Theory-of-Mind Continuum Model: Why Mind Matters in Philosophy, Psychology and Education

Theory-of-Mind has been defined as the ability to explain and predict human behaviour by imputing mental states, such as attention, intention, desire, emotion, perception and belief, to the self and others (Astington & Barriault, 2001). Theory-of-Mind study began with Piaget and continued through a tradition of meta-cognitive research projects (Flavell, 2004). A study by Baron-Cohen, Leslie and Frith (1985) of Theory-of-Mind abilities in atypically developing children reported major difficulties experienced by children with autism spectrum disorder (ASD) in imputing mental states to others. Since then, a wide range of follow-up research has been conducted to confirm these results. Traditional Theory-of-Mind research on ASD has been based on an either-or assumption that Theory-of-Mind is something one either possesses or does not. However, this approach fails to take account of how the ASD population themselves experience Theory-of-Mind. This paper suggests an alternative approach, Theory-of-Mind continuum model, to understand the Theory-of-Mind experience of people with ASD. The Theory-of-Mind continuum model will be developed through a comparison of subjective and objective aspects of mind, and phenomenal and psychological concepts of mind. This paper will demonstrate the importance of balancing qualitative and quantitative research methods in investigating the minds of people with ASD. It will enrich our theoretical understanding of Theory-of-Mind, as well as contain methodological implications for further studies in Theory-of-Mind

Alternative analytical methods for the identification of cancer-related symptom clusters

Advances in symptom management strategies through a better understanding of cancer symptom clusters depend on the identification of symptom clusters that are valid and reliable. The purpose of this exploratory research was to investigate alternative analytical approaches to identify symptom clusters for patients with cancer, using readily accessible statistical methods, and to justify which methods of identification may be appropriate for this context. Three studies were undertaken: (1) a systematic review of the literature, to identify analytical methods commonly used for symptom cluster identification for cancer patients; (2) a secondary data analysis to identify symptom clusters and compare alternative methods, as a guide to best practice approaches in cross-sectional studies; and (3) a secondary data analysis to investigate the stability of symptom clusters over time. The systematic literature review identified, in 10 years prior to March 2007, 13 cross-sectional studies implementing multivariate methods to identify cancer related symptom clusters. The methods commonly used to group symptoms were exploratory factor analysis, hierarchical cluster analysis and principal components analysis. Common factor analysis methods were recommended as the best practice cross-sectional methods for cancer symptom cluster identification. A comparison of alternative common factor analysis methods was conducted, in a secondary analysis of a sample of 219 ambulatory cancer patients with mixed diagnoses, assessed within one month of commencing chemotherapy treatment. Principal axis factoring, unweighted least squares and image factor analysis identified five consistent symptom clusters, based on patient self-reported distress ratings of 42 physical symptoms. Extraction of an additional cluster was necessary when using alpha factor analysis to determine clinically relevant symptom clusters. The recommended approaches for symptom cluster identification using nonmultivariate normal data were: principal axis factoring or unweighted least squares for factor extraction, followed by oblique rotation; and use of the scree plot and Minimum Average Partial procedure to determine the number of factors. In contrast to other studies which typically interpret pattern coefficients alone, in these studies symptom clusters were determined on the basis of structure coefficients. This approach was adopted for the stability of the results as structure coefficients are correlations between factors and symptoms unaffected by the correlations between factors. Symptoms could be associated with multiple clusters as a foundation for investigating potential interventions. The stability of these five symptom clusters was investigated in separate common factor analyses, 6 and 12 months after chemotherapy commenced. Five qualitatively consistent symptom clusters were identified over time (Musculoskeletal-discomforts/lethargy, Oral-discomforts, Gastrointestinaldiscomforts, Vasomotor-symptoms, Gastrointestinal-toxicities), but at 12 months two additional clusters were determined (Lethargy and Gastrointestinal/digestive symptoms). Future studies should include physical, psychological, and cognitive symptoms. Further investigation of the identified symptom clusters is required for validation, to examine causality, and potentially to suggest interventions for symptom management. Future studies should use longitudinal analyses to investigate change in symptom clusters, the influence of patient related factors, and the impact on outcomes (e.g., daily functioning) over time.

Novel analytical and numerical methods for solving fractional dynamical systems

During the past three decades, the subject of fractional calculus (that is, calculus of integrals and derivatives of arbitrary order) has gained considerable popularity and importance, mainly due to its demonstrated applications in numerous diverse and widespread fields in science and engineering. For example, fractional calculus has been successfully applied to problems in system biology, physics, chemistry and biochemistry, hydrology, medicine, and finance. In many cases these new fractional-order models are more adequate than the previously used integer-order models, because fractional derivatives and integrals enable the description of the memory and hereditary properties inherent in various materials and processes that are governed by anomalous diffusion. Hence, there is a growing need to find the solution behaviour of these fractional differential equations. However, the analytic solutions of most fractional differential equations generally cannot be obtained. As a consequence, approximate and numerical techniques are playing an important role in identifying the solution behaviour of such fractional equations and exploring their applications. The main objective of this thesis is to develop new effective numerical methods and supporting analysis, based on the finite difference and finite element methods, for solving time, space and time-space fractional dynamical systems involving fractional derivatives in one and two spatial dimensions. A series of five published papers and one manuscript in preparation will be presented on the solution of the space fractional diffusion equation, space fractional advectiondispersion equation, time and space fractional diffusion equation, time and space fractional Fokker-Planck equation with a linear or non-linear source term, and fractional cable equation involving two time fractional derivatives, respectively. One important contribution of this thesis is the demonstration of how to choose different approximation techniques for different fractional derivatives. Special attention has been paid to the Riesz space fractional derivative, due to its important application in the field of groundwater flow, system biology and finance. We present three numerical methods to approximate the Riesz space fractional derivative, namely the L1/ L2-approximation method, the standard/shifted Gr¨unwald method, and the matrix transform method (MTM). The first two methods are based on the finite difference method, while the MTM allows discretisation in space using either the finite difference or finite element methods. Furthermore, we prove the equivalence of the Riesz fractional derivative and the fractional Laplacian operator under homogeneous Dirichlet boundary conditions – a result that had not previously been established. This result justifies the aforementioned use of the MTM to approximate the Riesz fractional derivative. After spatial discretisation, the time-space fractional partial differential equation is transformed into a system of fractional-in-time differential equations. We then investigate numerical methods to handle time fractional derivatives, be they Caputo type or Riemann-Liouville type. This leads to new methods utilising either finite difference strategies or the Laplace transform method for advancing the solution in time. The stability and convergence of our proposed numerical methods are also investigated. Numerical experiments are carried out in support of our theoretical analysis. We also emphasise that the numerical methods we develop are applicable for many other types of fractional partial differential equations.

Analytical modeling and sensitivity analysis for travel time estimation on signalized urban networks

This paper presents a model for estimation of average travel time and its variability on signalized urban networks using cumulative plots. The plots are generated based on the availability of data: a) case-D, for detector data only; b) case-DS, for detector data and signal timings; and c) case-DSS, for detector data, signal timings and saturation flow rate. The performance of the model for different degrees of saturation and different detector detection intervals is consistent for case-DSS and case-DS whereas, for case-D the performance is inconsistent. The sensitivity analysis of the model for case-D indicates that it is sensitive to detection interval and signal timings within the interval. When detection interval is integral multiple of signal cycle then it has low accuracy and low reliability. Whereas, for detection interval around 1.5 times signal cycle both accuracy and reliability are high.

Analytical and numerical solutions for the time and space-symmetric fractional diffusion equation

We consider a time and space-symmetric fractional diffusion equation (TSS-FDE) under homogeneous Dirichlet conditions and homogeneous Neumann conditions. The TSS-FDE is obtained from the standard diffusion equation by replacing the first-order time derivative by a Caputo fractional derivative, and the second order space derivative by a symmetric fractional derivative. First, a method of separating variables expresses the analytical solution of the TSS-FDE in terms of the Mittag--Leffler function. Second, we propose two numerical methods to approximate the Caputo time fractional derivative: the finite difference method; and the Laplace transform method. The symmetric space fractional derivative is approximated using the matrix transform method. Finally, numerical results demonstrate the effectiveness of the numerical methods and to confirm the theoretical claims.

Analytical and numerical solutions for the time and space-symmetric fractional diffusion equation

We consider a time and space-symmetric fractional diffusion equation (TSS-FDE) under homogeneous Dirichlet conditions and homogeneous Neumann conditions. The TSS-FDE is obtained from the standard diffusion equation by replacing the first-order time derivative by the Caputo fractional derivative and the second order space derivative by the symmetric fractional derivative. Firstly, a method of separating variables is used to express the analytical solution of the tss-fde in terms of the Mittag–Leffler function. Secondly, we propose two numerical methods to approximate the Caputo time fractional derivative, namely, the finite difference method and the Laplace transform method. The symmetric space fractional derivative is approximated using the matrix transform method. Finally, numerical results are presented to demonstrate the effectiveness of the numerical methods and to confirm the theoretical claims.

Embedding 'philosophy in the classroom' in pre-service teacher education

The holistic conception of the troika, as described in the first chapter, centres on the relationship between the implicit and explicit teaching of values the nurturing of the specific dimensions of quality teaching and the opportunity to ‘walk the talk’ of the values education program through aspects such as practical citizenship (Lovat, Toomey, Clement, Crotty & Nielsen, 2009). It is proposed in this chapter that the conception can be realized through the embedding of Philosophy in the Classroom within pre-service teaching programs. The troika, a Russian sleigh with three horses, only function well when there is complete synergy and balance between all Classroom is a scaffold for ensuring that all three elements of the troika, namely, quality teaching, values education and service learning in the form of education for citizenship, exist within the classroom to achieve an optimal learning, growth and wellbeing for all students. For this to be more widely accomplished Philosophy in the Classroom and discusses how it constitutes a successful synergy and balance of the troika for effective teaching. It then proposes how it might be embedded into pre-service teacher education.

Embracing Philosophy and Raising the Standard of Pre-service Teacher Education Programs

In this chapter, a rationale is developed for incorporating philosophy into teacher training programs as a means of both preparing quality teachers for the 21st century and meeting the expectations detailed in the professional standards established by the statutory authority that regulates the profession in Queensland, the Queensland College of Teaching is presented. Furthermore, in-service teachers from Buranda State School, a Brisbane primary school that has been successfully teaching philosophy to its students for over 10 years, shares their experiences of teaching philosophy and how it has enhanced student learning and the quality of teaching and professionalism of the teachers. Finally, the implications of embedding philosophy into teacher training programs are explored in terms of developing the personal integrity of beginning teachers.

An analytical method to solve a general class of nonlinear reactive transport models

Three recent papers published in Chemical Engineering Journal studied the solution of a model of diffusion and nonlinear reaction using three different methods. Two of these studies obtained series solutions using specialized mathematical methods, known as the Adomian decomposition method and the homotopy analysis method. Subsequently it was shown that the solution of the same particular model could be written in terms of a transcendental function called Gauss’ hypergeometric function. These three previous approaches focused on one particular reactive transport model. This particular model ignored advective transport and considered one specific reaction term only. Here we generalize these previous approaches and develop an exact analytical solution for a general class of steady state reactive transport models that incorporate (i) combined advective and diffusive transport, and (ii) any sufficiently differentiable reaction term R(C). The new solution is a convergent Maclaurin series. The Maclaurin series solution can be derived without any specialized mathematical methods nor does it necessarily involve the computation of any transcendental function. Applying the Maclaurin series solution to certain case studies shows that the previously published solutions are particular cases of the more general solution outlined here. We also demonstrate the accuracy of the Maclaurin series solution by comparing with numerical solutions for particular cases.

Street-level drug law enforcement : a meta-analytical review

Our paper presents the results of a meta-analytical review of street level drug law enforcement. We conducted a series of meta-analyses to compare and contrast the effectiveness of four types of drug law enforcement approaches, including community-wide policing, problem-oriented/ partnership approaches that were geographically focused, hotspots policing and standard, unfocused law enforcement efforts. We examined the relative impact of these different crime control tactics on streetlevel drug problems as well as associated problems such as property crime, disorder and violent crime. The results of the meta-analyses, together with examination of forest plots, reveal that problem-oriented policing and geographically-focused interventions involving cooperative partnerships between police and third parties tend to be more effective at controlling drug problems than community-wide policing efforts that are unfocused and spread out across a community. But geographically focused and community-wide drug law enforcement interventions that leverage partnerships are more effective at dealing with drug problems than traditional, law enforcement-only interventions. Our results suggest that the key to successful drug law enforcement lies in the capacity of the police to forge productive partnerships with third parties rather than simply increasing police presence or intervention (e.g., arrests) at drug hotspots.