in New York City and New Zealand reinforce the difficulties practitioners face when attempting to cultivate video practices without supportive structures. Comparatively with other case studies in India and New York, individual practices with long-term organizational support navigate challenges and re-assemble their practices in order to remain sustainable and influential.

This study also engages with assemblage theory in the context of documentary history and contemporary digital video practices and reassesses the historic relationship between emerging photographic, film and video tools and the lens based practitioners that harness these apparatuses for documentary purposes. Like assemblings themselves, these creative associations are never smooth at their inception, but require adaptable solutions and adjustable reassemblings in order to maintain the potential for sustainable practices to develop and flourish. This dissertation argues that as digital video practices continue to evolve, they have the potential to redefine creative approaches to documentary media and the opportunity to confront historic traditions of the documentary form.

text: Meaningful Witnessing in the United States, India & New Zealand: The Possibility Space for Digital Video Within Human Rights, Protest Movements and Activist Practices This dissertation examines the emergence of digital video practices rooted in human rights, social justice issues and protest movements through a number of select case studies in the United States, India and New Zealand. This project analyzes and critiques the formation of digital video practices through the lens of Manuel DeLanda’s interpretation of assemblage theory. Examining interactions between crucial elements present in a possibility space that aid in the cultivation and assembling of budding forms of digital video, this study considers the implications in the relationships between both material and expressive qualities of these assemblings. The central argument of this thesis asserts that digital video practices centered on human rights, social justice and protest movements require adaptable linkages between supportive structures, creative capacities and digital video technologies in order to produce sustainable and creative digital video practices buttressed by documentary agendas that fuel their dynamic evolution.

My research seeks to engage with the complexities of agency and technology and examines their significance in different contexts by providing a constructive outlet for practitioners to share the process behind their methods in order to offer insight into their creative workflow. Digital video technologies are proliferating at a rapid pace, yet very few video practices have formed that suggest linkages to documentary traditions. One can bear witness, yet to traverse video documentation in order to create a rhetorical argument of meaningful witnessing is a complex process that requires more than easy access to mobile video tools connected to the Internet. The case studies analyzed in these three democratic nations support the argument threaded throughout the project; digital video practices have the potential to thrive, albeit in pockets where formal or informal support systems are present and through assemblages where digital video technologies are constantly being adapted and an investment in human capital is paramount to the privileging of digital video tools or online platforms. Case studies that focus on individual practices in New York City and New Zealand reinforce the difficulties practitioners face when attempting to cultivate video practices without supportive structures. Comparatively with other case studies in India and New York, individual practices with long-term organizational support navigate challenges and re-assemble their practices in order to remain sustainable and influential.

This study also engages with assemblage theory in the context of documentary history and contemporary digital video practices and reassesses the historic relationship between emerging photographic, film and video tools and the lens based practitioners that harness these apparatuses for documentary purposes. Like assemblings themselves, these creative associations are never smooth at their inception, but require adaptable solutions and adjustable reassemblings in order to maintain the potential for sustainable practices to develop and flourish. This dissertation argues that as digital video practices continue to evolve, they have the potential to redefine creative approaches to documentary media and the opportunity to confront historic traditions of the documentary form.

year: 2015

title: Ngati Rahiri versus Ngati Tamatera

authors: Hart, Philip

abstract: Conflict between Ngati Tamatera, of Ohinemuri, and Ngati Rahiri, of Te Aroha, was provoked by the latter believing that members of other hapu had received money for the Aroha Block to which they were not entitled. In addition, the two hapu disagreed over the block’s northern boundary. In early 1877 Ngati Rahiri threatened violence and even fired over the heads of several rangatira passing through their land, thereby challenging their right to intrude on it. In response, Ngati Tamatera, with the assistance of Ngati Koi, blocked the road to Te Aroha and also the Waihou River against Ngati Rahiri, although they permitted Pakeha to pass. Pakeha took a relaxed attitude to the conflict, not expecting any real battles occurring during a squabble they understood to have been caused by members of an inferior hapu having their names wrongly included in Crown grants.
After Ngati Tamatera erected two small and unimpressive pa to block both road and river, Ngati Rahiri retaliated by constructing a similarly unimpressive pa at Omahu, their settlement at Te Aroha. Apart from much posturing, the only actions taken were Ngati Tamatera sending back to Omahu an aged woman who had come down the river in a canoe and Ngati Rahiri stealing pigs and peaches and firing shots near a settlement. The Native Minister and various officials, notably James Mackay, intervened to resolve the conflict, which was ended with a reconciliation initiated by Ngati Tamatera and formalized by a large meeting of both hapu at Omahu.
Once this quarrel was settled, negotiations to enable the Crown to purchase the Aroha Block were resumed.

text: Ngati Rahiri versus Ngati Tamatera Conflict between Ngati Tamatera, of Ohinemuri, and Ngati Rahiri, of Te Aroha, was provoked by the latter believing that members of other hapu had received money for the Aroha Block to which they were not entitled. In addition, the two hapu disagreed over the block’s northern boundary. In early 1877 Ngati Rahiri threatened violence and even fired over the heads of several rangatira passing through their land, thereby challenging their right to intrude on it. In response, Ngati Tamatera, with the assistance of Ngati Koi, blocked the road to Te Aroha and also the Waihou River against Ngati Rahiri, although they permitted Pakeha to pass. Pakeha took a relaxed attitude to the conflict, not expecting any real battles occurring during a squabble they understood to have been caused by members of an inferior hapu having their names wrongly included in Crown grants.
After Ngati Tamatera erected two small and unimpressive pa to block both road and river, Ngati Rahiri retaliated by constructing a similarly unimpressive pa at Omahu, their settlement at Te Aroha. Apart from much posturing, the only actions taken were Ngati Tamatera sending back to Omahu an aged woman who had come down the river in a canoe and Ngati Rahiri stealing pigs and peaches and firing shots near a settlement. The Native Minister and various officials, notably James Mackay, intervened to resolve the conflict, which was ended with a reconciliation initiated by Ngati Tamatera and formalized by a large meeting of both hapu at Omahu.
Once this quarrel was settled, negotiations to enable the Crown to purchase the Aroha Block were resumed.

year: 2016