TensorPack : a Maple-based software package for the manipulation of algebraic expressions of tensors in general relativity

In this paper we: (1) introduce TensorPack, a software package for the algebraic manipulation of tensors in covariant index format in Maple; (2) briefly demonstrate the use of the package with an orthonormal tensor proof of the shearfree conjecture for dust. TensorPack is based on the Riemann and Canon tensor software packages and uses their functions to express tensors in an indexed covariant format. TensorPack uses a string representation as input and provides functions for output in index form. It extends the functionality to basic algebra of tensors, substitution, covariant differentiation, contraction, raising/lowering indices, symmetry functions and other accessory functions. The output can be merged with text in the Maple environment to create a full working document with embedded dynamic functionality. The package offers potential for manipulation of indexed algebraic tensor expressions in a flexible software environment.

Implementation of an integrated, technology-based, discovery mode assessment item involving an incubation period to enhance learning outcomes for engineering maths students

In this paper we discuss our current efforts to develop and implement an exploratory, discovery mode assessment item into the total learning and assessment profile for a target group of about 100 second level engineering mathematics students. The assessment item under development is composed of 2 parts, namely, a set of "pre-lab" homework problems (which focus on relevant prior mathematical knowledge, concepts and skills), and complementary computing laboratory exercises which are undertaken within a fixed (1 hour) time frame. In particular, the computing exercises exploit the algebraic manipulation and visualisation capabilities of the symbolic algebra package MAPLE, with the aim of promoting understanding of certain mathematical concepts and skills via visual and intuitive reasoning, rather than a formal or rigorous approach. The assessment task we are developing is aimed at providing students with a significant learning experience, in addition to providing feedback on their individual knowledge and skills. To this end, a noteworthy feature of the scheme is that marks awarded for the laboratory work are primarily based on the extent to which reflective, critical thinking is demonstrated, rather than the amount of CBE-style tasks completed by the student within the allowed time. With regard to student learning outcomes, a novel and potentially critical feature of our scheme is that the assessment task is designed to be intimately linked to the overall course content, in that it aims to introduce important concepts and skills (via individual student exploration) which will be revisited somewhat later in the pedagogically more restrictive formal lecture component of the course (typically a large group plenary format). Furthermore, the time delay involved, or "incubation period", is also a deliberate design feature: it is intended to allow students the opportunity to undergo potentially important internal re-adjustments in their understanding, before being exposed to lectures on related course content which are invariably delivered in a more condensed, formal and mathematically rigorous manner. In our presentation, we will discuss in more detail our motivation and rationale for trailing such a scheme for the targeted student group. Some of the advantages and disadvantages of our approach (as we perceived them at the initial stages) will also be enumerated. In a companion paper, the theoretical framework for our approach will be more fully elaborated, and measures of student learning outcomes (as obtained from eg. student provided feedback) will be discussed.

FaceXpress : an integrated software suite for facial emotion stimulus manipulation and facial measurement

The characterisation of facial expression through landmark-based analysis methods such as FACEM (Pilowsky & Katsikitis, 1994) has a variety of uses in psychiatric and psychological research. In these systems, important structural relationships are extracted from images of facial expressions by the analysis of a pre-defined set of feature points. These relationship measures may then be used, for instance, to assess the degree of variability and similarity between different facial expressions of emotion. FaceXpress is a multimedia software suite that provides a generalised workbench for landmark-based facial emotion analysis and stimulus manipulation. It is a flexible tool that is designed to be specialised at runtime by the user. While FaceXpress has been used to implement the FACEM process, it can also be configured to support any other similar, arbitrary system for quantifying human facial emotion. FaceXpress also implements an integrated set of image processing tools and specialised tools for facial expression stimulus production including facial morphing routines and the generation of expression-representative line drawings from photographs.

Formal description, compression and transformation of digital pictures

This paper describes the application of vector spaces over Galois fields, for obtaining a formal description of a picture in the form of a very compact, non-redundant, unique syntactic code. Two different methods of encoding are described. Both these methods consist in identifying the given picture as a matrix (called picture matrix) over a finite field. In the first method, the eigenvalues and eigenvectors of this matrix are obtained. The eigenvector expansion theorem is then used to reconstruct the original matrix. If several of the eigenvalues happen to be zero this scheme results in a considerable compression. In the second method, the picture matrix is reduced to a primitive diagonal form (Hermite canonical form) by elementary row and column transformations. These sequences of elementary transformations constitute a unique and unambiguous syntactic code-called Hermite code—for reconstructing the picture from the primitive diagonal matrix. A good compression of the picture results, if the rank of the matrix is considerably lower than its order. An important aspect of this code is that it preserves the neighbourhood relations in the picture and the primitive remains invariant under translation, rotation, reflection, enlargement and replication. It is also possible to derive the codes for these transformed pictures from the Hermite code of the original picture by simple algebraic manipulation. This code will find extensive applications in picture compression, storage, retrieval, transmission and in designing pattern recognition and artificial intelligence systems.

Sheaves, local homeomorphisms and local sets as Hilbert locale modules

We give a thorough account of the various equivalent notions for \sheaf" on a locale, namely the separated and complete presheaves, the local home- omorphisms, and the local sets, and to provide a new approach based on quantale modules whereby we see that sheaves can be identi¯ed with certain Hilbert modules in the sense of Paseka. This formulation provides us with an interesting category that has immediate meaningful relations to those of sheaves, local homeomorphisms and local sets. The concept of B-set (local set over the locale B) present in [3] is seen as a simetric idempotent matrix with entries on B, and a map of B-sets as de¯ned in [8] is shown to be also a matrix satisfying some conditions. This gives us useful tools that permit the algebraic manipulation of B-sets. The main result is to show that the existing notions of \sheaf" on a locale B are also equivalent to a new concept what we call a Hilbert module with an Hilbert base. These modules are the projective modules since they are the image of a free module by a idempotent automorphism On the ¯rst chapter, we recall some well known results about partially ordered sets and lattices. On chapter two we introduce the category of Sup-lattices, and the cate- gory of locales, Loc. We describe the adjunction between this category and the category Top of topological spaces whose restriction to spacial locales give us a duality between this category and the category of sober spaces. We ¯nish this chapter with the de¯nitions of module over a quantale and Hilbert Module. Chapter three concerns with various equivalent notions namely: sheaves of sets, local homeomorphisms and local sets (projection matrices with entries on a locale). We ¯nish giving a direct algebraic proof that each local set is isomorphic to a complete local set, whose rows correspond to the singletons. On chapter four we de¯ne B-locale, study open maps and local homeo- morphims. The main new result is on the ¯fth chapter where we de¯ne the Hilbert modules and Hilbert modules with an Hilbert and show this latter concept is equivalent to the previous notions of sheaf over a locale.

Design and control of multi-finger haptic devices for dexterous manipulation

En la interacción con el entorno que nos rodea durante nuestra vida diaria (utilizar un cepillo de dientes, abrir puertas, utilizar el teléfono móvil, etc.) y en situaciones profesionales (intervenciones médicas, procesos de producción, etc.), típicamente realizamos manipulaciones avanzadas que incluyen la utilización de los dedos de ambas manos. De esta forma el desarrollo de métodos de interacción háptica multi-dedo dan lugar a interfaces hombre-máquina más naturales y realistas. No obstante, la mayoría de interfaces hápticas disponibles en el mercado están basadas en interacciones con un solo punto de contacto; esto puede ser suficiente para la exploración o palpación del entorno pero no permite la realización de tareas más avanzadas como agarres. En esta tesis, se investiga el diseño mecánico, control y aplicaciones de dispositivos hápticos modulares con capacidad de reflexión de fuerzas en los dedos índice, corazón y pulgar del usuario. El diseño mecánico de la interfaz diseñada, ha sido optimizado con funciones multi-objetivo para conseguir una baja inercia, un amplio espacio de trabajo, alta manipulabilidad y reflexión de fuerzas superiores a 3 N en el espacio de trabajo. El ancho de banda y la rigidez del dispositivo se han evaluado mediante simulación y experimentación real. Una de las áreas más importantes en el diseño de estos dispositivos es el efector final, ya que es la parte que está en contacto con el usuario. Durante este trabajo se ha diseñado un dedal de bajo peso, adaptable a diferentes usuarios que, mediante la incorporación de sensores de contacto, permite estimar fuerzas normales y tangenciales durante la interacción con entornos reales y virtuales. Para el diseño de la arquitectura de control, se estudiaron los principales requisitos para estos dispositivos. Entre estos, cabe destacar la adquisición, procesado e intercambio a través de internet de numerosas señales de control e instrumentación; la computación de equaciones matemáticas incluyendo la cinemática directa e inversa, jacobiana, algoritmos de detección de agarres, etc. Todos estos componentes deben calcularse en tiempo real garantizando una frecuencia mínima de 1 KHz. Además, se describen sistemas para manipulación de precisión virtual y remota; así como el diseño de un método denominado "desacoplo cinemático iterativo" para computar la cinemática inversa de robots y la comparación con otros métodos actuales. Para entender la importancia de la interacción multimodal, se ha llevado a cabo un estudio para comprobar qué estímulos sensoriales se correlacionan con tiempos de respuesta más rápidos y de mayor precisión. Estos experimentos se desarrollaron en colaboración con neurocientíficos del instituto Technion Israel Institute of Technology. Comparando los tiempos de respuesta en la interacción unimodal (auditiva, visual y háptica) con combinaciones bimodales y trimodales de los mismos, se demuestra que el movimiento sincronizado de los dedos para generar respuestas de agarre se basa principalmente en la percepción háptica. La ventaja en el tiempo de procesamiento de los estímulos hápticos, sugiere que los entornos virtuales que incluyen esta componente sensorial generan mejores contingencias motoras y mejoran la credibilidad de los eventos. Se concluye que, los sistemas que incluyen percepción háptica dotan a los usuarios de más tiempo en las etapas cognitivas para rellenar información de forma creativa y formar una experiencia más rica. Una aplicación interesante de los dispositivos hápticos es el diseño de nuevos simuladores que permitan entrenar habilidades manuales en el sector médico. En colaboración con fisioterapeutas de Griffith University en Australia, se desarrolló un simulador que permite realizar ejercicios de rehabilitación de la mano. Las propiedades de rigidez no lineales de la articulación metacarpofalange del dedo índice se estimaron mediante la utilización del efector final diseñado. Estos parámetros, se han implementado en un escenario que simula el comportamiento de la mano humana y que permite la interacción háptica a través de esta interfaz. Las aplicaciones potenciales de este simulador están relacionadas con entrenamiento y educación de estudiantes de fisioterapia. En esta tesis, se han desarrollado nuevos métodos que permiten el control simultáneo de robots y manos robóticas en la interacción con entornos reales. El espacio de trabajo alcanzable por el dispositivo háptico, se extiende mediante el cambio de modo de control automático entre posición y velocidad. Además, estos métodos permiten reconocer el gesto del usuario durante las primeras etapas de aproximación al objeto para su agarre. Mediante experimentos de manipulación avanzada de objetos con un manipulador y diferentes manos robóticas, se muestra que el tiempo en realizar una tarea se reduce y que el sistema permite la realización de la tarea con precisión. Este trabajo, es el resultado de una colaboración con investigadores de Harvard BioRobotics Laboratory. ABSTRACT When we interact with the environment in our daily life (using a toothbrush, opening doors, using cell-phones, etc.), or in professional situations (medical interventions, manufacturing processes, etc.) we typically perform dexterous manipulations that involve multiple fingers and palm for both hands. Therefore, multi-Finger haptic methods can provide a realistic and natural human-machine interface to enhance immersion when interacting with simulated or remote environments. Most commercial devices allow haptic interaction with only one contact point, which may be sufficient for some exploration or palpation tasks but are not enough to perform advanced object manipulations such as grasping. In this thesis, I investigate the mechanical design, control and applications of a modular haptic device that can provide force feedback to the index, thumb and middle fingers of the user. The designed mechanical device is optimized with a multi-objective design function to achieve a low inertia, a large workspace, manipulability, and force-feedback of up to 3 N within the workspace; the bandwidth and rigidity for the device is assessed through simulation and real experimentation. One of the most important areas when designing haptic devices is the end-effector, since it is in contact with the user. In this thesis the design and evaluation of a thimble-like, lightweight, user-adaptable, and cost-effective device that incorporates four contact force sensors is described. This design allows estimation of the forces applied by a user during manipulation of virtual and real objects. The design of a real-time, modular control architecture for multi-finger haptic interaction is described. Requirements for control of multi-finger haptic devices are explored. Moreover, a large number of signals have to be acquired, processed, sent over the network and mathematical computations such as device direct and inverse kinematics, jacobian, grasp detection algorithms, etc. have to be calculated in Real Time to assure the required high fidelity for the haptic interaction. The Hardware control architecture has different modules and consists of an FPGA for the low-level controller and a RT controller for managing all the complex calculations (jacobian, kinematics, etc.); this provides a compact and scalable solution for the required high computation capabilities assuring a correct frequency rate for the control loop of 1 kHz. A set-up for dexterous virtual and real manipulation is described. Moreover, a new algorithm named the iterative kinematic decoupling method was implemented to solve the inverse kinematics of a robotic manipulator. In order to understand the importance of multi-modal interaction including haptics, a subject study was carried out to look for sensory stimuli that correlate with fast response time and enhanced accuracy. This experiment was carried out in collaboration with neuro-scientists from Technion Israel Institute of Technology. By comparing the grasping response times in unimodal (auditory, visual, and haptic) events with the response times in events with bimodal and trimodal combinations. It is concluded that in grasping tasks the synchronized motion of the fingers to generate the grasping response relies on haptic cues. This processing-speed advantage of haptic cues suggests that multimodalhaptic virtual environments are superior in generating motor contingencies, enhancing the plausibility of events. Applications that include haptics provide users with more time at the cognitive stages to fill in missing information creatively and form a richer experience. A major application of haptic devices is the design of new simulators to train manual skills for the medical sector. In collaboration with physical therapists from Griffith University in Australia, we developed a simulator to allow hand rehabilitation manipulations. First, the non-linear stiffness properties of the metacarpophalangeal joint of the index finger were estimated by using the designed end-effector; these parameters are implemented in a scenario that simulates the behavior of the human hand and that allows haptic interaction through the designed haptic device. The potential application of this work is related to educational and medical training purposes. In this thesis, new methods to simultaneously control the position and orientation of a robotic manipulator and the grasp of a robotic hand when interacting with large real environments are studied. The reachable workspace is extended by automatically switching between rate and position control modes. Moreover, the human hand gesture is recognized by reading the relative movements of the index, thumb and middle fingers of the user during the early stages of the approximation-to-the-object phase and then mapped to the robotic hand actuators. These methods are validated to perform dexterous manipulation of objects with a robotic manipulator, and different robotic hands. This work is the result of a research collaboration with researchers from the Harvard BioRobotics Laboratory. The developed experiments show that the overall task time is reduced and that the developed methods allow for full dexterity and correct completion of dexterous manipulations.

Strong shift equivalence, algebraic K-theory, and isolating zero-dimensional dynamics on manifolds

We study the relations of shift equivalence and strong shift equivalence for matrices over a ring $\mathcal{R}$, and establish a connection between these relations and algebraic K-theory. We utilize this connection to obtain results in two areas where the shift and strong shift equivalence relations play an important role: the study of finite group extensions of shifts of finite type, and the Generalized Spectral Conjectures of Boyle and Handelman for nonnegative matrices over subrings of the real numbers. We show the refinement of the shift equivalence class of a matrix $A$ over a ring $\mathcal{R}$ by strong shift equivalence classes over the ring is classified by a quotient $NK_{1}(\mathcal{R}) / E(A,\mathcal{R})$ of the algebraic K-group $NK_{1}(\calR)$. We use the K-theory of non-commutative localizations to show that in certain cases the subgroup $E(A,\mathcal{R})$ must vanish, including the case $A$ is invertible over $\mathcal{R}$. We use the K-theory connection to clarify the structure of algebraic invariants for finite group extensions of shifts of finite type. In particular, we give a strong negative answer to a question of Parry, who asked whether the dynamical zeta function determines up to finitely many topological conjugacy classes the extensions by $G$ of a fixed mixing shift of finite type. We apply the K-theory connection to prove the equivalence of a strong and weak form of the Generalized Spectral Conjecture of Boyle and Handelman for primitive matrices over subrings of $\mathbb{R}$. We construct explicit matrices whose class in the algebraic K-group $NK_{1}(\mathcal{R})$ is non-zero for certain rings $\mathcal{R}$ motivated by applications. We study the possible dynamics of the restriction of a homeomorphism of a compact manifold to an isolated zero-dimensional set. We prove that for $n \ge 3$ every compact zero-dimensional system can arise as an isolated invariant set for a homeomorphism of a compact $n$-manifold. In dimension two, we provide obstructions and examples.

The symbolic, socio-economic and exchange value of Imperial German and National Socialist medals and badges, 1701 to the present

This thesis examines the manufacture, use, exchange (including gift exchange), collecting and commodification of German medals and badges from the early 18th century until the present-day, with particular attention being given to the symbols that were deployed by the National Socialist German Workers’ Party (NSDAP) between 1919 and 1945. It does so by focusing in particular on the construction of value through insignia, and how such badges and their symbolic and monetary value changed over time. In order to achieve this, the thesis adopts a chronological structure, which encompasses the creation of Prussia in 1701, the Napoleonic wars and the increased democratisation of military awards such as the Iron Cross during the Great War. The collapse of the Kaiserreich in 1918 was the major factor that led to the creation of the NSDAP under the eventual strangle-hold of Hitler, a fundamentally racist and anti-Semitic movement that continued the German tradition of awarding and wearing badges. The traditional symbols of Imperial Germany, such as the eagle, were then infused with the swastika, an emblem that was meant to signify anti-Semitism, thus creating a hybrid identity. This combination was then replicated en-masse, and eventually eclipsed all the symbols that had possessed symbolic significance in Germany’s past. After Hitler was appointed Chancellor in 1933, millions of medals and badges were produced in an effort to create a racially based “People’s Community”, but the steel and iron that were required for munitions eventually led to substitute materials being utilised and developed in order to manufacture millions of politically oriented badges. The Second World War unleashed Nazi terror across Europe, and the conscripts and volunteers who took part in this fight for living-space were rewarded with medals that were modelled on those that had been instituted during Imperial times. The colonial conquest and occupation of the East by the Wehrmacht, the Order Police and the Waffen-SS surpassed the brutality of former wars that finally culminated in the Holocaust, and some of these horrific crimes and the perpetrators of them were perversely rewarded with medals and badges. Despite Nazism being thoroughly discredited, many of the Allied soldiers who occupied Germany took part in the age-old practice of obtaining trophies of war, which reconfigured the meaning of Nazi badges as souvenirs, and began the process of their increased commodification on an emerging secondary collectors’ market. In order to analyse the dynamics of this market, a “basket” of badges is examined that enables a discussion of the role that aesthetics, scarcity and authenticity have in determining the price of the artefacts. In summary, this thesis demonstrates how the symbolic, socio-economic and exchange value of German military and political medals and badges has changed substantially over time, provides a stimulus for scholars to conduct research in this under-developed area, and encourages collectors to investigate the artefacts that they collect in a more historically contextualised manner.

Integrated visual perception architecture for robotic clothes perception and manipulation

This thesis proposes a generic visual perception architecture for robotic clothes perception and manipulation. This proposed architecture is fully integrated with a stereo vision system and a dual-arm robot and is able to perform a number of autonomous laundering tasks. Clothes perception and manipulation is a novel research topic in robotics and has experienced rapid development in recent years. Compared to the task of perceiving and manipulating rigid objects, clothes perception and manipulation poses a greater challenge. This can be attributed to two reasons: firstly, deformable clothing requires precise (high-acuity) visual perception and dexterous manipulation; secondly, as clothing approximates a non-rigid 2-manifold in 3-space, that can adopt a quasi-infinite configuration space, the potential variability in the appearance of clothing items makes them difficult to understand, identify uniquely, and interact with by machine. From an applications perspective, and as part of EU CloPeMa project, the integrated visual perception architecture refines a pre-existing clothing manipulation pipeline by completing pre-wash clothes (category) sorting (using single-shot or interactive perception for garment categorisation and manipulation) and post-wash dual-arm flattening. To the best of the author’s knowledge, as investigated in this thesis, the autonomous clothing perception and manipulation solutions presented here were first proposed and reported by the author. All of the reported robot demonstrations in this work follow a perception-manipulation method- ology where visual and tactile feedback (in the form of surface wrinkledness captured by the high accuracy depth sensor i.e. CloPeMa stereo head or the predictive confidence modelled by Gaussian Processing) serve as the halting criteria in the flattening and sorting tasks, respectively. From scientific perspective, the proposed visual perception architecture addresses the above challenges by parsing and grouping 3D clothing configurations hierarchically from low-level curvatures, through mid-level surface shape representations (providing topological descriptions and 3D texture representations), to high-level semantic structures and statistical descriptions. A range of visual features such as Shape Index, Surface Topologies Analysis and Local Binary Patterns have been adapted within this work to parse clothing surfaces and textures and several novel features have been devised, including B-Spline Patches with Locality-Constrained Linear coding, and Topology Spatial Distance to describe and quantify generic landmarks (wrinkles and folds). The essence of this proposed architecture comprises 3D generic surface parsing and interpretation, which is critical to underpinning a number of laundering tasks and has the potential to be extended to other rigid and non-rigid object perception and manipulation tasks. The experimental results presented in this thesis demonstrate that: firstly, the proposed grasp- ing approach achieves on-average 84.7% accuracy; secondly, the proposed flattening approach is able to flatten towels, t-shirts and pants (shorts) within 9 iterations on-average; thirdly, the proposed clothes recognition pipeline can recognise clothes categories from highly wrinkled configurations and advances the state-of-the-art by 36% in terms of classification accuracy, achieving an 83.2% true-positive classification rate when discriminating between five categories of clothes; finally the Gaussian Process based interactive perception approach exhibits a substantial improvement over single-shot perception. Accordingly, this thesis has advanced the state-of-the-art of robot clothes perception and manipulation.

Examining the antecedents and consequences of ritualized fan behavior [Abstract]

One of the features of the sporting industry is the ritualized way in which it is consumed across the world. Fans of every sport have rituals and superstitions to help them enjoy the spectacle, socialize with other like-minded fans, and reduce some of the anxiety of watching their team play. These rituals include dress, barracking styles and pre and post match behaviors. What is not known are the factors that lead fans to engage in ritual behaviors and what relationship rituals have with desirable outcomes such as increased attendance, attitudinal loyalty or satisfaction. Given that some ritual behaviors are clearly undesirable, (e.g., hooliganism), understanding these relationships is important to managers who may be questioning whether rituals should be encouraged. Although ritualized behavior amongst fans is clearly visible, the symbolic and emotional nature of ritual poses challenges to researchers. Most previous ritual research is exploratory and qualitative in nature. This study, however, uses a behavior-based scale to measure fan ritual and relates it to desirable outcomes such as commitment and attendance. Over 2,000 season ticket holders of a football (soccer) team in Australia’s professional A-League competition were surveyed to investigate the antecedents and consequences of fan ritual behavior. Cluster analysis was used to explore the characteristics of respondents, and it revealed that those fans that engage in ritual behavior also differed on many other demographic and attitudinal dimensions. The associations between ritual and psychological commitment, and ritual and attendance are positive and significant. When used in conjunction with other constructs, fan ritual also improves the explanation of attendance behavior. The findings support previous research that found a significant and positive relationship between team identification, involvement and attendance, and extend previous research by finding a significant and positive relationship between rituals and attendance. For sports marketing practitioners, the results indicate the importance of developing and managing consumption rituals tied to game day attendance, with a view to generating uncommon loyalty.

Wavelet based approaches and high resolution methods for complex process models

Many industrial processes and systems can be modelled mathematically by a set of Partial Differential Equations (PDEs). Finding a solution to such a PDF model is essential for system design, simulation, and process control purpose. However, major difficulties appear when solving PDEs with singularity. Traditional numerical methods, such as finite difference, finite element, and polynomial based orthogonal collocation, not only have limitations to fully capture the process dynamics but also demand enormous computation power due to the large number of elements or mesh points for accommodation of sharp variations. To tackle this challenging problem, wavelet based approaches and high resolution methods have been recently developed with successful applications to a fixedbed adsorption column model. Our investigation has shown that recent advances in wavelet based approaches and high resolution methods have the potential to be adopted for solving more complicated dynamic system models. This chapter will highlight the successful applications of these new methods in solving complex models of simulated-moving-bed (SMB) chromatographic processes. A SMB process is a distributed parameter system and can be mathematically described by a set of partial/ordinary differential equations and algebraic equations. These equations are highly coupled; experience wave propagations with steep front, and require significant numerical effort to solve. To demonstrate the numerical computing power of the wavelet based approaches and high resolution methods, a single column chromatographic process modelled by a Transport-Dispersive-Equilibrium linear model is investigated first. Numerical solutions from the upwind-1 finite difference, wavelet-collocation, and high resolution methods are evaluated by quantitative comparisons with the analytical solution for a range of Peclet numbers. After that, the advantages of the wavelet based approaches and high resolution methods are further demonstrated through applications to a dynamic SMB model for an enantiomers separation process. This research has revealed that for a PDE system with a low Peclet number, all existing numerical methods work well, but the upwind finite difference method consumes the most time for the same degree of accuracy of the numerical solution. The high resolution method provides an accurate numerical solution for a PDE system with a medium Peclet number. The wavelet collocation method is capable of catching up steep changes in the solution, and thus can be used for solving PDE models with high singularity. For the complex SMB system models under consideration, both the wavelet based approaches and high resolution methods are good candidates in terms of computation demand and prediction accuracy on the steep front. The high resolution methods have shown better stability in achieving steady state in the specific case studied in this Chapter.

Lost children and imaginary mothers in Sonya Hartnett's Of A Boy

In Powers of Horror, Julia Kristeva writes about lost children. These are what she calls “dejects,” who, in the psychodrama of subject formation, fail to fully absent the body of the mother, to accept the Law of the Father and the Symbolic, and subsequently to establish “clear boundaries which constitute the object-world for normal subjects.” Dejects are “strays” looking for a place to belong, a place that is bound up with the Imaginary mother of the pre-Oedipal period. Kristeva’s sketch of the deject as one who is unable to negotiate a proper path to the Symbolicis useful to a reading of Hartnett’s Of A Boy (2002),a novel that also deals with lost children and imaginary mothers. However, in its portrayal of children who are doomed to never achieve adulthood, Of A Boy enacts a haunting retrieval of the pre-Oedipal from the dark side of phallocentric representation, privileging the semiotic (Kristeva’s concept) and the maternal as necessary disruptive checks on a patriarchal Symbolic Order.

Exploring the relationship between grandparents and their grandchild who has a disability

This thesis reports on the findings of a study which sought to explore the relationship between grandparents and their grandchild who has a disability. In contrast to previous studies, it presents the grandparents’ perspective on the roles and relationships they maintain within their families and adopts a qualitative approach to identify the meanings, symbols and beliefs grandparents attribute to their experiences. Grandparents have played and continue to play an important role in the lives of many families, contributing both symbolic and instrumental support to their grandchildren. Changing life expectancy for older people has meant that many more grandparents and grandchildren now have the opportunity to participate in meaningful interactions and to develop strong relationships. In the future, this will be true for great grandparents and in some cases great great grandparents as well. This presents a number of challenges to all concerned as family members negotiate the often complex arena of family life in the 21st Century. Realizing that a grandchild has a disability adds another degree of complexity to the negotiation of roles and responsibilities of grandparents within families. By focussing on grandparents experiences when their grandchild has a disability, this research both explores a knowledge gap in the current literature and more practicably, will inform both grandparents and their families as they negotiate these challenges. This research makes a significant contribution to knowledge in this area by exploring grandparents’ views on the differences in the relationship they have with their typically developing grandchildren and their grandchild with a disability; the impact having a grandchild with a disability had had on their grandparent identity and whether it impacted on quality of life. As well as reporting on the aims of the study, the papers presented in this thesis report on the key topics and themes identified in the analysis of the transcribed interviews conducted with 22 grandparents whose grandchild has a disability. Article 1 presents an overview of the literature which informs current knowledge in relation to grandparents, presenting a historical and theoretical perspective. Additionally, it presents previous literature which discusses the roles and styles grandparents adopt thus providing a framework which is later used to examine the roles and styles adopted by the grandparents in the study. Article 2 addresses the emotional responses grandparents in the study experienced as they grandparented a child with a disability. Comparing these emotions to that of a roller coaster ride, ranging from absolute sadness and grief to pride and delight, these findings highlight their unique experiences and will be reassuring for other grandparents who experience similar emotional responses. Article 3 discusses from the grandparents’ perspective, how having a grandchild with a disability has impacted on their family. Whilst reporting on the day to day challenges of competing family commitments and conflict, a number of grandparents in this study also commented that the experience had made them closer as a family and that there had been significant changes in how some individual family members now viewed people with disability. Article 4 explores the impact having a grandchild with a disability may have on the grandparents’ sense of identity and enactment of the grandparent role, utilising Neugarten and Weinstein’s (1964) classic grandparenting styles and Kornhaber’s (1996) concepts of latent and functional grandparent identity as a basis for comparison. It provides important insight into grandparenting identity when a child has a disability, suggesting that the grandparenting experience and role enactment may be universal with only the context and delivery varying. In summary, this thesis confirms the valuable role grandparents play in the lives of grandchildren who have a disability and their families. It identifies a number of implications and makes recommendations for future research and practice.

Crisis communication under transformative change : the emergent context and roles of primary and secondary organisations

In an era of complex challenges that draw sustained media attention and entangle multiple organisational actors, this thesis addresses the gap between current trends in society and business, and existing scholarship in public relations and crisis communication. By responding to calls from crisis communication researchers to develop theory (Coombs, 2006a), to examine the interdependencies of crises (Seeger, Sellnow, & Ulmer, 1998), and to consider variation in crisis response (Seeger, 2002), this thesis contributes to theory development in crisis communication and public relations. Through transformative change, this thesis extends existing scholarship built on a preservation or conservation logic where public relations is used to maintain stability by incrementally responding to changes in an organisation‘s environment (Cutlip, Center, & Broom, 2006; Everett, 2001; Grunig, 2000; Spicer, 1997). Based on the opportunity to contribute to ongoing theoretical development in the literature, the overall research problem guiding this thesis asks: How does transformative change during crisis influence corporate actors’ communication? This thesis adopts punctuated equilibrium theory, which describes change as alternating between long periods of stability and short periods of revolutionary or transformative change (Gersick, 1991; Romanelli & Tushman, 1994; Siggelkow, 2002; Tushman, Newman, & Romanelli, 1986; Tushman & Romanelli, 1985). As a theory for change, punctuated equilibrium provides an opportunity to examine public relations and transformative change, building on scholarship that is based primarily on incremental change. Further, existing scholarship in public relations and crisis communication focuses on the actions of single organisations in situational or short-term crisis events. Punctuated equilibrium theory enables the study of multiple crises and multiple organisational responses during transformative change. In doing so, punctuated equilibrium theory provides a framework to explain both the context for transformative change and actions or strategies enacted by organisations during transformative change (Tushman, Newman, & Romanelli, 1986; Tushman & Romanelli, 1985; Tushman, Virany, & Romanelli, 1986). The connections between context and action inform the research questions that guide this thesis: RQ1: What symbolic and substantive strategies persist and change as crises develop from situational events to transformative and multiple linked events? RQ2: What features of the crisis context influence changes in symbolic and substantive strategies? To shed light on these research questions, the thesis adopts a qualitative approach guided by process theory and methods to explicate the events, sequences and activities that were essential to change (Pettigrew, 1992; Van de Ven, 1992). Specifically, the thesis draws on an alternative template strategy (Langley, 1999) that provides several alternative interpretations of the same events (Allison, 1971; Allison & Zelikow, 1999). Following Allison (1971) and Allison and Zelikow (1999), this thesis uses three alternative templates of crisis or strategic response typologies to construct three narratives using media articles and organisational documents. The narratives are compared to identify and draw out different patterns of crisis communication strategies that operate within different crisis contexts. The thesis is based on the crisis events that affected three organisations within the pharmaceutical industry for four years. The primary organisation is Merck, as its product recall crisis triggered transformative change affecting, in different ways, the secondary organisations of Pfizer and Novartis. Three narratives are presented based on the crisis or strategic response typologies of Coombs (2006b), Allen and Caillouet (1994), and Oliver (1991). The findings of this thesis reveal different stories about crisis communication under transformative change. By zooming in to a micro perspective (Nicolini, 2009) to focus on the crisis communication and actions of a single organisation and zooming out to a macro perspective (Nicolini, 2009) to consider multiple organisations, new insights about crisis communication, change and the relationships among multiple organisations are revealed at context and action levels. At the context level, each subsequent narrative demonstrates greater connections among multiple corporate actors. By zooming out from Coombs‘ (2006b) focus on single organisations to consider Allen and Caillouet‘s (1994) integration of the web of corporate actors, the thesis demonstrates how corporate actors add accountability pressures to the primary organisation. Next, by zooming further out to the macro perspective by considering Oliver‘s (1991) strategic responses to institutional processes, the thesis reveals a greater range of corporate actors that are caught up in the process of transformative change and accounts for their varying levels of agency over their environment. By zooming in to a micro perspective and out to a macro perspective (Nicolini, 2009) across alternative templates, the thesis sheds light on sequences, events, and actions of primary and secondary organisations. Although the primary organisation remains the focus of sustained media attention across the four-year time frame, the secondary organisations, even when one faced a similar starting situation to the primary organisation, were buffered by the process of transformative change. This understanding of crisis contexts in transforming environments builds on existing knowledge in crisis communication. At the action level, the thesis also reveals different interpretations from each alternative template. Coombs‘ (2006b) narrative shows persistence in the primary organisation‘s crisis or strategic responses over the four-year time frame of the thesis. That is, the primary organisation consistently applies a diminish crisis response. At times, the primary organisation drew on denial responses when corporate actors questioned its legitimacy or actions. To close the crisis, the primary organisation uses a rebuild crisis posture (Coombs, 2006). These finding are replicated in Allen and Caillouet‘s (1994) narrative, noting this template‘s limitation to communication messages only. Oliver‘s (1991) narrative is consistent with Coombs‘ (2006b) but also demonstrated a shift from a strategic response that signals conformity to the environment to one that signals more active resistance to the environment over time. Specifically, the primary organisation‘s initial response demonstrates conformity but these same messages were used some three years later to set new expectations in the environment in order to shape criteria and build acceptance for future organisational decisions. In summary, the findings demonstrate the power of crisis or strategic responses when considered over time and in the context of transformative change. The conclusions of this research contribute to scholarship in the public relations and management literatures. Based on the significance of organisational theory, the primary contribution of the theory relates to the role of interorganisational linkages or legitimacy buffers that form during the punctuation of equilibrium. The network of linkages among the corporate actors are significant also to the crisis communication literature as they form part of the process model of crisis communication under punctuated equilibrium. This model extends existing research that focuses on crisis communication of single organisations to consider the emergent context that incorporates secondary organisations as well as the localised contests of legitimacy and buffers from regulatory authorities. The thesis also provides an empirical base for punctuated equilibrium in public relations and crisis communication, extending Murphy‘s (2000) introduction of the theory to the public relations literature. In doing this, punctuated equilibrium theory reinvigorates theoretical development in crisis communication by extending existing scholarship around incrementalist approaches and demonstrating how public relations works in the context of transformative change. Further research in this area could consider using alternative templates to study transformative change caused by a range of crisis types from natural disasters to product tampering, and to add further insight into the dynamics between primary and secondary organisations. This thesis contributes to practice by providing guidelines for crisis response strategy selection and indicators related to the emergent context for crises under transformative change that will help primary and secondary organisations‘ responses to crises.