Experiences with implementing common mathematical operations using field programmable gate arrays

Many computationally intensive scientific applications involve repetitive floating point operations other than addition and multiplication which may present a significant performance bottleneck due to the relatively large latency or low throughput involved in executing such arithmetic primitives on commod- ity processors. A promising alternative is to execute such primitives on Field Programmable Gate Array (FPGA) hardware acting as an application-specific custom co-processor in a high performance reconfig- urable computing platform. The use of FPGAs can provide advantages such as fine-grain parallelism but issues relating to code development in a hardware description language and efficient data transfer to and from the FPGA chip can present significant application development challenges. In this paper, we discuss our practical experiences in developing a selection of floating point hardware designs to be implemented using FPGAs. Our designs include some basic mathemati cal library functions which can be implemented for user defined precisions suitable for novel applications requiring non-standard floating point represen- tation. We discuss the details of our designs along with results from performance and accuracy analysis tests.

Exploiting SNOMED CT concepts and relationships for clinical information retrieval : Australian e-Health Research Centre and Queensland University of Technology at the TREC 2012 Medical Track

The Australian e-Health Research Centre and Queensland University of Technology recently participated in the TREC 2012 Medical Records Track. This paper reports on our methods, results and experience using an approach that exploits the concept and inter-concept relationships defined in the SNOMED CT medical ontology. Our concept-based approach is intended to overcome specific challenges in searching medical records, namely vocabulary mismatch and granularity mismatch. Queries and documents are transformed from their term-based originals into medical concepts as defined by the SNOMED CT ontology, this is done to tackle vocabulary mismatch. In addition, we make use of the SNOMED CT parent-child `is-a' relationships between concepts to weight documents that contained concept subsumed by the query concepts; this is done to tackle the problem of granularity mismatch. Finally, we experiment with other SNOMED CT relationships besides the is-a relationship to weight concepts related to query concepts. Results show our concept-based approach performed significantly above the median in all four performance metrics. Further improvements are achieved by the incorporation of weighting subsumed concepts, overall leading to improvement above the median of 28% infAP, 10% infNDCG, 12% R-prec and 7% Prec@10. The incorporation of other relations besides is-a demonstrated mixed results, more research is required to determined which SNOMED CT relationships are best employed when weighting related concepts.

Semantic judgement of medical concepts : combining syntagmatic and paradigmatic information with the tensor encoding model

This paper outlines a novel approach for modelling semantic relationships within medical documents. Medical terminologies contain a rich source of semantic information critical to a number of techniques in medical informatics, including medical information retrieval. Recent research suggests that corpus-driven approaches are effective at automatically capturing semantic similarities between medical concepts, thus making them an attractive option for accessing semantic information. Most previous corpus-driven methods only considered syntagmatic associations. In this paper, we adapt a recent approach that explicitly models both syntagmatic and paradigmatic associations. We show that the implicit similarity between certain medical concepts can only be modelled using paradigmatic associations. In addition, the inclusion of both types of associations overcomes the sensitivity to the training corpus experienced by previous approaches, making our method both more effective and more robust. This finding may have implications for researchers in the area of medical information retrieval.

Key concepts in creative industries

Creativity is an attribute of individual people, but also a feature of organizations like firms, cultural institutions and social networks. In the knowledge economy of today, creativity is of increasing value, for developing, emergent and advanced countries, and for competing cities. This book is the first to present an organized study of the key concepts that underlie and motivate the field of creative industries. Written by a world-leading team of experts, it presents readers with compact accounts of the history of terms, the debates and tensions associated with their usage, and examples of how they apply to the creative industries around the world. Crisp and relevant, this is an invaluable text for students of the creative industries across a range of disciplines, especially media, communication, economics, sociology, creative and performing arts and regional studies.

Students’ approaches to learning a new mathematical model

In this article, we report on the findings of an exploratory study into the experience of undergraduate students as they learn new mathematical models. Qualitative and quanti- tative data based around the students’ approaches to learning new mathematical models were collected. The data revealed that students actively adopt three approaches to under- standing a new mathematical model: gathering information for the task of understanding the model, practising with and using the model, and finding interrelationships between elements of the model. We found that the students appreciate mathematical models that have a real world application and that this can be used to engage students in higher level learning approaches.

Threshold concepts in property education : a case study

First year Property Economics students enrolled in the Bachelor of Urban Development at QUT are required to undertake a number of compulsory subjects, alongside students undertaking studies in other disciplines. One such common unit is ‘Stewardship of Land’, an interdisciplinary unit that introduces students to the characteristics of land and land tenure with a focus on land use and property rights. It covers a range of issues including: native title, land contamination, heritage values, alternative uses, the property development process, impact of environmental and social factors, and the management of land, both urban and regional. Teaching such a diverse content to a diverse audience has in previous years proved difficult, from the perspectives of relevance, engagement and content overload. In 2011 a project was undertake to redevelop this unit to reflect ‘threshold concepts’, concepts that are “transformative, probably irreversible, integrative, often troublesome and probably bounded” (Meyer & Land, 2003) . This project involved the development of a new set of underlying concepts students should draw from the unit, application of these to the unit curriculum, and a survey of the student response to these changes. This paper reports on the threshold concepts developed for this unit, the changes this made to the unit curriculum, and a preliminary report on survey responses. Recommendations for other educators seeking to incorporate threshold concepts into their curricula are provided.

Australian learning and teaching council projects in the mathematical sciences : a retrospective

Since 2004, the Australian Learning and Teaching Council (ALTC) and its predecessor, the Carrick Institute for Learning and Teaching in Higher Education, have funded numerous teaching and educational research-based projects in the Mathematical Sciences. In light of the Commonwealth Government’s decision to close the ALTC in 2011, it is appropriate to take account of the ALTCs input into the Mathe- matical Sciences in higher education. Here we present an overview of ALTC projects in the Mathematical Sciences, as well as report on the contributions they have made to the Discipline.

Numerical methods for strong solutions of stochastic differential equations : an overview

This paper gives a review of recent progress in the design of numerical methods for computing the trajectories (sample paths) of solutions to stochastic differential equations. We give a brief survey of the area focusing on a number of application areas where approximations to strong solutions are important, with a particular focus on computational biology applications, and give the necessary analytical tools for understanding some of the important concepts associated with stochastic processes. We present the stochastic Taylor series expansion as the fundamental mechanism for constructing effective numerical methods, give general results that relate local and global order of convergence and mention the Magnus expansion as a mechanism for designing methods that preserve the underlying structure of the problem. We also present various classes of explicit and implicit methods for strong solutions, based on the underlying structure of the problem. Finally, we discuss implementation issues relating to maintaining the Brownian path, efficient simulation of stochastic integrals and variable-step-size implementations based on various types of control.

Modeling as a means for making powerful ideas accessible to children at an early age

The SimCalc Vision and Contributions Advances in Mathematics Education 2013, pp 419-436 Modeling as a Means for Making Powerful Ideas Accessible to Children at an Early Age Richard Lesh, Lyn English, Serife Sevis, Chanda Riggs … show all 4 hide » Look Inside » Get Access Abstract In modern societies in the 21st century, significant changes have been occurring in the kinds of “mathematical thinking” that are needed outside of school. Even in the case of primary school children (grades K-2), children not only encounter situations where numbers refer to sets of discrete objects that can be counted. Numbers also are used to describe situations that involve continuous quantities (inches, feet, pounds, etc.), signed quantities, quantities that have both magnitude and direction, locations (coordinates, or ordinal quantities), transformations (actions), accumulating quantities, continually changing quantities, and other kinds of mathematical objects. Furthermore, if we ask, what kind of situations can children use numbers to describe? rather than restricting attention to situations where children should be able to calculate correctly, then this study shows that average ability children in grades K-2 are (and need to be) able to productively mathematize situations that involve far more than simple counts. Similarly, whereas nearly the entire K-16 mathematics curriculum is restricted to situations that can be mathematized using a single input-output rule going in one direction, even the lives of primary school children are filled with situations that involve several interacting actions—and which involve feedback loops, second-order effects, and issues such as maximization, minimization, or stabilizations (which, many years ago, needed to be postponed until students had been introduced to calculus). …This brief paper demonstrates that, if children’s stories are used to introduce simulations of “real life” problem solving situations, then average ability primary school children are quite capable of dealing productively with 60-minute problems that involve (a) many kinds of quantities in addition to “counts,” (b) integrated collections of concepts associated with a variety of textbook topic areas, (c) interactions among several different actors, and (d) issues such as maximization, minimization, and stabilization.

Matching relevance features with ontological concepts

In order to comprehend user information needs by concepts, this paper introduces a novel method to match relevance features with ontological concepts. The method first discovers relevance features from user local instances. Then, a concept matching approach is developed for matching these features to accurate concepts in a global knowledge base. This approach is significant for the transition of informative descriptor and conceptional descriptor. The proposed method is elaborately evaluated by comparing against three information gathering baseline models. The experimental results shows the matching approach is successful and achieves a series of remarkable improvements on search effectiveness.

Assessing the Impact of Sensor Accuracy and Sensor Choice on Air Traffic Conflict Risk Estimation using Risk-Ratio Concepts

One of the primary desired capabilities of any future air traffic separation management system is the ability to provide early conflict detection and resolution effectively and efficiently. In this paper, we consider the risk of conflict as a primary measurement to be used for early conflict detection. This paper focuses on developing a novel approach to assess the impact of different measurement uncertainty models on the estimated risk of conflict. The measurement uncertainty model can be used to represent different sensor accuracy and sensor choices. Our study demonstrates the value of modelling measurement uncertainty in the conflict risk estimation problem and presents techniques providing a means of assessing sensor requirements to achieve desired conflict detection performance.

Concepts, water and reflections on practice

This paper discusses the nature of the conceptual structure in art practice, by example. It draws on insights gained from a practice based research (PBR) approach to making art. The PBR methods used include Reflective Practice and are briefly described. They have informed an understanding of the conceptual structure as an instance of problem framing. This is demonstrated by two creative examples, taken from two interactive artworks. These were informed by an evolving conceptual structure concerned with water.

Investigating homework as a social practice : a qualitative approach

This thesis examines the social practice of homework. It explores how homework is shaped by the discourses, policies and guidelines in circulation in a society at any given time with particular reference to one school district in the province of Newfoundland and Labrador, Canada. This study investigates how contemporary homework reconstitutes the home as a pedagogical site where the power of the institution of schooling circulates regularly from school to home. It examines how the educational system shapes the organization of family life and how family experiences with homework may be different in different sites depending on the accessibility of various forms of cultural capital. This study employs a qualitative approach, incorporating multiple case studies, and is complemented by insights from institutional ethnography and critical discourse analysis. It draws on the theoretical concepts of Foucault including power and power relations, and governmentality and surveillance, as well as Bourdieu’s concepts of economic, social and cultural capital for analysis. It employs concepts from Bourdieu’s work as they have been expanded on by researchers including Reay (1998), Lareau (2000), and Griffith and Smith (2005). The studies of these researchers allowed for an examination of homework as it related to families and mothers’ work. Smith’s (1987; 1999) concepts of ruling relations, mothers’ unpaid labour, and the engine of inequality were also employed in the analysis. Family interviews with ten volunteer families, teacher focus group sessions with 15 teachers from six schools, homework artefacts, school newsletters, homework brochures, and publicly available assessment and evaluation policy documents from one school district were analyzed. From this analysis key themes emerged and the findings are documented throughout five data analysis chapters. This study shows a change in education in response to a system shaped by standards, accountability and testing. It documents an increased transference of educational responsibility from one educational stakeholder to another. This transference of responsibility shifts downward until it eventually reaches the family in the form of homework and educational activities. Texts in the form of brochures and newsletters, sent home from school, make available to parents specific subject positions that act as instruments of normalization. These subject positions promote a particular ‘ideal’ family that has access to certain types of cultural capital needed to meet the school’s expectations. However, the study shows that these resources are not equally available to all and some families struggle to obtain what is necessary to complete educational activities in the home. The increase in transference of educational work from the school to the home results in greater work for parents, particularly mothers. As well, consideration is given to mother’s role in homework and how, in turn, classroom instructional practices are sometimes dependent on the work completed at home with differential effects for children. This study confirms previous findings that it is mothers who assume the greatest role in the educational trajectory of their children. An important finding in this research is that it is not only middle-class mothers who dedicate extensive time working hard to ensure their children’s educational success; working-class mothers also make substantial contributions of time and resources to their children’s education. The assignments and educational activities distributed as homework require parents’ knowledge of technical school pedagogy to help their children. Much of the homework being sent home from schools is in the area of literacy, particularly reading, but requires parents to do more than read with children. A key finding is that the practices of parents are changing and being reconfigured by the expectations of schools in regard to reading. Parents are now being required to monitor and supervise children’s reading, as well as help children complete reading logs, written reading responses, and follow up questions. The reality of family life as discussed by the participants in this study does not match the ‘ideal’ as portrayed in the educational documents. Homework sessions often create frustrations and tensions between parents and children. Some of the greatest struggles for families were created by mathematical homework, homework for those enrolled in the French Immersion program, and the work required to complete Literature, Heritage and Science Fair projects. Even when institutionalized and objectified capital was readily available, many families still encountered struggles when trying to carry out the assigned educational tasks. This thesis argues that homework and education-related activities play out differently in different homes. Consideration of this significance may assist educators to better understand and appreciate the vast difference in families and the ways in which each family can contribute to their children’s educational trajectory.

Numerical techniques for simulating a fractional mathematical model of epidermal wound healing

A number of mathematical models investigating certain aspects of the complicated process of wound healing are reported in the literature in recent years. However, effective numerical methods and supporting error analysis for the fractional equations which describe the process of wound healing are still limited. In this paper, we consider the numerical simulation of a fractional mathematical model of epidermal wound healing (FMM-EWH), which is based on the coupled advection-diffusion equations for cell and chemical concentration in a polar coordinate system. The space fractional derivatives are defined in the Left and Right Riemann-Liouville sense. Fractional orders in the advection and diffusion terms belong to the intervals (0, 1) or (1, 2], respectively. Some numerical techniques will be used. Firstly, the coupled advection-diffusion equations are decoupled to a single space fractional advection-diffusion equation in a polar coordinate system. Secondly, we propose a new implicit difference method for simulating this equation by using the equivalent of Riemann-Liouville and Grünwald-Letnikov fractional derivative definitions. Thirdly, its stability and convergence are discussed, respectively. Finally, some numerical results are given to demonstrate the theoretical analysis.