Constructive development of the solutions of linear equations in introductory ordinary differential equations

The solution of linear ordinary differential equations (ODEs) is commonly taught in first year undergraduate mathematics classrooms, but the understanding of the concept of a solution is not always grasped by students until much later. Recognising what it is to be a solution of a linear ODE and how to postulate such solutions, without resorting to tables of solutions, is an important skill for students to carry with them to advanced studies in mathematics. In this study we describe a teaching and learning strategy that replaces the traditional algorithmic, transmission presentation style for solving ODEs with a constructive, discovery based approach where students employ their existing skills as a framework for constructing the solutions of first and second order linear ODEs. We elaborate on how the strategy was implemented and discuss the resulting impact on a first year undergraduate class. Finally we propose further improvements to the strategy as well as suggesting other topics which could be taught in a similar manner.

A review on degradation models in reliability analysis

With increasingly complex engineering assets and tight economic requirements, asset reliability becomes more crucial in Engineering Asset Management (EAM). Improving the reliability of systems has always been a major aim of EAM. Reliability assessment using degradation data has become a significant approach to evaluate the reliability and safety of critical systems. Degradation data often provide more information than failure time data for assessing reliability and predicting the remnant life of systems. In general, degradation is the reduction in performance, reliability, and life span of assets. Many failure mechanisms can be traced to an underlying degradation process. Degradation phenomenon is a kind of stochastic process; therefore, it could be modelled in several approaches. Degradation modelling techniques have generated a great amount of research in reliability field. While degradation models play a significant role in reliability analysis, there are few review papers on that. This paper presents a review of the existing literature on commonly used degradation models in reliability analysis. The current research and developments in degradation models are reviewed and summarised in this paper. This study synthesises these models and classifies them in certain groups. Additionally, it attempts to identify the merits, limitations, and applications of each model. It provides potential applications of these degradation models in asset health and reliability prediction.

Using self-referencing to explain the effectiveness of ethnic minority models in advertising

Advertising research has generally not gone beyond offering support for a positive effect where ethnic models in advertising are viewed by consumers of the same ethnicity. This study offers an explanation behind this phenomenon that can be useful to marketers using self-reference theory. Our experiment reveals a strong self-referencing effect for ethnic minority individuals. Specifically, Asian subjects (the ethnic minority group) self-referenced ads with Asian models more than white subjects (the ethnic majority group). However, this result was not evident for white subjects. Implications for academics and advertisers are discussed.

Latent variable models in statistical genetics

Understanding the complexities that are involved in the genetics of multifactorial diseases is still a monumental task. In addition to environmental factors that can influence the risk of disease, there is also a number of other complicating factors. Genetic variants associated with age of disease onset may be different from those variants associated with overall risk of disease, and variants may be located in positions that are not consistent with the traditional protein coding genetic paradigm. Latent Variable Models are well suited for the analysis of genetic data. A latent variable is one that we do not directly observe, but which is believed to exist or is included for computational or analytic convenience in a model. This thesis presents a mixture of methodological developments utilising latent variables, and results from case studies in genetic epidemiology and comparative genomics. Epidemiological studies have identified a number of environmental risk factors for appendicitis, but the disease aetiology of this oft thought useless vestige remains largely a mystery. The effects of smoking on other gastrointestinal disorders are well documented, and in light of this, the thesis investigates the association between smoking and appendicitis through the use of latent variables. By utilising data from a large Australian twin study questionnaire as both cohort and case-control, evidence is found for the association between tobacco smoking and appendicitis. Twin and family studies have also found evidence for the role of heredity in the risk of appendicitis. Results from previous studies are extended here to estimate the heritability of age-at-onset and account for the eect of smoking. This thesis presents a novel approach for performing a genome-wide variance components linkage analysis on transformed residuals from a Cox regression. This method finds evidence for a dierent subset of genes responsible for variation in age at onset than those associated with overall risk of appendicitis. Motivated by increasing evidence of functional activity in regions of the genome once thought of as evolutionary graveyards, this thesis develops a generalisation to the Bayesian multiple changepoint model on aligned DNA sequences for more than two species. This sensitive technique is applied to evaluating the distributions of evolutionary rates, with the finding that they are much more complex than previously apparent. We show strong evidence for at least 9 well-resolved evolutionary rate classes in an alignment of four Drosophila species and at least 7 classes in an alignment of four mammals, including human. A pattern of enrichment and depletion of genic regions in the profiled segments suggests they are functionally significant, and most likely consist of various functional classes. Furthermore, a method of incorporating alignment characteristics representative of function such as GC content and type of mutation into the segmentation model is developed within this thesis. Evidence of fine-structured segmental variation is presented.

Explaining usage of process modeling grammars : comparing three theoretical models in the study of two grammars

Our objective was to determine the factors that lead users to continue working with process modeling grammars after their initial adoption. We examined the explanatory power of three theoretical models of IT usage by applying them to two popular process modeling grammars. We found that a hybrid model of technology acceptance and expectation-confirmation best explained user intentions to continue using the grammars. We examined differences in the model results, and used them to provide three contributions. First, the study confirmed the applicability of IT usage models to the domain of process modeling. Second, we discovered that differences in continued usage intentions depended on the grammar type instead of the user characteristics. Third, we suggest implications and practice.

Analysis of linear relationships in block ciphers

This thesis is devoted to the study of linear relationships in symmetric block ciphers. A block cipher is designed so that the ciphertext is produced as a nonlinear function of the plaintext and secret master key. However, linear relationships within the cipher can still exist if the texts and components of the cipher are manipulated in a number of ways, as shown in this thesis. There are four main contributions of this thesis. The first contribution is the extension of the applicability of integral attacks from word-based to bitbased block ciphers. Integral attacks exploit the linear relationship between texts at intermediate stages of encryption. This relationship can be used to recover subkey bits in a key recovery attack. In principle, integral attacks can be applied to bit-based block ciphers. However, specific tools to define the attack on these ciphers are not available. This problem is addressed in this thesis by introducing a refined set of notations to describe the attack. The bit patternbased integral attack is successfully demonstrated on reduced-round variants of the block ciphers Noekeon, Present and Serpent. The second contribution is the discovery of a very small system of equations that describe the LEX-AES stream cipher. LEX-AES is based heavily on the 128-bit-key (16-byte) Advanced Encryption Standard (AES) block cipher. In one instance, the system contains 21 equations and 17 unknown bytes. This is very close to the upper limit for an exhaustive key search, which is 16 bytes. One only needs to acquire 36 bytes of keystream to generate the equations. Therefore, the security of this cipher depends on the difficulty of solving this small system of equations. The third contribution is the proposal of an alternative method to measure diffusion in the linear transformation of Substitution-Permutation-Network (SPN) block ciphers. Currently, the branch number is widely used for this purpose. It is useful for estimating the possible success of differential and linear attacks on a particular SPN cipher. However, the measure does not give information on the number of input bits that are left unchanged by the transformation when producing the output bits. The new measure introduced in this thesis is intended to complement the current branch number technique. The measure is based on fixed points and simple linear relationships between the input and output words of the linear transformation. The measure represents the average fraction of input words to a linear diffusion transformation that are not effectively changed by the transformation. This measure is applied to the block ciphers AES, ARIA, Serpent and Present. It is shown that except for Serpent, the linear transformations used in the block ciphers examined do not behave as expected for a random linear transformation. The fourth contribution is the identification of linear paths in the nonlinear round function of the SMS4 block cipher. The SMS4 block cipher is used as a standard in the Chinese Wireless LAN Wired Authentication and Privacy Infrastructure (WAPI) and hence, the round function should exhibit a high level of nonlinearity. However, the findings in this thesis on the existence of linear relationships show that this is not the case. It is shown that in some exceptional cases, the first four rounds of SMS4 are effectively linear. In these cases, the effective number of rounds for SMS4 is reduced by four, from 32 to 28. The findings raise questions about the security provided by SMS4, and might provide clues on the existence of a flaw in the design of the cipher.

Further notes on the application of zero-inflated models in highway safety

The intent of this note is to succinctly articulate additional points that were not provided in the original paper (Lord et al., 2005) and to help clarify a collective reluctance to adopt zero-inflated (ZI) models for modeling highway safety data. A dialogue on this important issue, just one of many important safety modeling issues, is healthy discourse on the path towards improved safety modeling. This note first provides a summary of prior findings and conclusions of the original paper. It then presents two critical and relevant issues: the maximizing statistical fit fallacy and logic problems with the ZI model in highway safety modeling. Finally, we provide brief conclusions.

Towards a classification of criterion referenced assessment models in mathematics courses : student and academic perspectives

We present the findings of a study into the implementation of explicitly criterion- referenced assessment in undergraduate courses in mathematics. We discuss students' concepts of criterion referencing and also the various interpretations that this concept has among mathematics educators. Our primary goal was to move towards a classification of criterion referencing models in quantitative courses. A secondary goal was to investigate whether explicitly presenting assessment criteria to students was useful to them and guided them in responding to assessment tasks. The data and feedback from students indicates that while students found the criteria easy to understand and useful in informing them as to how they would be graded, it did not alter the way the actually approached the assessment activity.

The constraints-based approach to motor learning : Implications for a non-linear pedagogy in sport and physical education

Recently, a constraints- led approach has been promoted as a framework for understanding how children and adults acquire movement skills for sport and exercise (see Davids, Button & Bennett, 2008; Araújo et al., 2004). The aim of a constraints- led approach is to identify the nature of interacting constraints that influence skill acquisition in learners. In this chapter the main theoretical ideas behind a constraints- led approach are outlined to assist practical applications by sports practitioners and physical educators in a non- linear pedagogy (see Chow et al., 2006, 2007). To achieve this goal, this chapter examines implications for some of the typical challenges facing sport pedagogists and physical educators in the design of learning programmes.

Refining animal models in fracture research: Seeking consensus in optimising both animal welfare and scientific validity for appropriate biomedical use

Background In an attempt to establish some consensus on the proper use and design of experimental animal models in musculoskeletal research, AOVET (the veterinary specialty group of the AO Foundation) in concert with the AO Research Institute (ARI), and the European Academy for the Study of Scientific and Technological Advance, convened a group of musculoskeletal researchers, veterinarians, legal experts, and ethicists to discuss, in a frank and open forum, the use of animals in musculoskeletal research. Methods The group narrowed the field to fracture research. The consensus opinion resulting from this workshop can be summarized as follows: Results & Conclusion Anaesthesia and pain management protocols for research animals should follow standard protocols applied in clinical work for the species involved. This will improve morbidity and mortality outcomes. A database should be established to facilitate selection of anaesthesia and pain management protocols for specific experimental surgical procedures and adopted as an International Standard (IS) according to animal species selected. A list of 10 golden rules and requirements for conduction of animal experiments in musculoskeletal research was drawn up comprising 1) Intelligent study designs to receive appropriate answers; 2) Minimal complication rates (5 to max. 10%); 3) Defined end-points for both welfare and scientific outputs analogous to quality assessment (QA) audit of protocols in GLP studies; 4) Sufficient details for materials and methods applied; 5) Potentially confounding variables (genetic background, seasonal, hormonal, size, histological, and biomechanical differences); 6) Post-operative management with emphasis on analgesia and follow-up examinations; 7) Study protocols to satisfy criteria established for a "justified animal study"; 8) Surgical expertise to conduct surgery on animals; 9) Pilot studies as a critical part of model validation and powering of the definitive study design; 10) Criteria for funding agencies to include requirements related to animal experiments as part of the overall scientific proposal review protocols. Such agencies are also encouraged to seriously consider and adopt the recommendations described here when awarding funds for specific projects. Specific new requirements and mandates related both to improving the welfare and scientific rigour of animal-based research models are urgently needed as part of international harmonization of standards.