title: Complete sets of invariants for dynamical systems that admit a separation of variables

authors: Kalnins, Ernie G.

subjects: Mathematics

abstract: Consider a classical Hamiltonian H in n dimensions consisting of a kinetic energy term plus a potential. If the associated Hamilton–Jacobi equation admits an orthogonal separation of variables, then it is possible to generate algorithmically a canonical basis Q, P where P1 = H, P2, ,Pn are the other second-order constants of the motion associated with the separable coordinates, and {Qi,Qj} = {Pi,Pj} = 0, {Qi,Pj} =  ij. The 2n–1 functions Q2, ,Qn,P1, ,Pn form a basis for the invariants. We show how to determine for exactly which spaces and potentials the invariant Qj is a polynomial in the original momenta. We shed light on the general question of exactly when the Hamiltonian admits a constant of the motion that is polynomial in the momenta. For n = 2 we go further and consider all cases where the Hamilton–Jacobi equation admits a second-order constant of the motion, not necessarily associated with orthogonal separable coordinates, or even separable coordinates at all. In each of these cases we construct an additional constant of the motion.

text: Complete sets of invariants for dynamical systems that admit a separation of variables Consider a classical Hamiltonian H in n dimensions consisting of a kinetic energy term plus a potential. If the associated Hamilton–Jacobi equation admits an orthogonal separation of variables, then it is possible to generate algorithmically a canonical basis Q, P where P1 = H, P2, ,Pn are the other second-order constants of the motion associated with the separable coordinates, and {Qi,Qj} = {Pi,Pj} = 0, {Qi,Pj} =  ij. The 2n–1 functions Q2, ,Qn,P1, ,Pn form a basis for the invariants. We show how to determine for exactly which spaces and potentials the invariant Qj is a polynomial in the original momenta. We shed light on the general question of exactly when the Hamiltonian admits a constant of the motion that is polynomial in the momenta. For n = 2 we go further and consider all cases where the Hamilton–Jacobi equation admits a second-order constant of the motion, not necessarily associated with orthogonal separable coordinates, or even separable coordinates at all. In each of these cases we construct an additional constant of the motion.

year: 2002-07

title: Interface design strategies for computer-assisted speech transcription

authors: Luz, Saturnino

subjects: computer science

abstract: A set of user interface design techniques for computer-assisted speech transcription are presented and evaluated with respect to task performance and usability. These techniques include error-correction mechanisms which originated in dictation systems and audio editors as well as new techniques developed by us which exploit specific characteristics of existing speech recognition technologies in order to facilitate transcription in settings that typically yield considerable recognition inaccuracy, such as when the speech to be transcribed was produced by different speakers. In particular, we describe a mechanism for dynamic propagation of user feedback which progressively adapts the system to different speakers and lexical contexts. Results of usability and performance evaluation trials indicate that feedback propagation, menu-based correction coupled with keyboard interaction and text-driven audio playback are positively perceived by users and result in improved transcript accuracy.

text: Interface design strategies for computer-assisted speech transcription A set of user interface design techniques for computer-assisted speech transcription are presented and evaluated with respect to task performance and usability. These techniques include error-correction mechanisms which originated in dictation systems and audio editors as well as new techniques developed by us which exploit specific characteristics of existing speech recognition technologies in order to facilitate transcription in settings that typically yield considerable recognition inaccuracy, such as when the speech to be transcribed was produced by different speakers. In particular, we describe a mechanism for dynamic propagation of user feedback which progressively adapts the system to different speakers and lexical contexts. Results of usability and performance evaluation trials indicate that feedback propagation, menu-based correction coupled with keyboard interaction and text-driven audio playback are positively perceived by users and result in improved transcript accuracy.

year: 2008

title: The New Zealand Wars Documentary Series: Discursive Struggle and Cultural Memory.

authors: Perrott, Lisa

subjects: Television Documentary

abstract: The 1998 television broadcast of The New Zealand Wars documentary series was a significant public event, which had a major impact on a broad range of communities and individuals in Aotearoa New Zealand. This popular television history engaged with issues of historical veracity, race, culture and nationhood and challenged previously dominant discourses associated with these concepts. In doing so, it provoked heated debate, and a re-imagining of 'nation', and also opened up spaces for alternative ways of engaging with historical narrative. 

Informed by post-colonialism, cultural studies and cultural memory, this thesis explores the discursive and affective role of The New Zealand Wars, as it has operated within the turbulent climate of 1990s New Zealand cultural relations. This catalytic function is described in this thesis as a phenomenon of a television series shaped by, whilst also intervening in, processes of cultural colonisation and decolonisation. 

While both of these processes involve the transmission of discourse via cultural forms, the act of cultural decolonisation requires, in addition, the convergence of a number of agents (people and communities, discursive and memory resources) and circumstances, within particular contextual conditions. Such a convergence provided the conditions for the discursive synthesis, which shaped the production, construction and reception of this series. 

The role of audio-visual media (and specifically television documentary) in transmitting cultural memory is significant as it enables the flow of memory through channels or forms (such as visual, oral and aural traditions) that can bring about new perspectives and critical reflections upon colonial discourse and dominant concepts of nation and culture. In addition to these social and intellectual processes of audience engagement, this thesis argues that experiential and affective dimensions of cultural memory can (in these specific circumstances) open up radical spaces, offering the potential for generating awareness and sparking political action. 

These issues are explored through a tripartite analysis of the production context, construction and reception of The New Zealand Wars series. The integration of these three phases of analysis has generated a number of insights into the potential of audio-visual forms, including their producers and audiences, to participate in the negotiation of, and resistance to, colonial discourse. Such insights serve to challenge taken-for-granted constructions of nation and history, and suggest the increasing relevance of alternative concepts such as community-building and cultural memory. Ultimately, this thesis argues that television documentary can serve as a prime site for the articulation of these concepts. The New Zealand Wars serves as a case study, which demonstrates both the potential of this site, and the significance of the social-historical and cultural context in framing this series.

text: The New Zealand Wars Documentary Series: Discursive Struggle and Cultural Memory. The 1998 television broadcast of The New Zealand Wars documentary series was a significant public event, which had a major impact on a broad range of communities and individuals in Aotearoa New Zealand. This popular television history engaged with issues of historical veracity, race, culture and nationhood and challenged previously dominant discourses associated with these concepts. In doing so, it provoked heated debate, and a re-imagining of 'nation', and also opened up spaces for alternative ways of engaging with historical narrative. 

Informed by post-colonialism, cultural studies and cultural memory, this thesis explores the discursive and affective role of The New Zealand Wars, as it has operated within the turbulent climate of 1990s New Zealand cultural relations. This catalytic function is described in this thesis as a phenomenon of a television series shaped by, whilst also intervening in, processes of cultural colonisation and decolonisation. 

While both of these processes involve the transmission of discourse via cultural forms, the act of cultural decolonisation requires, in addition, the convergence of a number of agents (people and communities, discursive and memory resources) and circumstances, within particular contextual conditions. Such a convergence provided the conditions for the discursive synthesis, which shaped the production, construction and reception of this series. 

The role of audio-visual media (and specifically television documentary) in transmitting cultural memory is significant as it enables the flow of memory through channels or forms (such as visual, oral and aural traditions) that can bring about new perspectives and critical reflections upon colonial discourse and dominant concepts of nation and culture. In addition to these social and intellectual processes of audience engagement, this thesis argues that experiential and affective dimensions of cultural memory can (in these specific circumstances) open up radical spaces, offering the potential for generating awareness and sparking political action. 

These issues are explored through a tripartite analysis of the production context, construction and reception of The New Zealand Wars series. The integration of these three phases of analysis has generated a number of insights into the potential of audio-visual forms, including their producers and audiences, to participate in the negotiation of, and resistance to, colonial discourse. Such insights serve to challenge taken-for-granted constructions of nation and history, and suggest the increasing relevance of alternative concepts such as community-building and cultural memory. Ultimately, this thesis argues that television documentary can serve as a prime site for the articulation of these concepts. The New Zealand Wars serves as a case study, which demonstrates both the potential of this site, and the significance of the social-historical and cultural context in framing this series.

year: 2007