Gauging the conformal group

It is demonstrated that Kibble’s method of gauging the Poincaré group can be applied to the gauging of the conformal group. The action of the gauge transformations is the action of general spacetime diffeomorphisms (or coordinate transformations) combined with a local action of an 11-parameter subgroup of SO(4,2). Because the translational subgroup is not an invariant subgroup of the conformal group the appropriate generalisation of the derivative of a physical field is not a covariant derivative in the usual sense, but this does not lead to any inconsistencies.

Representation of Stereoisomers in ALWIN

Tlhe well-known Cahn-lngold-Prelog method of specifying the stereoisomers is introduced within the framework of ALWIN-Algorithmic Wiswesser Notation. Given the structural diagram, the structural ALWIN is first formed; the speclflcation symbols are then introduced at the appropriate places to describe the stereoisomers.

Struggles over resources and representations in territorial conflicts in the Northern Autonomous Atlantic Region (RAAN), Nicaragua

Territoriality is a central issue in indigenous peoples struggles. The territorial struggles involve struggles over the control of natural resources and over political participation and representation, but also over the perception of territorial rights and the symbolic representation of the territory. These struggles are carried through both in material and symbolic ways through recurring to different discourses and representations that provide legitimation for the territorial claims of the group. The study is located in the Northern Autonomous Atlantic Region of Nicaragua. The study concerns the territorial strategies, conceptions and practices of the indigenous people and other actors. Territorial conflicts exist between the autonomous region and the central government of Nicaragua, between mestizo settlers and indigenous people, between different indigenous groups, and between these and development agents such as conservation projects. The study focuses on how territorial discourses and representations are used to legitimate territorial control. Environmental, historical and cartographical discourses are the most important discourses recurred to. The influence of discourses and representations on the territorial practices and policies of the different actors, the links between the local struggles and global processes, and the broader structural factors impacting on the territorial struggles are also analysed. Among the structural factors are the problems related to land tenure and management and the use of natural resources, the advance of the agricultural frontier, the institutional weaknesses of the central and regional governments and the legislative processes. The territorial discourses are both recurred to in a strategic way and also grounded in local ideals and practices. The discourses have produced real effects for example in legislation, land tenure systems, political representation and environmental practices. Although the use of discourses and representations are an important power tool in territorial struggles, territorial control cannot be effectively accomplished merely through representing territorial claims in a legitimate way or through reforming legislation, as the conflicts are also largely a result of structural factors affecting the region. The fieldwork was carried out during a total of twelve months between 2000 and 2002. The research methods used were semi-structured interviews, participant observation and participatory research methods. A broad range of literary sources were also used to collect data. The study is located within the field of critical political geography with a discursive political ecology approach. It can be called a critical realist approach to the discursive analysis of indigenous territoriality.

The evolution of entrepreneurial learning

- Purpose The purpose of this paper is to present an evolutionary perspective on entrepreneurial learning, whilst also accounting for fundamental ecological processes, by focusing on the development of key recurring, knowledge components within nascent and growing small businesses. - Design/methodology/approach The paper relates key developments within the organizational evolution literature to research on entrepreneurial learning, with arguments presented in favor of adopting a multi‐level co‐evolutionary perspective that captures and explains hidden ecological process, such as niche‐construction. - Findings It is argued in the paper that such a multi‐level focus on key recurring knowledge components can shed new light on the process of entrepreneurial learning and lead to the cross‐fertilization of ideas across different domains of study, by offering researchers the opportunity to use the framework of variation‐selection‐retention to develop a multi‐level representation of organizational and entrepreneurial learning. - Originality/value Entrepreneurial learning viewed in this way, as a multi‐level struggle for survival amongst competing knowledge components, can provide entrepreneurs with a set of evolutionary heuristics as they re‐interpret their understanding of the evolution of their business.

On the Geometry of Infinite-Dimensional Grassmannian Manifolds and Gauge Theory

This PhD Thesis is about certain infinite-dimensional Grassmannian manifolds that arise naturally in geometry, representation theory and mathematical physics. From the physics point of view one encounters these infinite-dimensional manifolds when trying to understand the second quantization of fermions. The many particle Hilbert space of the second quantized fermions is called the fermionic Fock space. A typical element of the fermionic Fock space can be thought to be a linear combination of the configurations m particles and n anti-particles . Geometrically the fermionic Fock space can be constructed as holomorphic sections of a certain (dual)determinant line bundle lying over the so called restricted Grassmannian manifold, which is a typical example of an infinite-dimensional Grassmannian manifold one encounters in QFT. The construction should be compared with its well-known finite-dimensional analogue, where one realizes an exterior power of a finite-dimensional vector space as the space of holomorphic sections of a determinant line bundle lying over a finite-dimensional Grassmannian manifold. The connection with infinite-dimensional representation theory stems from the fact that the restricted Grassmannian manifold is an infinite-dimensional homogeneous (Kähler) manifold, i.e. it is of the form G/H where G is a certain infinite-dimensional Lie group and H its subgroup. A central extension of G acts on the total space of the dual determinant line bundle and also on the space its holomorphic sections; thus G admits a (projective) representation on the fermionic Fock space. This construction also induces the so called basic representation for loop groups (of compact groups), which in turn are vitally important in string theory / conformal field theory. The Thesis consists of three chapters: the first chapter is an introduction to the backround material and the other two chapters are individually written research articles. The first article deals in a new way with the well-known question in Yang-Mills theory, when can one lift the action of the gauge transformation group on the space of connection one forms to the total space of the Fock bundle in a compatible way with the second quantized Dirac operator. In general there is an obstruction to this (called the Mickelsson-Faddeev anomaly) and various geometric interpretations for this anomaly, using such things as group extensions and bundle gerbes, have been given earlier. In this work we give a new geometric interpretation for the Faddeev-Mickelsson anomaly in terms of differentiable gerbes (certain sheaves of categories) and central extensions of Lie groupoids. The second research article deals with the question how to define a Dirac-like operator on the restricted Grassmannian manifold, which is an infinite-dimensional space and hence not in the landscape of standard Dirac operator theory. The construction relies heavily on infinite-dimensional representation theory and one of the most technically demanding challenges is to be able to introduce proper normal orderings for certain infinite sums of operators in such a way that all divergences will disappear and the infinite sum will make sense as a well-defined operator acting on a suitable Hilbert space of spinors. This research article was motivated by a more extensive ongoing project to construct twisted K-theory classes in Yang-Mills theory via a Dirac-like operator on the restricted Grassmannian manifold.

Multiple instance dictionary learning for activity representation

This paper presents an effective feature representation method in the context of activity recognition. Efficient and effective feature representation plays a crucial role not only in activity recognition, but also in a wide range of applications such as motion analysis, tracking, 3D scene understanding etc. In the context of activity recognition, local features are increasingly popular for representing videos because of their simplicity and efficiency. While they achieve state-of-the-art performance with low computational requirements, their performance is still limited for real world applications due to a lack of contextual information and models not being tailored to specific activities. We propose a new activity representation framework to address the shortcomings of the popular, but simple bag-of-words approach. In our framework, first multiple instance SVM (mi-SVM) is used to identify positive features for each action category and the k-means algorithm is used to generate a codebook. Then locality-constrained linear coding is used to encode the features into the generated codebook, followed by spatio-temporal pyramid pooling to convey the spatio-temporal statistics. Finally, an SVM is used to classify the videos. Experiments carried out on two popular datasets with varying complexity demonstrate significant performance improvement over the base-line bag-of-feature method.

Fungus-feeding Thysanoptera: Phlaeothripinae of the Idiothrips genus-group in Australia, with nine new species

In a group of fungus-feeding Phlaeothripinae characterized by complex body sculpture, identification keys are provided to three genera and 15 species from Australia, including nine new species. In the genus Azaleothrips one new species is described, and one Asian species is newly recorded from Australia. The genus Stictothrips is recorded from Australia for the first time, with two new species. Within the genus Strepterothrips considerable structural diversity is recorded including three new species in which antennal segment III is greatly reduced and bears no sense cones. Some species in this genus exhibit the unusual condition of having several setae on the pelta, the first abdominal tergite. Problems in the production of generic diagnoses within the Phlaeothripinae are discussed.

Tannakian Formalism Applied to the Category of Mixed Hodge Structures

Many problems in analysis have been solved using the theory of Hodge structures. P. Deligne started to treat these structures in a categorical way. Following him, we introduce the categories of mixed real and complex Hodge structures. Category of mixed Hodge structures over the field of real or complex numbers is a rigid abelian tensor category, and in fact, a neutral Tannakian category. Therefore it is equivalent to the category of representations of an affine group scheme. The direct sums of pure Hodge structures of different weights over real or complex numbers can be realized as a representation of the torus group, whose complex points is the Cartesian product of two punctured complex planes. Mixed Hodge structures turn out to consist of information of a direct sum of pure Hodge structures of different weights and a nilpotent automorphism. Therefore mixed Hodge structures correspond to the representations of certain semidirect product of a nilpotent group and the torus group acting on it.

The neuroscience of inspirational leadership: the importance of collective-oriented language and shared group membership

Effective leaders are believed to inspire followers by providing inclusive visions of the future that followers can identify with. In the present study, we examined the neural mechanisms underlying this process, testing key hypotheses derived from transformational and social identity approaches to leadership. While undergoing functional MRI, supporters from the two major Australian political parties (Liberal vs. Labor) were presented with inspirational collective-oriented and noninspirational personal-oriented statements made by in-group and out-group leaders. Imaging data revealed that inspirational (rather than noninspirational) statements from in-group leaders were associated with increased activation in the bilateral rostral inferior parietal lobule, pars opercularis, and posterior midcingulate cortex: brain areas that are typically implicated in controlling semantic information processing. In contrast, for out-group leaders, greater activation in these areas was associated with noninspirational statements. In addition, noninspirational statements by in-group (but not out-group) leaders resulted in increased activation in the medial prefrontal cortex, an area typically associated with reasoning about a person’s mental state. These results show that followers processed identical statements qualitatively differently as a function of leaders’ group membership, thus demonstrating that shared identity acts as an amplifier for inspirational leadership communication.

New light on the optical equivalence theorem and a new type of discrete diagonal coherent state representation

In many instances we find it advantageous to display a quantum optical density matrix as a generalized statistical ensemble of coherent wave fields. The weight functions involved in these constructions turn out to belong to a family of distributions, not always smooth functions. In this paper we investigate this question anew and show how it is related to the problem of expanding an arbitrary state in terms of an overcomplete subfamily of the overcomplete set of coherent states. This provides a relatively transparent derivation of the optical equivalence theorem. An interesting by-product is the discovery of a new class of discrete diagonal representations.

Creative writing: A practice-based account of designing and facilitating life-writing workshops for a group With severe mental illness

This chapter is based on the experience and findings of a pilot project developed to investigate the feasibility of providing a writing workshop for people participating in psychosocial rehabilitation programmes provided by a non-government agency in Brisbane, Queensland, Australia. It was a qualitative study, making use of observational data, interviews with participants, and informal reports. We did not seek to test theoretical models concerning the link between creative writing and recovery through the pilot project, but rather to evaluate the immediate impact of a writing workshop conducted in the manner outlined in the preceding chapter by Philip Neilsen (chapter 7).