title: Cardigan: SDN distributed routing fabric going live at an Internet exchange

authors: Stringer, Jonathan

abstract: Software Defined Networking (SDN) is an active area for network research, with many organizations exploring the opportunities provided by the decoupling of network control from packet forwarding. However, questions remain over the operation of such systems in production. In order to build operational confidence, we built Cardigan -a distributed router using OpenFlow-and deployed it at a public Internet exchange. Cardigan applies a routing as a service abstraction to a RouteFlow controlled IP network in an effort to reduce operational complexity. The implementation and deployment efforts provide insights into the challenges involved with using these technologies, and suggests the viability of mixed device environments despite the limitations of early OpenFlow implementations.

text: Cardigan: SDN distributed routing fabric going live at an Internet exchange Software Defined Networking (SDN) is an active area for network research, with many organizations exploring the opportunities provided by the decoupling of network control from packet forwarding. However, questions remain over the operation of such systems in production. In order to build operational confidence, we built Cardigan -a distributed router using OpenFlow-and deployed it at a public Internet exchange. Cardigan applies a routing as a service abstraction to a RouteFlow controlled IP network in an effort to reduce operational complexity. The implementation and deployment efforts provide insights into the challenges involved with using these technologies, and suggests the viability of mixed device environments despite the limitations of early OpenFlow implementations.

year: 2014

title: Bôcher contractions of conformally superintegrable Laplace equations

authors: Kalnins, Ernie G.

abstract: The explicit solvability of quantum superintegrable systems is due to symmetry, but the symmetry is often “hidden”. The symmetry generators of 2nd order superintegrable systems in 2 dimensions close under commutation to define quadratic algebras, a generalization of Lie algebras. Distinct systems on constant curvature spaces are related by geometric limits, induced by generalized Inönü–Wigner Lie algebra contractions of the symmetry algebras of the underlying spaces. These have physical/geometric implications, such as the Askey scheme for hypergeometric orthogonal polynomials. However, the limits have no satisfactory Lie algebra contraction interpretations for underlying spaces with 1- or 0-dimensional Lie algebras. We show that these systems can be best understood by transforming them to Laplace conformally superintegrable systems, with flat space conformal symmetry group SO(4, ℂ), and using ideas introduced in the 1894 thesis of Bôcher to study separable solutions of the wave equation in terms of roots of quadratic forms. We show that Bôcher’s prescription for coalescing roots of these forms induces contractions of the conformal algebra so(4, ℂ) to itself and yields a mechanism for classifying all Helmholtz superintegrable systems and their limits. In the paperActa Polytechnica, to appear, arXiv:1510.09067], we announced our main findings. This paper provides the proofs and more details.

text: Bôcher contractions of conformally superintegrable Laplace equations The explicit solvability of quantum superintegrable systems is due to symmetry, but the symmetry is often “hidden”. The symmetry generators of 2nd order superintegrable systems in 2 dimensions close under commutation to define quadratic algebras, a generalization of Lie algebras. Distinct systems on constant curvature spaces are related by geometric limits, induced by generalized Inönü–Wigner Lie algebra contractions of the symmetry algebras of the underlying spaces. These have physical/geometric implications, such as the Askey scheme for hypergeometric orthogonal polynomials. However, the limits have no satisfactory Lie algebra contraction interpretations for underlying spaces with 1- or 0-dimensional Lie algebras. We show that these systems can be best understood by transforming them to Laplace conformally superintegrable systems, with flat space conformal symmetry group SO(4, ℂ), and using ideas introduced in the 1894 thesis of Bôcher to study separable solutions of the wave equation in terms of roots of quadratic forms. We show that Bôcher’s prescription for coalescing roots of these forms induces contractions of the conformal algebra so(4, ℂ) to itself and yields a mechanism for classifying all Helmholtz superintegrable systems and their limits. In the paperActa Polytechnica, to appear, arXiv:1510.09067], we announced our main findings. This paper provides the proofs and more details.

year: 2016

title: “It’s becoming part of their knowing”: a study of bicultural development in an early childhood teacher education setting in Aotearoa/New Zealand

authors: Ritchie, Jenny

abstract: This study is an exploration of the implementation of bicultural development within a university-based early childhood teacher education programme in Aotearoa/New Zealand, which can be considered to be a bicultural country (Walker, 1987, p. 221). Bicultural development is a process in line with obligations contained within the Te Tiriti o Waitangi/The Treaty of Waitangi, which are reflected within the New Zealand Ministry of Education’s Revised Statement of Desirable Objectives and Practices (Ministry of Education, 1996a) and the early childhood curriculum, Te Whāriki (Ministry of Education, 1996b). The study adopts a critical, transformative theoretical paradigm, and employed an eclectic and emergent qualitative methodological approach, that reflected aspects from ethnographic, narrative and grounded theory methodologies. Interviews with university lecturers, early childhood care and education teachers, and professional development facilitators within the early childhood field; observations within early childhood care and education centres; audio taping of university class discussions; samples of university student assignments; and a written survey of graduates of the university teacher education programme provide the sources of data for the study. Central to the methodological process is a commitment to ethical care for participants, which involves attentive accountability to the interpretations that they place on the material that they contribute to the study and to the overall theorising of the significance of the findings. 

Key research questions of the study were to define ‘bicultural development’ in the context of early childhood care and education in this country; to identify key components of the bicultural development implementation process employed within the university teacher early childhood education programme; to distinguish some useful ‘indicators’ of bicultural development within early childhood centres; and to consider the implications for the teacher education programme in terms of preparing graduates to facilitate bicultural development within their future work in early childhood education. 

A significant finding of the study was the identification of a range of strategies for implementing bicultural development in early childhood education teacher education and care and education settings. The key strategies include Tiriti-based partnership models of teaching whereby Māori and Pākehā work alongside each other, enabling the paralleling of Māori and Western perspectives within both university teacher education and early childhood care and education programmes. It was considered essential that universities employ Māori lecturers to enable Māori content within the teacher education programme to be adequately provisioned. Since there are few Māori educators employed in mainstream early childhood services, it was suggested that teachers might seek to employ a “whanaungatanga” approach. This involves the early childhood centre staff creating a climate and environment in which Māori families/whānau are comfortable to participate fully in programme planning, implementation, and evaluation, which will enable all children attending to access Māori perspectives alongside the Western curriculum content. This approach is consistent with Article Two of Te Tiriti o Waitangi, which guaranteed to Māori their tino rangatiratanga, or self-determination. 

An implication for management and staff of early childhood teacher education programmes in Aotearoa/New Zealand is the need to equip graduates with the knowledge bases and commitment that will enable them to implement bicultural development, ideally through adopting, a whanaungatanga approach. This involves facilitating teacher education students to move beyond the dysconscious racism (King, 1994) that is deeply embedded in mainstream Pākehā culture in this country, to the position where they are able to adopt a critical, transformative stance that is humble, respectful and responsive to cultural difference. This stance includes valuing the inclusion of te reo me ōna tikanga throughout early childhood programmes, in a partnership initiated by teachers, but one in which whānau Māori are then able to take the lead in determining the nature and application of Māori content.

text: “It’s becoming part of their knowing”: a study of bicultural development in an early childhood teacher education setting in Aotearoa/New Zealand This study is an exploration of the implementation of bicultural development within a university-based early childhood teacher education programme in Aotearoa/New Zealand, which can be considered to be a bicultural country (Walker, 1987, p. 221). Bicultural development is a process in line with obligations contained within the Te Tiriti o Waitangi/The Treaty of Waitangi, which are reflected within the New Zealand Ministry of Education’s Revised Statement of Desirable Objectives and Practices (Ministry of Education, 1996a) and the early childhood curriculum, Te Whāriki (Ministry of Education, 1996b). The study adopts a critical, transformative theoretical paradigm, and employed an eclectic and emergent qualitative methodological approach, that reflected aspects from ethnographic, narrative and grounded theory methodologies. Interviews with university lecturers, early childhood care and education teachers, and professional development facilitators within the early childhood field; observations within early childhood care and education centres; audio taping of university class discussions; samples of university student assignments; and a written survey of graduates of the university teacher education programme provide the sources of data for the study. Central to the methodological process is a commitment to ethical care for participants, which involves attentive accountability to the interpretations that they place on the material that they contribute to the study and to the overall theorising of the significance of the findings. 

Key research questions of the study were to define ‘bicultural development’ in the context of early childhood care and education in this country; to identify key components of the bicultural development implementation process employed within the university teacher early childhood education programme; to distinguish some useful ‘indicators’ of bicultural development within early childhood centres; and to consider the implications for the teacher education programme in terms of preparing graduates to facilitate bicultural development within their future work in early childhood education. 

A significant finding of the study was the identification of a range of strategies for implementing bicultural development in early childhood education teacher education and care and education settings. The key strategies include Tiriti-based partnership models of teaching whereby Māori and Pākehā work alongside each other, enabling the paralleling of Māori and Western perspectives within both university teacher education and early childhood care and education programmes. It was considered essential that universities employ Māori lecturers to enable Māori content within the teacher education programme to be adequately provisioned. Since there are few Māori educators employed in mainstream early childhood services, it was suggested that teachers might seek to employ a “whanaungatanga” approach. This involves the early childhood centre staff creating a climate and environment in which Māori families/whānau are comfortable to participate fully in programme planning, implementation, and evaluation, which will enable all children attending to access Māori perspectives alongside the Western curriculum content. This approach is consistent with Article Two of Te Tiriti o Waitangi, which guaranteed to Māori their tino rangatiratanga, or self-determination. 

An implication for management and staff of early childhood teacher education programmes in Aotearoa/New Zealand is the need to equip graduates with the knowledge bases and commitment that will enable them to implement bicultural development, ideally through adopting, a whanaungatanga approach. This involves facilitating teacher education students to move beyond the dysconscious racism (King, 1994) that is deeply embedded in mainstream Pākehā culture in this country, to the position where they are able to adopt a critical, transformative stance that is humble, respectful and responsive to cultural difference. This stance includes valuing the inclusion of te reo me ōna tikanga throughout early childhood programmes, in a partnership initiated by teachers, but one in which whānau Māori are then able to take the lead in determining the nature and application of Māori content.

year: 2002