Description:
During the planning of Wireless Local Area Network (WLAN) systems, it is important to determine the optimal number of access points (APs) in order to maximise their coverage with minimum cost. It is also essential to take proactive steps to secure their position in order to enhance the physical security of the network. In this paper we describe a mathematical model that finds the minimum number of APs for indoor buildings and places them in the area in a manner that the physical security of the network is maintained. A Global Optimisation Algorithm (AGOP) developed at the University of Ballarat is used to solve this problem. Results obtained demonstrate that the model and software are able to optimally solve the placement problem in areas that have different obstacles and number of users.
Description:
Selection is an important and critical aspect in evolutionary computation. This paper presents a novel parental selection technique that includes the advantages of both the deterministic and the stochastic selection techniques and helps to reduce the loss of diversity by distributing the reproduction opportunity among all the members of the population. Moreover, the proposed selection strategy promotes the concept of non-random mating by clustering the population into groups according to the fitness values and then by persuading the mating between individuals from different groups based on performance determined dynamically over the evolution. Computational results using widely used benchmark functions show significant improvements in the convergence characteristics of the proposed selection method over two well-known selection techniques.
Description:
The Douglas–Rachford algorithm is a classical and very successful method for solving optimization and feasibility problems. In this paper, we provide novel conditions sufficient for finite convergence in the context of convex feasibility problems. Our analysis builds upon, and considerably extends, pioneering work by Spingarn. Specifically, we obtain finite convergence in the presence of Slater’s condition in the affine-polyhedral and in a hyperplanar-epigraphical case. Various examples illustrate our results. Numerical experiments demonstrate the competitiveness of the Douglas–Rachford algorithm for solving linear equations with a positivity constraint when compared to the method of alternating projections and the method of reflection–projection.
Description:
Ensuring timeliness and mobility for multimedia computing is a crucial task for wireless communication. Previous algorithms that utilize information channels, such as the information bottleneck method, have shown great performance and efficiency, which guarantees timeliness. However, such methods suit only in handling single variable tasks such as image processing, but are inapplicable to multivariable applications such as video processing. To address this critical shortcoming, we propose a novel tensor information channel which extends the current single-input single-output matrix information channel to a more practical multi-input single-output tensor information channel. In comparison with the classic information channel, our tensor information channel not only performs better in experiments, but also allows for a wider range of practical applications. We further build an innovative tensor-information bottleneck method upon the state-of-the-art information bottleneck method. Experiments on video shot boundary detection are conducted using benchmark data sets to demonstrate the effectiveness of our proposed approach compared with state-of-the-art methods. In specific, our approach yields a 6.2% increase compared with the information channel-based method, and when compared to other state-of-the-art methods, we achieve 0.1%–17.7% performance gains under different experimental configurations.
Description:
First-year engineering students often struggle to see the relevance of theoretical mathematical concepts for their future studies and professional careers. This is an issue, as students who do not see relevance in fundamental parts of their studies may disengage from these parts and focus their efforts on other subjects they think will be more useful to them. In this study, we surveyed engineering students enrolled in a first-year mathematics subject on their perceptions of the relevance of the individual mathematical topics taught. Surveys were administered at the start of semester when some of these topics were unknown to them, and again at the end of semester when students had not only studied all these topics but also watched a set of animated videos. These videos had been produced by higher-year students to explain where they had seen applications of the mathematical concepts presented in the first year. We notice differences between the perceived relevance of topics for future study and for professional careers, with relevance to study rated higher than relevance to careers. We also find that the animations are seen as helpful in understanding the relevance of first-year mathematics. The majority of students indicated that lecturers with students as partners should work collaboratively to produce future videos.
Description:
In Australian universities, mathematics is often an essential core subject for disciplines such as engineering, information technology and science. These first-year mathematics subjects may have large enrolments of which a significant number fail the subject and repeat. While interventions to retain students are common, those who have failed before and are repeating the subject are often overlooked. In this paper, we undertook a statistical analysis based on demographic and performance data of six cohorts of students undertaking a first-year university-level mathematics subject. We found that pass rates for students on their second attempt were significantly lower than pass rates for students enrolled on their first attempt, and that age, degree enrolled in and pathway into university were predictors for who was more likely to repeat. Students in their second attempt were less likely to complete all assessment items and were more than twice as likely not to attend the final exam. We argue for an increased focus on and efforts targeting repeating students that demographic data are used to predict students likely to repeat before they have failed a subject, and that this group of students, as well as those repeating, are supported to increase their chances to pass.
Description:
In Australian universities, mathematics is often an essential core subject for disciplines such as engineering, information technology and science. These first-year mathematics subjects may have large enrolments of which a significant number fail the subject and repeat. While interventions to retain students are common, those who have failed before and are repeating the subject are often overlooked. In this paper, we undertook a statistical analysis based on demographic and performance data of six cohorts of students undertaking a first-year university-level mathematics subject. We found that pass rates for students on their second attempt were significantly lower than pass rates for students enrolled on their first attempt, and that age, degree enrolled in and pathway into university were predictors for who was more likely to repeat. Students in their second attempt were less likely to complete all assessment items and were more than twice as likely not to attend the final exam. We argue for an increased focus on and efforts targeting repeating students that demographic data are used to predict students likely to repeat before they have failed a subject, and that this group of students, as well as those repeating, are supported to increase their chances to pass.
Description:
With the myriad theories generated through research over the years, a continuing challenge for researchers is to navigate the multitude of theories in order to communicate their research, integrate empirical results, and make progress as a field by building upon empirical research. The Social Unit of Learning project was purposefully designed so that researchers from multiple disciplines with different theoretical perspectives could work together to examine the complexity of the mathematics classroom. In this paper, we reflect on the multiple analytical accounts generated from the project, drawing from the notions of complementarity and commensurability. Two parallel analyses, applying the commognitive framework and the theory of representations respectively, are used as illustrative examples for discussion regarding complementarity and commensurability. The paper addresses two focal questions, as follows: in what ways do divergence or contradiction in incommensurable analytical accounts reflect methodological discrepancies or fundamental differences in the underpinning theories? Furthermore, in what ways do the accounts generated by the parallel analyses predicated on different theories lead to differences in instructional advocacy? The answers to these questions provide empirically-grounded insights into the consideration of incommensurability in educational research, and suggest ways in which researchers and practitioners might apply the notion of complementarity to reconcile or exploit incommensurable analytical accounts that have resulted in different instructional advocacies. [Author abstract]
Description:
With the myriad theories generated through research over the years, a continuing challenge for researchers is to navigate the multitude of theories in order to communicate their research, integrate empirical results, and make progress as a field by building upon empirical research. The Social Unit of Learning project was purposefully designed so that researchers from multiple disciplines with different theoretical perspectives could work together to examine the complexity of the mathematics classroom. In this paper, we reflect on the multiple analytical accounts generated from the project, drawing from the notions of complementarity and commensurability. Two parallel analyses, applying the commognitive framework and the theory of representations respectively, are used as illustrative examples for discussion regarding complementarity and commensurability. The paper addresses two focal questions, as follows: in what ways do divergence or contradiction in incommensurable analytical accounts reflect methodological discrepancies or fundamental differences in the underpinning theories? Furthermore, in what ways do the accounts generated by the parallel analyses predicated on different theories lead to differences in instructional advocacy? The answers to these questions provide empirically-grounded insights into the consideration of incommensurability in educational research, and suggest ways in which researchers and practitioners might apply the notion of complementarity to reconcile or exploit incommensurable analytical accounts that have resulted in different instructional advocacies. [Author abstract]
Description:
Through the lenses of statistical investigations and cognitive demands, we examined bivariate data tasks offered in US high school mathematics textbook series—a popular representative of three curriculum types: traditional, integrated, and hybrid. We developed a framework grounded in literature of association topics for the inclusion and exclusion of tasks. Using the Guidelines for Assessment and Instruction of Statistics Education (GAISE) framework, textbook tasks were coded for four investigation components (formulate questions, collect data, analyze data, and interpret results) and levels of statistical sophistication, as well as levels of cognitive demand as suggested by the Mathematical Complexity framework. Across the three series 582 statistical association tasks, all components of statistical investigation were evident with different levels of treatment: (a) all questions for statistical investigations were provided by textbook authors (b) tasks rarely afforded student opportunities to collect data and (c) nearly all of the tasks required students to analyze data and most required them to interpret results. Tasks in the integrated series were more numerous ( n = 246) and required higher levels of mathematical complexity and statistical sophistication than tasks in the traditional and hybrid series. The vast majority of tasks were coded at the GAISE Level B for analyze data and interpret results and moderate level for mathematical complexity. Further analyses show the concordance between the developmental levels for statistical sophistication and mathematical complexity. Suggestions for curriculum development, content analysis, and future research are provided.
Description:
To address the upcoming reform curriculum initiative following competency-based learning in Vietnam, this study examines how variations of a contextualized task allow students to experience the mathematical modelling process. We explore how Grade 10 students respond to tasks with different levels of authenticity when they first attempt such tasks. Adapting the Theory of Authentic Task Situations, we designed variations of the Goat Cage task and implemented them with six small groups of students. Results showed that the modelling processes that the students progressed through differed in mathematical models used and real-world considerations, with diverse approaches when solving the more-authentic variation. Not all phases of the modelling process were observed explicitly when they engaged in the tasks. Students showed a positive disposition towards tasks with more authentic contextual information. The study suggests ways to adapt contextualized tasks to make them more authentic, which allows students to experience a holistic modelling process.