GPU accelerated algorithms for computing matrix function vector products with applications to exponential integrators and fractional diffusion

The efficient computation of matrix function vector products has become an important area of research in recent times, driven in particular by two important applications: the numerical solution of fractional partial differential equations and the integration of large systems of ordinary differential equations. In this work we consider a problem that combines these two applications, in the form of a numerical solution algorithm for fractional reaction diffusion equations that after spatial discretisation, is advanced in time using the exponential Euler method. We focus on the efficient implementation of the algorithm on Graphics Processing Units (GPU), as we wish to make use of the increased computational power available with this hardware. We compute the matrix function vector products using the contour integration method in [N. Hale, N. Higham, and L. Trefethen. Computing Aα, log(A), and related matrix functions by contour integrals. SIAM J. Numer. Anal., 46(5):2505–2523, 2008]. Multiple levels of preconditioning are applied to reduce the GPU memory footprint and to further accelerate convergence. We also derive an error bound for the convergence of the contour integral method that allows us to pre-determine the appropriate number of quadrature points. Results are presented that demonstrate the effectiveness of the method for large two-dimensional problems, showing a speedup of more than an order of magnitude compared to a CPU-only implementation.

Bayesian computational methods for spatial analysis of images

This thesis introduces a new way of using prior information in a spatial model and develops scalable algorithms for fitting this model to large imaging datasets. These methods are employed for image-guided radiation therapy and satellite based classification of land use and water quality. This study has utilized a pre-computation step to achieve a hundredfold improvement in the elapsed runtime for model fitting. This makes it much more feasible to apply these models to real-world problems, and enables full Bayesian inference for images with a million or more pixels.

Bitboard methods for games

Bitboards allow the efficient encoding of games for computer play and the application of fast bitwiseparallel algorithms for common game-related operations. This article describes: (1) a selection of bitboard techniques including an introduction to bitboards and bitwise operations; (2) a classification scheme that distinguishes filter, query and update methods, and; (3) a sampling of bitboard algorithms for a range of games other than chess, with notes on their performance and practical application.

Stochastic analysis of a radial-inflow turbine in the presence of parametric uncertainties

This paper presents an uncertainty quantification study of the performance analysis of the high pressure ratio single stage radial-inflow turbine used in the Sundstrand Power Systems T-100 Multi-purpose Small Power Unit. A deterministic 3D volume-averaged Computational Fluid Dynamics (CFD) solver is coupled with a non-statistical generalized Polynomial Chaos (gPC) representation based on a pseudo-spectral projection method. One of the advantages of this approach is that it does not require any modification of the CFD code for the propagation of random disturbances in the aerodynamic and geometric fields. The stochastic results highlight the importance of the blade thickness and trailing edge tip radius on the total-to-static efficiency of the turbine compared to the angular velocity and trailing edge tip length. From a theoretical point of view, the use of the gPC representation on an arbitrary grid also allows the investigation of the sensitivity of the blade thickness profiles on the turbine efficiency. The gPC approach is also applied to coupled random parameters. The results show that the most influential coupled random variables are trailing edge tip radius coupled with the angular velocity.

Comparison of visual inspection and structural-health monitoring as bridge condition assessment methods

This paper presents the results of a research project aimed at examining the capabilities and challenges of two distinct but not mutually exclusive approaches to in-service bridge assessment: visual inspection and installed monitoring systems. In this study, the intended functionality of both approaches was evaluated on its ability to identify potential structural damage and to provide decision-making support. Inspection and monitoring are compared in terms of their functional performance, cost, and barriers (real and perceived) to implementation. Both methods have strengths and weaknesses across the metrics analyzed, and it is likely that a hybrid evaluation technique that adopts both approaches will optimize efficiency of condition assessment and ultimately lead to better decision making.

Characterization of alluvial formation by stochastic modelling of paleo-fluvial processes: The concept and method

Modelling fluvial processes is an effective way to reproduce basin evolution and to recreate riverbed morphology. However, due to the complexity of alluvial environments, deterministic modelling of fluvial processes is often impossible. To address the related uncertainties, we derive a stochastic fluvial process model on the basis of the convective Exner equation that uses the statistics (mean and variance) of river velocity as input parameters. These statistics allow for quantifying the uncertainty in riverbed topography, river discharge and position of the river channel. In order to couple the velocity statistics and the fluvial process model, the perturbation method is employed with a non-stationary spectral approach to develop the Exner equation as two separate equations: the first one is the mean equation, which yields the mean sediment thickness, and the second one is the perturbation equation, which yields the variance of sediment thickness. The resulting solutions offer an effective tool to characterize alluvial aquifers resulting from fluvial processes, which allows incorporating the stochasticity of the paleoflow velocity.

Bhutanese eighth grade students' and teachers' perceptions of their classroom learning environment in relation to the new mathematics curriculum

This thesis examined how Bhutanese eighth grade students and teachers perceived their classroom learning environment in relation to a new standards-based mathematics curriculum. Data were gathered from administering surveys to a sample of 608 students and 98 teachers, followed by semi-structured interviews with selected participants. The findings of the study indicated that participants generally perceived their learning environments favorably. However, there were differences in terms of gender, school level, and school location. The study provides teachers, educational leaders, and policy-makers in Bhutan new insights into students' and teachers' perceptions of their mathematics classroom environments.

Agent-based simulation as a component of mixed methods in entrepreneurship research

As a new research method supplementing the existing qualitative and quantitative approaches, agent-based modelling and simulation (ABMS) may fit well within the entrepreneurship field because the core concepts and basic premises of entrepreneurship coincide with the characteristics of ABMS (McKelvey, 2004; Yang & Chandra, 2013). Agent-based simulation is a simulation method based on agent-based models. The agentbased models are composed of heterogeneous agents and their behavioural rules. By repeatedly carrying out agent-based simulations on a computer, the simulations reproduce each agent’s behaviour, their interactive process, and the emerging macroscopic phenomenon according to the flow of time. Using agent-based simulations, researchers may investigate temporal or dynamic effects of each agent’s behaviours.

Wrapped optoelectronic devices and methods for making same

In various embodiments, optoelectronic devices are described herein. The optoelectronic device may include an optoelectronic cell arranged so as to wrap around a central axis wherein the cell includes a first conductive layer, a semi-conductive layer disposed over and in electrical communication with the first conductive layer, and a second conductive layer disposed over and in electrical communication with the semi-conductive layer. In various embodiments, methods for making optoelectronic devices are described herein. The methods may include forming an optoelectronic cell while flat and wrapping the optoelectronic cell around a central axis. The optoelectronic devices may be photovoltaic devices. Alternatively, the optoelectronic devices may be organic light emitting diodes.

Mathematics knowledge for teaching and the classroom environment

This study investigated the classroom environment in an underperforming mathematics classroom. The objectives were: (1) to investigate the classroom environment and identify influences upon it, and (2) to further explore those influences (i.e., teacher knowledge). This was completed using a diachronic case study approach in which data were gathered during lesson observations and coaching sessions. These data were analysed to describe and exemplify the classroom environment, then further described against forms of teacher knowledge. Conjectures regarding the importance of teacher knowledge of content were made which formed a base for developing a model of teacher planning and pedagogy.

Anatomy of a trending topic : Methods for the visualisation of retweet chains [Anatomie eines Trending Topics: Methoden zur Visualisierung von Retweet-Ketten]

Twitter and other social networking sites play an ever more present role in the spread of current events. The dynamics of information dissemination through digital network structures are still relatively unexplored, however. At what time an issue is taken up by whom? Who forwards a message when to whom else? What role do individual communication participants, existing digital communities or the technical foundations of each network platform play in the spread of news? In this chapter we discuss, using the example of a video on a current sociopolitical issue in Australia that was shared on Twitter, a number of new methods for the dynamic visualisation and analysis of communication processes. Our method combines temporal and spatial analytical approaches and provides new insights into the spread of news in digital networks. [Social media dienen immer häufger als Disseminationsmechanismen für Medieninhalte. Auf Twitter ermöglicht besonders die Retweet-Funktion den schnellen und weitläufgen Transfer von Nachrichten. In diesem Beitrag etablieren neue methodische Ansätze zur Erfassung, Visualisierung und Analyse von Retweet-Ketten. Insbesondere heben wir hervor, wie bestehende Netzwerkanalysemethoden ergänzt werden können, um den Ablauf der Weiterleitung sowohl temporal als auch spatial zu erfassen. Unsere Fallstudie demonstriert die verbreitung des videoclips einer am 9. Oktober 2012 spontan gehaltenen Wutrede der australischen Premierministerin Julia Gillard, in der sie Oppositionsführer Tony Abbott als Frauenhasser brandmarkte. Durch die Erfassung von Hintergrunddaten zu den jeweiligen NutzerInnen, die sich an der Weiterleitung des Videoclips beteiligten, erstellen wir ein detailliertes Bild des Disseminationsablaufs im vorliegenden Fall. So lassen sich die wichtigsten AkteurInnen und der Ablauf der Weiterleitung darstellen und analysieren. Daraus entstehen Einblicke in die allgemeinen verbreitungsmuster von Nachrichten auf Twitter].

STEM: Challenges and opportunities for mathematics education

Climbing Mountains, Building Bridges is a rich theme for exploring some of the “challenges, obstacles, links, and connections” facing mathematics education within the current STEM climate (Science, Technology, Engineering and Mathematics). This paper first considers some of the issues and debates surrounding the nature of STEM education, including perspectives on its interdisciplinary nature. It is next argued that mathematics is in danger of being overshadowed, in particular by science, in the global urgency to advance STEM competencies in schools and the workforce. Some suggestions are offered for lifting the profile of mathematics education within an integrated STEM context, with examples drawn from modelling with data in the sixth grade.

Handbook of International Research in Mathematics Education [3rd Ed.]

"This third edition ofthe Handbook of International Research in Mathematics Education provides a comprehensive overview of the most recent theoretical and practical developments in the field of mathematics education. Authored by an array of internationally recognized scholars and edited by Lyn English and David Kirshner, this collection brings together overviews and advances in mathematics education research spanning established and emerging topics, diverse workplace and school environments, and globally representative research priorities. New perspectives are presented on a range of critical topics including embodied learning, the theory-practice divide, new developments in the early years, educating future mathematics education professors, problem solving in a 21st century curriculum, culture and mathematics learning, complex systems, critical analysis of design-based research, multimodal technologies, and e-textbooks. Comprised of 12 revised and 17 new chapters, this edition extends the Handbook’s original themes for international research in mathematics education and remains in the process a definitive resource for the field."--Publisher website

Investigating the effectiveness of an ecological approach to learning design in a first year mathematics for engineering unit

This paper reports on the results of a project aimed at creating a research-informed, pedagogically reliable, technology-enhanced learning and teaching environment that would foster engagement with learning. A first-year mathematics for engineering unit offered at a large, metropolitan Australian university provides the context for this research. As part of the project, the unit was redesigned using a framework that employed flexible, modular, connected e-learning and teaching experiences. The researchers, interested in an ecological perspective on educational processes, grounded the redesign principles in probabilistic learning design (Kirschner et al., 2004). The effectiveness of the redesigned environment was assessed through the lens of the notion of affordance (Gibson, 1977,1979, Greeno, 1994, Good, 2007). A qualitative analysis of the questionnaire distributed to students at the end of the teaching period provided insight into factors impacting on the successful creation of an environment that encourages complex, multidimensional and multilayered interactions conducive to learning.

Changing agendas in international research in mathematics education

Handbooks serve an important function for our research community in providing state-of-the-art summations, critiques, and extensions of existing trends in research. In the intervening years between the second and third editions of the Handbook of International Research in Mathematics Education, there have been stimulating developments in research, as well as new challenges in translating outcomes into practice. This third edition incorporates a number of new chapters representing areas of growth and challenge, in addition to substantially updated chapters from the second edition. As such, the Handbook addresses five core themes, namely, Priorities in International Mathematics Education Research, Democratic Access to Mathematics Learning, Transformations in Learning Contexts, Advances in Research Methodologies, and Influences of Advanced Technologies...