Construction of inverses with prescribed zero minors and applications to decentralized stabilization

We examine the following question: Suppose R is a principal ideal domain, and that F is an n × m matrix with elements in R, with n>m. When does there exist an m × n matrix G such that GF = Im, and such that certain prescribed minors of G equal zero? We show that there is a simple necessary condition for the existence of such a G, but that this condition is not sufficient in general. However, if the set of minors of G that are required to be zero has a certain pattern, then the condition is necessary as well as sufficient. We then show that the pattern mentioned above arises naturally in connection with the question of the existence of decentralized stabilizing controllers for a given plant. Hence our result allows us to derive an extremely simple proof of the fact that a necessary and sufficient condition for the existence of decentralized stabilizing controllers is the absence of unstable decentralized fixed modes, as well as to derive a very clean expression for these fixed modes. In addition to the application to decentralized stabilization, we believe that the result is of independent interest.

The Noether-Lefschetz theorem for the divisor class group

Let X be a normal projective threefold over a field of characteristic zero and vertical bar L vertical bar be a base-point free, ample linear system on X. Under suitable hypotheses on (X, vertical bar L vertical bar), we prove that for a very general member Y is an element of vertical bar L vertical bar, the restriction map on divisor class groups Cl(X) -> Cl(Y) is an isomorphism. In particular, we are able to recover the classical Noether-Lefschetz theorem, that a very general hypersurface X subset of P-C(3) of degree >= 4 has Pic(X) congruent to Z.

Stone baby: An exploration of affect and trauma in visual art

Stone Baby: An Exploration of Affect and Trauma in Visual Art was held at the Block, QUT Creative Industries Precinct on August 27-28, 2014. At the conclusion of my Masters project, this exhibition was a showcase of the outcomes of my material and digital explorations in the form of installation, sculpture and film. My primary motivation can be described as a relational and ethical attempt to find a balance between the erotic and the aggressive. This is experienced in the self as feelings of attraction and repulsion in response to the new and unknown "other". Consequently creative practice is necessarily a complex affair that is experienced as a completely immersive and self-contained psychological space. It is within this space that both physical sensation and raw emotion are able to tangibly and conceptually interact with psychoanalytic theory, and concrete materials video and sound.

15 Artists 2014

15 Artists 2014 was a group exhibition of 2D and 3D works held at the Redcliffe City Art Gallery between October 23 - December 6, 2014. My contribution to the group show was a collective series of 10 soft sculptures entitled Organs Without Bodies. These works were composed of latex, plaster, wool, thread, wax and rosin. I seek through my art practice to transform bodily affect into concrete knowledge. My primary motivation can be described as a relational and ethical attempt to find balance between the erotic and the aggressive. These objects are outcomes from an ongoing creative meditation of the simultaneity of dichotomies: inside and outside, cognition and emotion, past and present, connection and differentiation, the erotic and the aggressive. Each of these can be perceived separately with a penetrating focus of attention, yet all are contained within the 'space' of an expansive bodily-felt sense of awareness.

Algebraic Cryptanalysis of CTRU Cryptosystem

CTRU, a public key cryptosystem was proposed by Gaborit, Ohler and Sole. It is analogue of NTRU, the ring of integers replaced by the ring of polynomials $\mathbb{F}_2[T]$ . It attracted attention as the attacks based on either LLL algorithm or the Chinese Remainder Theorem are avoided on it, which is most common on NTRU. In this paper we presents a polynomial-time algorithm that breaks CTRU for all recommended parameter choices that were derived to make CTRU secure against popov normal form attack. The paper shows if we ascertain the constraints for perfect decryption then either plaintext or private key can be achieved by polynomial time linear algebra attack.

Boson-fermion duality in SU(m vertical bar n) supersymmetric Haldane-Shastry spin chain

By using the Y(gl(m|n)) super Yangian symmetry of the SU(m|n) supersymmetric Haldane-Shastry spin chain, we show that the partition function of this model satisfies a duality relation under the exchange of bosonic and fermionic spin degrees of freedom. As a byproduct of this study of the duality relation, we find a novel combinatorial formula for the super Schur polynomials associated with some irreducible representations of the Y(gl(m|n)) Yangian algebra. Finally, we reveal an intimate connection between the global SU(m|n) symmetry of a spin chain and the boson-fermion duality relation. (C) 2007 Elsevier B.V. All rights reserved.

Giant magnons in the D1-D5 system

We study giant magnons in the the D1-D5 system from both the boundary CFT and as classical solutions of the string sigma model in AdS(3) x S-3 x T-4. Re-examining earlier studies of the symmetric product conformal field theory we argue that giant magnons in the symmetric product are BPS states in a centrally extended SU(1 vertical bar 1) x SU(1 vertical bar 1) superalgebra with two more additional central charges. The magnons carry these additional central charges locally but globally they vanish. Using a spin chain description of these magnons and the extended superalgebra we show that these magnons obey a dispersion relation which is periodic in momentum. We then identify these states on the string theory side and show that here too they are BPS in the same centrally extended algebra and obey the same dispersion relation which is periodic in momentum. This dispersion relation arises as the BPS condition for the extended algebra and is similar to that of magnons in N = 4 Yang-Mills Yang-Mills.

The prankster’s passion: Using theatrical terms to unpack players motivations in popular social performance

Amongst social players, the prank, as a social performance form, holds a lot of potential to impact on personal, relational and social status within a group or between one group and another group. More than simply showing off, a prank in the strictest definition of the term, is a social performance in which one player, a prankster, deploys mischief, trickery or deceit, to cause a moment of anxiety, fear or anger about a happening for another spectator-become-collaborating-player, a prankee – to enhance social bonds, entertain, or comment on a social, cultural or political phenomenon. During a prank, the prankster’s ability to be creative, clever or culturally astute, and the prankee’s ability to be duped, be a good sport, play along, or even play/pay the prankster back, both become fodder for other spectators and society to scrutinize. In Australia, pranking traditions are popular with many social groups, from the community-building pranks of footballers, bucks parties and ‘drop bear’ tales told to tourists, to the more controversial pranks of radio shock jocks, activists and artists. In this paper, I consider whether theatrical terms – theoretical terms from the stage such as actor, acting, objective, arc, performance, audience and emotion, such as those offered by Joseph Roach – are useful in understanding the passion some social players show for pranksterism. Are theatrical terms such as Roach’s as useful as analysts of social self-performance such as Erving Goffman suggest they are? Do they assist in understanding the personal actions, reactions and emotions of prankster and prankee? Do they assist in understanding the power relations between prankster and prankee? Do they assist in understanding the relation between the prank – be it an everyday prank amongst families, friends and coworkers, an entertainment program prank of the sort seen on Prank Patrol, Punked or Scare Tactics, or an activist pranks perpetrated by a guerrilla artist, ‘jammers’ or ‘hackers’ intent on turning dominant social systems back on themselves – the social players, and the public sphere in which the prank takes place? I reflect on how reading pranks as performances, by players, for highly participatory audiences, helps understand why they are so prevalent, and so recurrent across times, cultures and contexts, and also so controversial when not performed well enough – or when performed too well – prompting outrage from the prankster, prankee or society as passionate as any debate about a performance by players in a theatre.

Carer perspectives of factors affecting placement trajectories of children in out-of-home care

Carers are at the frontline working with children in the care of the child protection system. This paper reports carer's views about key factors influencing the placement trajectories of children and young people living in out-of-home care in Queensland, Australia. The study sample included 21 foster and kinship carers with a minimum two-year experience in the carer role. Study data were from semi-structured telephone interviews in which carers shared their experiences of the factors impacting upon placement stability and placement movement. Carers' responses were analysed thematically. Data analysis yielded an overarching theme regarding placement trajectory: Carer engagement, and its three sub-themes; with the child; with the child protection system; and, with the caring role. Findings suggested that carer engagement and ‘fit’ are complex constructs that play critical influential roles in placement outcomes (stability or movement) for individual children in out-of-home care. It is argued that practice needs to be better grounded in these relational dynamics, and better aligned concerning the power differentials that exist.

How do construction firms learn on collaborative infrastructure projects?

Construction firms that employ collaborative procurement approaches develop operating routines through joint learning so as to improve infrastructure project performance. This paper reports a study based on a survey sample of 320 construction practitioners which were involved in collaborative infrastructure delivery in Australia. The study developed valid and reliable scales for measuring collaborative learning capability (CLC), and used the scales to evaluate the CLC of contractor and consultant firms within the sample. The evaluation suggests that whilst these firms explore knowledge from both internal and external sources, transform both explicit and tacit knowledge, and apply and internalise new knowledge, they can improve the extent to which these routines are applied to optimise project performance.

Youth programs in remote Indigenous communities: Context matters

A diversity of programs oriented to young people seek to develop their capacities and their connection to the communities in which they live. Some focus on ameliorating a particular issue or ‘deficit’ whilst others, such as sporting, recreation and youth groups are more grounded in the community. This article reports a qualitative study undertaken in three remote Indigenous communities in Central Australia. Sixty interviews were conducted with a range of stakeholders involved in a diversity of youth programs. A range of critical challenges for and characteristics of remote Indigenous youth programs are identified if such programs are to be ‘fit for context’. ‘Youth centred-context specific’ provides a positive frame for the delivery of youth programs in remote Central Australia, encouraging an explicit focus on program logic; program content and processes; and relational, temporal, and, spatial aspects of the practice context. These provide lenses with which youth program planning and delivery may be enhanced in remote communities. Culturally safe service planning and delivery suggests locally determined processes for decision-making and community ownership. In some cases, this may mean a community preference for all ages to access the service to engage in culturally relevant activities. Where activities are targeted at young people, yet open to and inclusive of all ages, they provide a medium for cross-generational interaction that requires a high degree of flexibility on the part of staff and funding programs. Although the findings are focused in Central Australia, they may be relevant to similar contexts elsewhere.

Conformal Field Theory Methods for Variants of Schramm-Loewner Evolutions

This thesis consists of an introduction, four research articles and an appendix. The thesis studies relations between two different approaches to continuum limit of models of two dimensional statistical mechanics at criticality. The approach of conformal field theory (CFT) could be thought of as the algebraic classification of some basic objects in these models. It has been succesfully used by physicists since 1980's. The other approach, Schramm-Loewner evolutions (SLEs), is a recently introduced set of mathematical methods to study random curves or interfaces occurring in the continuum limit of the models. The first and second included articles argue on basis of statistical mechanics what would be a plausible relation between SLEs and conformal field theory. The first article studies multiple SLEs, several random curves simultaneously in a domain. The proposed definition is compatible with a natural commutation requirement suggested by Dubédat. The curves of multiple SLE may form different topological configurations, ``pure geometries''. We conjecture a relation between the topological configurations and CFT concepts of conformal blocks and operator product expansions. Example applications of multiple SLEs include crossing probabilities for percolation and Ising model. The second article studies SLE variants that represent models with boundary conditions implemented by primary fields. The most well known of these, SLE(kappa, rho), is shown to be simple in terms of the Coulomb gas formalism of CFT. In the third article the space of local martingales for variants of SLE is shown to carry a representation of Virasoro algebra. Finding this structure is guided by the relation of SLEs and CFTs in general, but the result is established in a straightforward fashion. This article, too, emphasizes multiple SLEs and proposes a possible way of treating pure geometries in terms of Coulomb gas. The fourth article states results of applications of the Virasoro structure to the open questions of SLE reversibility and duality. Proofs of the stated results are provided in the appendix. The objective is an indirect computation of certain polynomial expected values. Provided that these expected values exist, in generic cases they are shown to possess the desired properties, thus giving support for both reversibility and duality.

STBC's from representation of extended Clifford Algebras

A set of sufficient conditions to construct lambda-real symbol Maximum Likelihood (ML) decodable STBCs have recently been provided by Karmakar et al. STBCs satisfying these sufficient conditions were named as Clifford Unitary Weight (CUW) codes. In this paper, the maximal rate (as measured in complex symbols per channel use) of CUW codes for lambda = 2(a), a is an element of N is obtained using tools from representation theory. Two algebraic constructions of codes achieving this maximal rate are also provided. One of the constructions is obtained using linear representation of finite groups whereas the other construction is based on the concept of right module algebra over non-commutative rings. To the knowledge of the authors, this is the first paper in which matrices over non-commutative rings is used to construct STBCs. An algebraic explanation is provided for the 'ABBA' construction first proposed by Tirkkonen et al and the tensor product construction proposed by Karmakar et al. Furthermore, it is established that the 4 transmit antenna STBC originally proposed by Tirkkonen et al based on the ABBA construction is actually a single complex symbol ML decodable code if the design variables are permuted and signal sets of appropriate dimensions are chosen.

Women and Marital Breakdown in South India : Reconstructing Homes, Bonds and Persons

Women and Marital Breakdown in South India: Reconstructing Homes, Bonds and Persons is an ethnographic analysis of the situation of divorced and separated women and their families in the South Indian city of Bangalore. The study is based on 16 months of anthropological fieldwork, i.e., participant observation and life history interviews among 50 divorced and separated women from different socio-religious backgrounds in their homes, in the women s organisations and in the Family Court. The study follows the divorced and separated women from their natal homes to their affinal homes through homelessness and legal battles to their reconstructed natal, affinal or single homes in order to find out what it means to be a person within hierarchical gender and kinship relations in South India. Marital breakdown impacts on kin relations and discloses the existing gender relations and power structure through its consequences. It makes the transformability of relational personhood as well as the transformability of relational society and culture visible. Although the study reveals the painful history of women s ill-treatment in marriage, family and kinship systems, it also demonstrates the women s rejection of the domination; and shows their ability to re-negotiate and promote changes not only to their own positions but to the whole hierarchical system as well. The study explores the divorced and separated women s manifold dilemmas, complicated legal battles, and endless arrangements when they have to struggle with the very practical problems of supporting themselves financially, finding and making a new home for themselves, and re-arranging relationships with their kin and friends. As marital breakdown fundamentally transforms the women s relational field, it forces them to recreate substitutive relations in a flexible way and, simultaneously, to re-construct themselves and their lives without a ready or positive cultural or behavioural template. This process reveals the agency of the divorced and separated women as well as shedding light on issues of gender and the cultural construction of the person in South India. This topical study explores the previously neglected subject of marital breakdown in India and shows the new meaning of kinship in South India.