Descriptive set theory and the ergodic theory of countable groups

The primary focus of this thesis is on the interplay of descriptive set theory and the ergodic theory of group actions. This incorporates the study of turbulence and Borel reducibility on the one hand, and the theory of orbit equivalence and weak equivalence on the other. Chapter 2 is joint work with Clinton Conley and Alexander Kechris; we study measurable graph combinatorial invariants of group actions and employ the ultraproduct construction as a way of constructing various measure preserving actions with desirable properties. Chapter 3 is joint work with Lewis Bowen; we study the property MD of residually finite groups, and we prove a conjecture of Kechris by showing that under general hypotheses property MD is inherited by a group from one of its co-amenable subgroups. Chapter 4 is a study of weak equivalence. One of the main results answers a question of Abért and Elek by showing that within any free weak equivalence class the isomorphism relation does not admit classification by countable structures. The proof relies on affirming a conjecture of Ioana by showing that the product of a free action with a Bernoulli shift is weakly equivalent to the original action. Chapter 5 studies the relationship between mixing and freeness properties of measure preserving actions. Chapter 6 studies how approximation properties of ergodic actions and unitary representations are reflected group theoretically and also operator algebraically via a group's reduced C^*-algebra. Chapter 7 is an appendix which includes various results on mixing via filters and on Gaussian actions.

Axiomatic Characterization of the Antimedian Function on Paths and Hypercubes

An antimedian of a pro le = (x1; x2; : : : ; xk) of vertices of a graph G is a vertex maximizing the sum of the distances to the elements of the pro le. The antimedian function is de ned on the set of all pro les on G and has as output the set of antimedians of a pro le. It is a typical location function for nding a location for an obnoxious facility. The `converse' of the antimedian function is the median function, where the distance sum is minimized. The median function is well studied. For instance it has been characterized axiomatically by three simple axioms on median graphs. The median function behaves nicely on many classes of graphs. In contrast the antimedian function does not have a nice behavior on most classes. So a nice axiomatic characterization may not be expected. In this paper such a characterization is obtained for the two classes of graphs on which the antimedian is well-behaved: paths and hypercubes.

Stability and cycles in a cobweb model with heterogeneous expectations

We investigate the dynamics of a cobweb model with heterogeneous beliefs, generalizing the example of Brock and Hommes (1997). We examine situations where the agents form expectations by using either rational expectations, or a type of adaptive expectations with limited memory defined from the last two prices. We specify conditions that generate cycles. These conditions depend on a set of factors that includes the intensity of switching between beliefs and the adaption parameter. We show that both Flip bifurcation and Neimark-Sacker bifurcation can occur as primary bifurcation when the steady state is unstable.

Spectral graph theory with applications to quantum adiabatic optimization

In this dissertation I draw a connection between quantum adiabatic optimization, spectral graph theory, heat-diffusion, and sub-stochastic processes through the operators that govern these processes and their associated spectra. In particular, we study Hamiltonians which have recently become known as ``stoquastic'' or, equivalently, the generators of sub-stochastic processes. The operators corresponding to these Hamiltonians are of interest in all of the settings mentioned above. I predominantly explore the connection between the spectral gap of an operator, or the difference between the two lowest energies of that operator, and certain equilibrium behavior. In the context of adiabatic optimization, this corresponds to the likelihood of solving the optimization problem of interest. I will provide an instance of an optimization problem that is easy to solve classically, but leaves open the possibility to being difficult adiabatically. Aside from this concrete example, the work in this dissertation is predominantly mathematical and we focus on bounding the spectral gap. Our primary tool for doing this is spectral graph theory, which provides the most natural approach to this task by simply considering Dirichlet eigenvalues of subgraphs of host graphs. I will derive tight bounds for the gap of one-dimensional, hypercube, and general convex subgraphs. The techniques used will also adapt methods recently used by Andrews and Clutterbuck to prove the long-standing ``Fundamental Gap Conjecture''.

Education research and youth subculture theory

Recent theoretical developments (particularly those involving the work of Michel Foucault) have challenged the foundations upon which subcultural analysis is built. It is not the intention of this paper to take issue with the underpinning neo-Marxist assumptions concerning hegemony, consciousness and culture. Rather, the intention is simply to problematise the use of subculture theory in terms of its totalising, normalising and dichotomising nature.

Insights from ecological psychology and dynamical systems theory can underpin a philosophy of coaching

The aim of this paper is to show how principles of ecological psychology and dynamical systems theory can underpin a philosophy of coaching practice in a nonlinear pedagogy. Nonlinear pedagogy is based on a view of the human movement system as a nonlinear dynamical system. We demonstrate how this perspective of the human movement system can aid understanding of skill acquisition processes and underpin practice for sports coaches. We provide a description of nonlinear pedagogy followed by a consideration of some of the fundamental principles of ecological psychology and dynamical systems theory that underpin it as a coaching philosophy. We illustrate how each principle impacts on nonlinear pedagogical coaching practice, demonstrating how each principle can substantiate a framework for the coaching process.

Holding and opportunity cost theory in a property development context

This paper focuses on the varying approaches and methodologies adopted when the calculation of holding costs is undertaken, focusing on greenfield development. Whilst acknowledging there may be some consistency in embracing first principles relating to holding cost theory, a review of the literature reveals considerable lack of uniformity in this regard. There is even less clarity in quantitative determination, especially in Australia where there has been only limited empirical analysis undertaken. Despite a growing quantum of research undertaken in relation to various elements connected with housing affordability, the matter of holding costs has not been well addressed regardless of its part in the highly prioritised Australian Government’s housing research agenda. The end result has been a modicum of qualitative commentary relating to holding costs. There have been few attempts at finer-tuned analysis that exposes a quantified level of holding cost calculated with underlying rigour. Holding costs can take many forms, but they inevitably involve the computation of “carrying costs” of an initial outlay that has yet to fully realise its ultimate yield. Although sometimes considered a “hidden” cost, it is submitted that holding costs prospectively represent a major determinate of value. If this is the case, then considered in the context of housing affordability, it is therefore potentially pervasive.

Essays on irrigation development, farm production and unaccounted costs : theory and empirical evidence

A review of the literature related to issues involved in irrigation induced agricultural development (IIAD) reveals that: (1) the magnitude, sensitivity and distribution of social welfare of IIAD is not fully analysed; (2) the impacts of excessive pesticide use on farmers’ health are not adequately explained; (3) no analysis estimates the relationship between farm level efficiency and overuse of agro-chemical inputs under imperfect markets; and (4) the method of incorporating groundwater extraction costs is misleading. This PhD thesis investigates these issues by using primary data, along with secondary data from Sri Lanka. The overall findings of the thesis can be summarised as follows. First, the thesis demonstrates that Sri Lanka has gained a positive welfare change as a result of introducing new irrigation technology. The change in the consumer surplus is Rs.48,236 million, while the change in the producer surplus is Rs. 14,274 millions between 1970 and 2006. The results also show that the long run benefits and costs of IIAD depend critically on the magnitude of the expansion of the irrigated area, as well as the competition faced by traditional farmers (agricultural crowding out effects). The traditional sector’s ability to compete with the modern sector depends on productivity improvements, reducing production costs and future structural changes (spillover effects). Second, the thesis findings on pesticides used for agriculture show that, on average, a farmer incurs a cost of approximately Rs. 590 to 800 per month during a typical cultivation period due to exposure to pesticides. It is shown that the value of average loss in earnings per farmer for the ‘hospitalised’ sample is Rs. 475 per month, while it is approximately Rs. 345 per month for the ‘general’ farmers group during a typical cultivation season. However, the average willingness to pay (WTP) to avoid exposure to pesticides is approximately Rs. 950 and Rs. 620 for ‘hospitalised’ and ‘general’ farmers’ samples respectively. The estimated percentage contribution for WTP due to health costs, lost earnings, mitigating expenditure, and disutility are 29, 50, 5 and 16 per cent respectively for hospitalised farmers, while they are 32, 55, 8 and 5 per cent respectively for ‘general’ farmers. It is also shown that given market imperfections for most agricultural inputs, farmers are overusing pesticides with the expectation of higher future returns. This has led to an increase in inefficiency in farming practices which is not understood by the farmers. Third, it is found that various groundwater depletion studies in the economics literature have provided misleading optimal water extraction quantity levels. This is due to a failure to incorporate all production costs in the relevant models. It is only by incorporating quality changes to quantity deterioration, that it is possible to derive socially optimal levels. Empirical results clearly show that the benefits per hectare per month considering both the avoidance costs of deepening agro-wells by five feet from the existing average, as well as the avoidance costs of maintaining the water salinity level at 1.8 (mmhos/Cm), is approximately Rs. 4,350 for farmers in the Anuradhapura district and Rs. 5,600 for farmers in the Matale district.

Homo- and heteronuclear meso,meso-(E)-Ethene-1,2-diyl-Linked Diporphyrins : preparation, X-ray crystal structure, electronic absorption and emission spectra and density functional theory calculations

Homo-and heteronuclear meso,meso-(E)-ethene-1,2-diyl-linked diporphyrins have been prepared by the Suzuki coupling of porphyrinylboronates and iodovinylporphyrins. Combinations comprising 5,10,15-triphenylporphyrin (TriPP) on both ends of the ethene-1,2-diyl bridge M 210 (M 2=H 2/Ni, Ni 2, Ni/Zn, H 4, H 2Zn, Zn 2) and 5,15-bis(3,5-di-tert-butylphenyl)porphyrinato-nickel(II) on one end and H 2, Ni, and ZnTriPP on the other (M 211), enable the first studies of this class of compounds possessing intrinsic polarity. The compounds were characterized by electronic absorption and steady state emission spectra, 1H NMR spectra, and for the Ni 2 bis(TriPP) complex Ni 210, single crystal X-ray structure determination. The crystal structure shows ruffled distortions of the porphyrin rings, typical of Ni II porphyrins, and the (E)-C 2H 2 bridge makes a dihedral angle of 50° with the mean planes of the macrocycles. The result is a stepped parallel arrangement of the porphyrin rings. The dihedral angles in the solid state reflect the interplay of steric and electronic effects of the bridge on interporphyrin communication. The emission spectra in particular, suggest energy transfer across the bridge is fast in conformations in which the bridge is nearly coplanar with the rings. Comparisons of the fluorescence behaviour of H 410 and H 2Ni10 show strong quenching of the free base fluorescence when the complex is excited at the lower energy component of the Soret band, a feature associated in the literature with more planar conformations. TDDFT calculations on the gas-phase optimized geometry of Ni 210 reproduce the features of the experimental electronic absorption spectrum within 0.1 eV. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Integrating agency and resource dependence theory : firm profitability, industry regulation, and board task performance

Boards of directors are key governancemechanisms in organizations and fulfill twomain tasks:monitoringmanagers and firm performance, and providing advice and access to resources. In spite of a wealth of researchmuch remains unknown about how boards attend to the two tasks. This study investigates whether organizational (firm profitability) and environmental factors (industry regulation) affect board task performance. The data combine CEOs' responses to a questionnaire, and archival data from a sample of large Italian firms. Findings show that past firm performance is negatively associatedwith board monitoring and advice tasks; greater industry regulation enhances perceived board task performance; board monitoring and advice tasks tend to reinforce each other, despite their theoretical and practical distinction.

Are the offences in the Copyright Act 1968 (Cth) legitimate and effective? : an analysis based in harm and social norms theory

This thesis examines the effectiveness of offences in the Copyright Act 1968 (Cth) in the online environment. The application of social norm theories suggests that the offences will be ineffective in creating an effective deterrent to non-commercial copyright infringement.

Management of multiple heterogeneous UAVs using capability and autonomy visualisation: theory, experiment and result

The interest in utilising multiple heterogeneous Unmanned Aerial Vehicles (UAVs) in close proximity is growing rapidly. As such, many challenges are presented in the effective coordination and management of these UAVs; converting the current n-to-1 paradigm (n operators operating a single UAV) to the 1-to-n paradigm (one operator managing n UAVs). This paper introduces an Information Abstraction methodology used to produce the functional capability framework initially proposed by Chen et al. and its Level Of Detail (LOD) indexing scale. This framework was validated through comparing the operator workload and Situation Awareness (SA) of three experiment scenarios involving multiple autonomously heterogeneous UAVs. The first scenario was set in a high LOD configuration with highly abstracted UAV functional information; the second scenario was set in a mixed LOD configuration; and the final scenario was set in a low LOD configuration with maximal UAV functional information. Results show that there is a significant statistical decrease in operator workload when a UAV’s functional information is displayed at its physical form (low LOD - maximal information) when comparing to the mixed LOD configuration.

Directing experience : an exploration of active analysis and visual cognition theory in the training of contemporary directors

The focus of this research is the creation of a stage-directing training manual on the researcher's site at the National Institute of Dramatic Art. The directing procedures build on the work of Stanislavski's Active Analysis and findings from present-day visual cognition studies. Action research methodology and evidence-based data collection are employed to improve the efficacy of both the directing procedures and the pedagogical manual. The manual serves as a supplement to director training and a toolkit for the more experienced practitioner. The manual and research findings provide a unique and innovative contribution to the field of theatre directing.

Human resource management and entrepreneurship : building theory at the intersection

In 2008 we brought together much work at the intersection of entrepreneurship and human resource management (HRM) (Barrett & Mayson, 2008), after calls for more research (Baron, 2003; Katz, Aldrich, Welbourne & Williams, 2000; Tansky & Heneman, 2003). More has been collated since (Soriano, Dobon & Tansky, 2010; Tansky, Soriano & Dobon, 2010). We think it is now time again to regroup, pull conversational threads together and have a critical look at recent research at the intersection of HRM and Entrepreneurship. As editors of International Handbook of Entrepreneurship and HRM (Barrett & Mayson, 2008) we were privileged to collect 23 wonderfully diverse chapters from scholars around the globe addressing a range of issues at the intersection of the two pertinent disciplines or fields: HRM and entrepreneurship. This edition represented a coalescing of ideas that had been swirling about for some time. In three sections, the first dealt with theory and research methods, the second with the nature of HRM in small and entrepreneurial firms and the third with the functional aspects of HRM. At the time we were aware that the handbook did not cover the entire field and many topics were left unexplored. For example, the topic of regulation was generally absent while issues such as career advancement, performance management, organisational change and gender, diversity and ethnicity were also missing. In essence, the majority of those contributions sought to develop an understanding of the context in which particular aspects of HRM can be played out.