Closed Form Solutions of Integrable Nonlinear Evolution Equations

2010 Mathematics Subject Classification: 35Q55.

Racialized sexualities within the romance tour industry: The influence of affect and emotion upon transnational hierarchies of desire

Online international introduction sites that offer romance tours to American men in search of a foreign bride are an important and rapidly growing component of the internet dating industry; the number of these agencies in the U.S. tripled from two hundred to six hundred in the past 10 years. Previous scholars have examined the so-called `mail order bride' industry in order to demonstrate that the women involved are agents and not victims. Many scholars have also highlighted the importance of race in shaping American men's desires in one particular region or country. My dissertation provides an important addition to the literature surrounding romance tourism by including participants from all three major regions associated with romance tourism: Eastern Europe, South America, and Southeast Asia. I collected the data for the dissertation by becoming a participant observer of a romance tour in Ukraine, Colombia, and the Philippines. I argue that romance tourism is an important example of the global intimate, and the ways in which globalized processes are created and sustained through everyday intimate emotions and interactions. By examining the ways in which the emotions of desire, disgust, and anxiety influence individual romance tour participant's constructions of racialized hierarchies, the links between individual emotions and global systems are revealed. The concept of the global intimate challenges the hierarchy of scale that places the body, the home, and the intimate on a much lower level than the scale of the global or the national, and at the same time challenges the binary that divides the individual from the global. Through highlighting the different emotional negotiations that are constantly occurring in the romance tour industry, I highlight the important ways in which individual emotions and affects influence global processes on a large scale and vice versa.^

Opinion: Can coalescent models explain deep divergences in the diatoms and argue for the acceptance of paraphyletic taxa at all taxonomic hierarchies?

Although ancestral polymorphisms and incomplete lineage sorting are commonly used at the population level, increasing reports of these models have been invoked and tested to explain deep radiations. Hypotheses are put forward for ancestral polymorphisms being the likely reason for paraphyletic taxa at the class level in the diatoms based on an ancient rapid radiation of the entire groups. Models for ancestral deep coalescence are invoked to explain paraphyly and molecular evolution at the class level in the diatoms. Other examples at more recent divergences are also documented. Discussion as to whether or not paraphyletic groups seen in the diatoms at all taxonomic levels should be recognized is provided. The continued use of the terms centric and pennate diatoms is substantiated with additional evidence produced to support their use in diatoms both as descriptive terms for both groups and as taxonomic groups for the latter because new morphological evidence from the auxospores justifies the formal classification of the basal and core araphids as new subclasses of pennate diatoms in the Class Bacillariophyceae. Keys for higher levels of the diatoms showing how the terms centrics and araphid diatoms can be defined are provided.

Opinion: Can coalescent models explain deep divergences in the diatoms and argue for the acceptance of paraphyletic taxa at all taxonomic hierarchies?

Although ancestral polymorphisms and incomplete lineage sorting are commonly used at the population level, increasing reports of these models have been invoked and tested to explain deep radiations. Hypotheses are put forward for ancestral polymorphisms being the likely reason for paraphyletic taxa at the class level in the diatoms based on an ancient rapid radiation of the entire groups. Models for ancestral deep coalescence are invoked to explain paraphyly and molecular evolution at the class level in the diatoms. Other examples at more recent divergences are also documented. Discussion as to whether or not paraphyletic groups seen in the diatoms at all taxonomic levels should be recognized is provided. The continued use of the terms centric and pennate diatoms is substantiated with additional evidence produced to support their use in diatoms both as descriptive terms for both groups and as taxonomic groups for the latter because new morphological evidence from the auxospores justifies the formal classification of the basal and core araphids as new subclasses of pennate diatoms in the Class Bacillariophyceae. Keys for higher levels of the diatoms showing how the terms centrics and araphid diatoms can be defined are provided.

Approximation limits of linear programs (beyond hierarchies)

We develop a framework for proving approximation limits of polynomial size linear programs (LPs) from lower bounds on the nonnegative ranks of suitably defined matrices. This framework yields unconditional impossibility results that are applicable to any LP as opposed to only programs generated by hierarchies. Using our framework, we prove that O(n^1/2-ε)-approximations for CLIQUE require LPs of size 2^nΩ(ε). This lower bound applies to LPs using a certain encoding of CLIQUE as a linear optimization problem. Moreover, we establish a similar result for approximations of semidefinite programs by LPs. Our main technical ingredient is a quantitative improvement of Razborov's [38] rectangle corruption lemma for the high error regime, which gives strong lower bounds on the nonnegative rank of shifts of the unique disjointness matrix.

The D(D-3)-anyon chain: integrable boundary conditions and excitation spectra

Chains of interacting non-Abelian anyons with local interactions invariant under the action of the Drinfeld double of the dihedral group D-3 are constructed. Formulated as a spin chain the Hamiltonians are generated from commuting transfer matrices of an integrable vertex model for periodic and braided as well as open boundaries. A different anyonic model with the same local Hamiltonian is obtained within the fusion path formulation. This model is shown to be related to an integrable fusion interaction round the face model. Bulk and surface properties of the anyon chain are computed from the Bethe equations for the spin chain. The low-energy effective theories and operator content of the models (in both the spin chain and fusion path formulation) are identified from analytical and numerical studies of the finite-size spectra. For all boundary conditions considered the continuum theory is found to be a product of two conformal field theories. Depending on the coupling constants the factors can be a Z(4) parafermion or a M-(5,M-6) minimal model.

Friendship dynamics and popularity hierarchies among inclusive men

Previous research has demonstrated that aggression and marginalization are key components of maintaining popularity within male peer groups. However, more recent ethnographic studies have documented a significant shift in young men’s attitudes and behaviours, with more inclusive masculinities flourishing. My previous research has examined friendship dynamics and popularity hierarchies among boys, showing that contemporary popularity is stratified by a boy’s charisma, authenticity, emotional support, and social fluidity. In this article, I draw upon ethnographic research to provide an intersectional analysis of how adolescent masculinities are influenced by class, age and sexuality

Racialized Sexualities within the Romance Tour Industry: the Influence of Affect and Emotion Upon Transnational Hierarchies of Desire

Online international introduction sites that offer romance tours to American men in search of a foreign bride are an important and rapidly growing component of the internet dating industry; the number of these agencies in the U.S. tripled from two hundred to six hundred in the past 10 years. Previous scholars have examined the so-called ‘mail order bride’ industry in order to demonstrate that the women involved are agents and not victims. Many scholars have also highlighted the importance of race in shaping American men’s desires in one particular region or country. My dissertation provides an important addition to the literature surrounding romance tourism by including participants from all three major regions associated with romance tourism: Eastern Europe, South America, and Southeast Asia. I collected the data for the dissertation by becoming a participant observer of a romance tour in Ukraine, Colombia, and the Philippines. I argue that romance tourism is an important example of the global intimate, and the ways in which globalized processes are created and sustained through everyday intimate emotions and interactions. By examining the ways in which the emotions of desire, disgust, and anxiety influence individual romance tour participant’s constructions of racialized hierarchies, the links between individual emotions and global systems are revealed. The concept of the global intimate challenges the hierarchy of scale that places the body, the home, and the intimate on a much lower level than the scale of the global or the national, and at the same time challenges the binary that divides the individual from the global. Through highlighting the different emotional negotiations that are constantly occurring in the romance tour industry, I highlight the important ways in which individual emotions and affects influence global processes on a large scale and vice versa.

Multivariate orthogonal polynomials and integrable systems

Multivariate orthogonal polynomials in D real dimensions are considered from the perspective of the Cholesky factorization of a moment matrix. The approach allows for the construction of corresponding multivariate orthogonal polynomials, associated second kind functions, Jacobi type matrices and associated three term relations and also Christoffel-Darboux formulae. The multivariate orthogonal polynomials, their second kind functions and the corresponding Christoffel-Darboux kernels are shown to be quasi-determinants as well as Schur complements of bordered truncations of the moment matrix; quasi-tau functions are introduced. It is proven that the second kind functions are multivariate Cauchy transforms of the multivariate orthogonal polynomials. Discrete and continuous deformations of the measure lead to Toda type integrable hierarchy, being the corresponding flows described through Lax and Zakharov-Shabat equations; bilinear equations are found. Varying size matrix nonlinear partial difference and differential equations of the 2D Toda lattice type are shown to be solved by matrix coefficients of the multivariate orthogonal polynomials. The discrete flows, which are shown to be connected with a Gauss-Borel factorization of the Jacobi type matrices and its quasi-determinants, lead to expressions for the multivariate orthogonal polynomials and their second kind functions in terms of shifted quasi-tau matrices, which generalize to the multidimensional realm, those that relate the Baker and adjoint Baker functions to ratios of Miwa shifted tau-functions in the 1D scenario. In this context, the multivariate extension of the elementary Darboux transformation is given in terms of quasi-determinants of matrices built up by the evaluation, at a poised set of nodes lying in an appropriate hyperplane in R^D, of the multivariate orthogonal polynomials. The multivariate Christoffel formula for the iteration of m elementary Darboux transformations is given as a quasi-determinant. It is shown, using congruences in the space of semi-infinite matrices, that the discrete and continuous flows are intimately connected and determine nonlinear partial difference-differential equations that involve only one site in the integrable lattice behaving as a Kadomstev-Petviashvili type system. Finally, a brief discussion of measures with a particular linear isometry invariance and some of its consequences for the corresponding multivariate polynomials is given. In particular, it is shown that the Toda times that preserve the invariance condition lay in a secant variety of the Veronese variety of the fixed point set of the linear isometry.

Improving the Traversal of Large Hierarchical Process Repositories

Business Process Management (BPM) has increased in popularity and maturity in recent years. Large enterprises engage use process management approaches to model, manage and refine repositories of process models that detail the whole enterprise. These process models can run to the thousands in number, and may contain large hierarchies of tasks and control structures that become cumbersome to maintain. Tools are therefore needed to effectively traverse this process model space in an efficient manner, otherwise the repositories remain hard to use, and thus are lowered in their effectiveness. In this paper we analyse a range of BPM tools for their effectiveness in handling large process models. We establish that the present set of commercial tools is lacking in key areas regarding visualisation of, and interaction with, large process models. We then present six tool functionalities for the development of advanced business process visualisation and interaction, presenting a design for a tool that will exploit the latest advances in 2D and 3D computer graphics to enable fast and efficient search, traversal and modification of process models.

Diagramming the interior

Mark Taylor's new essay assesses the impact of the diagram on interior design from the late 19th century to the present. Taylor identifies the pop-cultural discourse of advice writing in both books and magazines as a starting point for his analysis. Drawing on diverse sources, his analysis focuses on texts relating to the dynamics of use and flexibility by Catherine Beecher, Harriet Beecher Stowe, Melusina Fay Peirce, Mary Haweis and Christine Frederick among others. The examples in these texts use the home, domestic housekeeping and kitchens as the sites and practices of intervention through which interior design innovations can be enacted. Taylor's analysis identified the innovations in both the social and the political aspects of space and the critique of static space behind these seemingly amateurish and innocuous texts. Identifying these contributions as early precursors of Modernism's open-plan and flexible, dynamic spaces, Taylor also interprets them with a critical concern for the oppositions and hierarchies that can exist in spatial design, and which are the hallmarks of recent Postmodern, phenomenological approaches to interior design and its theorisations. The progressive and subversive "paradigms for living" implicit in these diagrams can be argued to present a model of greater economic, social and political equality as well as representing a more balanced set of power relations in the home. Progressing through the 20th century to the present, Taylor's analysis shifts byond the dressed body and on to the more intimate rituals of the revealed body to further examine how diagrams of the interior, and the interior as a set of diagrams, are also mediators, sites and grounds for the design of social and sexual intimacy. Through a consideration of the link between design, indentity and intimacy (whether of the invisible, fashioned or sexualised body), the diagrms of interiors are reconfigured as radical and critical tools for an animate, material and emancipatory "redressing" of the balance between the body, identity, sexuality, gender, function, mis(use), aesthetics and the interior.

Performance Research in Rangeland Communities

In 2003, Bill Dunstone, John McCallum and Paul Makeham began a collaboration with researchers at the Centre for the Management of Arid Environments (CMAE) in Kalgoorlie, Western Australia. CMAE researchers are keen to develop 'people-oriented' strategies for implementing agricultural extension initiatives in their region. Traditional hierarchies of knowledge-transfer have impeded the 'connectedness' between community and researchers that gives meaning and relevance to useful practice (Ison and Russell, 2000). Our aim is to establish a partnership between the Live Events Research Network (LERN) and CMAE, investigating ways to link creative, performance-based research and practice with the scientific methodologies associated with natural resources management. This accords with recent work undertaken by Deborah Mills and Paul Brown, showing how community cultural development strategies enhance the implementation of policy concerned with community wellbeing. Mills and Brown 'adopted a concept of wellbeing which builds on a social and environmental view of health', and considered such themes as ecological sustainability, rural economic revitalisation, community strengthening, health and wellbeing (Mills, 2003). We propose that rangeland communities can creatively manage some of the challenges confronting them through performance-based projects which: - activate the stories through which a community enacts its sense of place; - facilitate live events in which the community enacts ownership of its culture and identity; - directly involve the community in the formulation of research issues

Geekdom for Grrrls health : Australian undergraduate experiences developing and promoting women’s health in cyberspace

There is an increasing global reliance on the Internet for retrieving information on health, illness, and recovery (Sillence et al, 2007; Laurent et al, 2009; Adams, 2010). People suffering from a vast array of illnesses, conditions, and complaints, as well as healthy travelers seeking advice about safe practices abroad, and teens seeking information about safe sexual practices are all now more likely to go to the internet for information than they are to rely solely on a general practitioner or physician (Santor et al, 2007; Moreno et al, 2009; Bartlett et al, 2010). Women in particular seek advice and support online for a number of health-related concerns regarding issues such as puberty, conception, pregnancy, postnatal depression, mothering, breast-cancer recovery, and ageing healthily (van Zutphen, 2008; Raymond et al, 2005). In keeping with this increasing socio-technological trend, the Women’s Health Unit at the Queensland University of Technology (Q.U.T), Brisbane, Australia, introduced the research, design, and development of online information resources for issues affecting the health of Australian women as an assessment item for students in the undergraduate Public Health curriculum. Students were required to research a particular health issue affecting Australian women, including pregnancy, pregnancy terminations, postnatal depression, returning to the work force after having a baby, breast cancer recovery, chronic disease prevention, health and safety for sex-workers, and ageing healthily. Students were required to design and develop websites that supported people living with these conditions, or who were in these situations. The websites were designed for communicating effectively with both women seeking information about their health, and their health practitioners. The pedagogical challenge inherent in this exercise was twofold: firstly, to encourage students to develop the skills to design and maintain software for online health forums; and secondly, to challenge public health students to go beyond generating ‘awareness’ and imparting health information to developing a nuanced understanding of the worlds and perspectives of their audiences, who require supportive networks and options that resonate with their restrictions, capabilities, and dispositions. This latter challenge spanned the realms of research, communication, and aesthetic design. This paper firstly, discusses an increasing reliance on the Internet by women seeking health-related information and the potential health risks and benefits of this trend. Secondly, it applies a post-structural analysis of the de-centred and mobile female self, as online social ‘spaces’ and networks supersede geographical ‘places’ and hierarchies, with implications for democracy, equality, power, and ultimately women’s health. Thirdly, it depicts the processes (learning reflections) and products (developed websites) created within this Women’s Health Unit by the students. Finally, we review this development in the undergraduate curriculum in terms of the importance of providing students with skills in research, communication, and technology in order to share and implement improved health care and social marketing for women as both recipients and providers of health care in the Internet Age.

The Australian Parliament: a gendered organisation

This study, drawing on interviews with 13 male and 15 female members of the Australian parliament, has two aims. The first is to contribute to knowledge about the nature of the Australian parliament, an institution which has seldom been subjected to gender analysis. This is particularly pertinent given the significant increase in women's representative status over the past decade. The second of the paper's aims is to demonstrate the efficacy of contemporary gender and organisational theory, particularly work on men and masculinities, for investigating questions related to women's involvement in politics. The paper draws on Joan Acker's (‘Hierarchies, Jobs, Bodies: A Theory of Gendered Organizations’, Gender and Society, 4, 1990, 139–58; ‘From Sex Roles to Gendered Institutions’, Contemporary Sociology, 21, 1992, 565–9.) notion of ‘gendered organisations’ to interrogate the data.