The use of explicit algorithms and episodic context to teach subtraction to students with learning problems in mathematics /

This research attempted to address the question of the role of explicit algorithms and episodic contexts in the acquisition of computational procedures for regrouping in subtraction. Three groups of students having difficulty learning to subtract with regrouping were taught procedures for doing so through either an explicit algorithm, an episodic content or an examples approach. It was hypothesized that the use of an explicit algorithm represented in a flow chart format would facilitate the acquisition and retention of specific procedural steps relative to the other two conditions. On the other hand, the use of paragraph stories to create episodic content was expected to facilitate the retrieval of algorithms, particularly in a mixed presentation format. The subjects were tested on similar, near, and far transfer questions over a four-day period. Near and far transfer algorithms were also introduced on Day Two. The results suggested that both explicit and episodic context facilitate performance on questions requiring subtraction with regrouping. However, the differential effects of these two approaches on near and far transfer questions were not as easy to identify. Explicit algorithms may facilitate the acquisition of specific procedural steps while at the same time inhibiting the application of such steps to transfer questions. Similarly, the value of episodic context in cuing the retrieval of an algorithm may be limited by the ability of a subject to identify and classify a new question as an exemplar of a particular episodically deflned problem type or category. The implications of these findings in relation to the procedures employed in the teaching of Mathematics to students with learning problems are discussed in detail.

The essence of a tacit intersection : a heuristic inquiry into nature-based leisure and personal transformation

There are a considerable number of programs and agencies that count on the existence of a unique relationship between nature and human development. In addition, there are significant bodies of literature dedicated to understanding developmentally focused nature-based experiences. This research project was designed to flirther the understanding of this phenomenon. Consequently, the purpose of this research endeavour was to discover the essence ofthe intersection ofpersonal transformation and nature-based leisure, culminating in a rich and detailed account of this otherwise tacit phenomenon. As such, this research built on the assumption of this beneficial intersection of nature and personal transformation and contributes to the understanding ofhow this context is supporting or generating of selfactualization and positive development. Heuristic methods were employed because heuristics is concerned with the quality and essence of an experience, not causal relationships (Moustakas, 1990). Heuristic inquiry begins with the primary researcher and her personal experience and knowledge of the phenomenon. This study also involved four other coresearchers who had also experienced this phenomenon intensely. Co-researchers were found through purposeful and snowball sampling. Rich narrative descriptions of their experiences were gathered through in-depth, semi-structured interviews, and artifact elicitation was employed as a means to get at co-researchers' tacit knowledge. Each coresearcher was interviewed twice (the first interview focused on personal transformation, the second on nature) for approximately four and a half hours in total. Transcripts were read repeatedly to discern patterns that emerged from the study of the narratives and were coded accordingly. Individual narratives were consolidated to create a composite narrative of the experience. Finally, a creative synthesis was developed to represent the essence of this tacit experience. In conclusion the essence of the intersection of nature-based leisure and personal transformation was found to lie in the convergence of the lived experience of authenticity. The physical environment of nature was perceived and experienced to be a space and context of authenticity, leisure experiences were experienced as an engagement of authenticity, and individuals themselves encountered a true or authentic self that emanated from within. The implications of these findings are many, offering suggestions, considerations and implications from reconsidered approaches to environmental education to support for selfdirected human development.

Properties and algorithms of the (n, k)-star graphs

The (n, k)-star interconnection network was proposed in 1995 as an attractive alternative to the n-star topology in parallel computation. The (n, k )-star has significant advantages over the n-star which itself was proposed as an attractive alternative to the popular hypercube. The major advantage of the (n, k )-star network is its scalability, which makes it more flexible than the n-star as an interconnection network. In this thesis, we will focus on finding graph theoretical properties of the (n, k )-star as well as developing parallel algorithms that run on this network. The basic topological properties of the (n, k )-star are first studied. These are useful since they can be used to develop efficient algorithms on this network. We then study the (n, k )-star network from algorithmic point of view. Specifically, we will investigate both fundamental and application algorithms for basic communication, prefix computation, and sorting, etc. A literature review of the state-of-the-art in relation to the (n, k )-star network as well as some open problems in this area are also provided.

Decoding algorithms using side-effect machines

Bioinformatics applies computers to problems in molecular biology. Previous research has not addressed edit metric decoders. Decoders for quaternary edit metric codes are finding use in bioinformatics problems with applications to DNA. By using side effect machines we hope to be able to provide efficient decoding algorithms for this open problem. Two ideas for decoding algorithms are presented and examined. Both decoders use Side Effect Machines(SEMs) which are generalizations of finite state automata. Single Classifier Machines(SCMs) use a single side effect machine to classify all words within a code. Locking Side Effect Machines(LSEMs) use multiple side effect machines to create a tree structure of subclassification. The goal is to examine these techniques and provide new decoders for existing codes. Presented are ideas for best practices for the creation of these two types of new edit metric decoders.

Properties and algorithms of the (n, k)-arrangement graphs

The (n, k)-arrangement interconnection topology was first introduced in 1992. The (n, k )-arrangement graph is a class of generalized star graphs. Compared with the well known n-star, the (n, k )-arrangement graph is more flexible in degree and diameter. However, there are few algorithms designed for the (n, k)-arrangement graph up to present. In this thesis, we will focus on finding graph theoretical properties of the (n, k)- arrangement graph and developing parallel algorithms that run on this network. The topological properties of the arrangement graph are first studied. They include the cyclic properties. We then study the problems of communication: broadcasting and routing. Embedding problems are also studied later on. These are very useful to develop efficient algorithms on this network. We then study the (n, k )-arrangement network from the algorithmic point of view. Specifically, we will investigate both fundamental and application algorithms such as prefix sums computation, sorting, merging and basic geometry computation: finding convex hull on the (n, k )-arrangement graph. A literature review of the state-of-the-art in relation to the (n, k)-arrangement network is also provided, as well as some open problems in this area.

Properties and algorithms of the hyper-star graph and its related graphs

The hyper-star interconnection network was proposed in 2002 to overcome the drawbacks of the hypercube and its variations concerning the network cost, which is defined by the product of the degree and the diameter. Some properties of the graph such as connectivity, symmetry properties, embedding properties have been studied by other researchers, routing and broadcasting algorithms have also been designed. This thesis studies the hyper-star graph from both the topological and algorithmic point of view. For the topological properties, we try to establish relationships between hyper-star graphs with other known graphs. We also give a formal equation for the surface area of the graph. Another topological property we are interested in is the Hamiltonicity problem of this graph. For the algorithms, we design an all-port broadcasting algorithm and a single-port neighbourhood broadcasting algorithm for the regular form of the hyper-star graphs. These algorithms are both optimal time-wise. Furthermore, we prove that the folded hyper-star, a variation of the hyper-star, to be maixmally fault-tolerant.

Quadtree representation and compression of spatial data

Spatial data representation and compression has become a focus issue in computer graphics and image processing applications. Quadtrees, as one of hierarchical data structures, basing on the principle of recursive decomposition of space, always offer a compact and efficient representation of an image. For a given image, the choice of quadtree root node plays an important role in its quadtree representation and final data compression. The goal of this thesis is to present a heuristic algorithm for finding a root node of a region quadtree, which is able to reduce the number of leaf nodes when compared with the standard quadtree decomposition. The empirical results indicate that, this proposed algorithm has quadtree representation and data compression improvement when in comparison with the traditional method.

Using genetic algorithms for the single allocation hub location problem

Hub location problem is an NP-hard problem that frequently arises in the design of transportation and distribution systems, postal delivery networks, and airline passenger flow. This work focuses on the Single Allocation Hub Location Problem (SAHLP). Genetic Algorithms (GAs) for the capacitated and uncapacitated variants of the SAHLP based on new chromosome representations and crossover operators are explored. The GAs is tested on two well-known sets of real-world problems with up to 200 nodes. The obtained results are very promising. For most of the test problems the GA obtains improved or best-known solutions and the computational time remains low. The proposed GAs can easily be extended to other variants of location problems arising in network design planning in transportation systems.

Comparison of classification ability of hyperball algorithms to neural network and k-nearest neighbour algorithms

The main focus of this thesis is to evaluate and compare Hyperbalilearning algorithm (HBL) to other learning algorithms. In this work HBL is compared to feed forward artificial neural networks using back propagation learning, K-nearest neighbor and 103 algorithms. In order to evaluate the similarity of these algorithms, we carried out three experiments using nine benchmark data sets from UCI machine learning repository. The first experiment compares HBL to other algorithms when sample size of dataset is changing. The second experiment compares HBL to other algorithms when dimensionality of data changes. The last experiment compares HBL to other algorithms according to the level of agreement to data target values. Our observations in general showed, considering classification accuracy as a measure, HBL is performing as good as most ANn variants. Additionally, we also deduced that HBL.:s classification accuracy outperforms 103's and K-nearest neighbour's for the selected data sets.

Heuristics for the Critical Node Detection Problem in Large Complex Networks

Complex networks have recently attracted a significant amount of research attention due to their ability to model real world phenomena. One important problem often encountered is to limit diffusive processes spread over the network, for example mitigating pandemic disease or computer virus spread. A number of problem formulations have been proposed that aim to solve such problems based on desired network characteristics, such as maintaining the largest network component after node removal. The recently formulated critical node detection problem aims to remove a small subset of vertices from the network such that the residual network has minimum pairwise connectivity. Unfortunately, the problem is NP-hard and also the number of constraints is cubic in number of vertices, making very large scale problems impossible to solve with traditional mathematical programming techniques. Even many approximation algorithm strategies such as dynamic programming, evolutionary algorithms, etc. all are unusable for networks that contain thousands to millions of vertices. A computationally efficient and simple approach is required in such circumstances, but none currently exist. In this thesis, such an algorithm is proposed. The methodology is based on a depth-first search traversal of the network, and a specially designed ranking function that considers information local to each vertex. Due to the variety of network structures, a number of characteristics must be taken into consideration and combined into a single rank that measures the utility of removing each vertex. Since removing a vertex in sequential fashion impacts the network structure, an efficient post-processing algorithm is also proposed to quickly re-rank vertices. Experiments on a range of common complex network models with varying number of vertices are considered, in addition to real world networks. The proposed algorithm, DFSH, is shown to be highly competitive and often outperforms existing strategies such as Google PageRank for minimizing pairwise connectivity.

Multi-Objective Genetic Algorithms for the Single Allocation Hub Location Problem

Hub Location Problems play vital economic roles in transportation and telecommunication networks where goods or people must be efficiently transferred from an origin to a destination point whilst direct origin-destination links are impractical. This work investigates the single allocation hub location problem, and proposes a genetic algorithm (GA) approach for it. The effectiveness of using a single-objective criterion measure for the problem is first explored. Next, a multi-objective GA employing various fitness evaluation strategies such as Pareto ranking, sum of ranks, and weighted sum strategies is presented. The effectiveness of the multi-objective GA is shown by comparison with an Integer Programming strategy, the only other multi-objective approach found in the literature for this problem. Lastly, two new crossover operators are proposed and an empirical study is done using small to large problem instances of the Civil Aeronautics Board (CAB) and Australian Post (AP) data sets.

Interpreting Quantifier Scope Ambiguity: Evidence of Heuristic First, Algorithmic Second Processing

The present work suggests that sentence processing requires both heuristic and algorithmic processing streams, where the heuristic processing strategy precedes the algorithmic phase. This conclusion is based on three self-paced reading experiments in which the processing of two-sentence discourses was investigated, where context sentences exhibited quantifier scope ambiguity. Experiment 1 demonstrates that such sentences are processed in a shallow manner. Experiment 2 uses the same stimuli as Experiment 1 but adds questions to ensure deeper processing. Results indicate that reading times are consistent with a lexical-pragmatic interpretation of number associated with context sentences, but responses to questions are consistent with the algorithmic computation of quantifier scope. Experiment 3 shows the same pattern of results as Experiment 2, despite using stimuli with different lexicalpragmatic biases. These effects suggest that language processing can be superficial, and that deeper processing, which is sensitive to structure, only occurs if required. Implications for recent studies of quantifier scope ambiguity are discussed.

Properties and Algorithms of the KCube Graphs

The KCube interconnection topology was rst introduced in 2010. The KCube graph is a compound graph of a Kautz digraph and hypercubes. Compared with the at- tractive Kautz digraph and well known hypercube graph, the KCube graph could accommodate as many nodes as possible for a given indegree (and outdegree) and the diameter of interconnection networks. However, there are few algorithms designed for the KCube graph. In this thesis, we will concentrate on nding graph theoretical properties of the KCube graph and designing parallel algorithms that run on this network. We will explore several topological properties, such as bipartiteness, Hamiltonianicity, and symmetry property. These properties for the KCube graph are very useful to develop efficient algorithms on this network. We will then study the KCube network from the algorithmic point of view, and will give an improved routing algorithm. In addition, we will present two optimal broadcasting algorithms. They are fundamental algorithms to many applications. A literature review of the state of the art network designs in relation to the KCube network as well as some open problems in this field will also be given.

Flourishing in the face of mental illness: A heuristic examination of the contribution of leisure to creating a meaningful life

The purpose of this research was to examine the ways in which individuals with mental illness create a life of purpose, satisfaction and meaning. The data supported the identification of four common themes: (1) the power of leisure in activation, (2) the power of leisure in resiliency, (3) the power of leisure in identity and (4) the power of leisure in reducing struggle. Through an exploration of the experience of having a mental illness, this project supports that leisure provides therapeutic benefits that transcend through negative life events. In addition, this project highlights the individual nature of recovery as a process of self-discovery. Through the creation of a visual model, this project provides a benchmark for how a small group of individuals have experienced living well with mental illness. As such, this work brings new thought to the growing body of mental health and leisure studies literature.

Characterizing Dynamic Optimization Benchmarks for the Comparison of Multi-Modal Tracking Algorithms

Population-based metaheuristics, such as particle swarm optimization (PSO), have been employed to solve many real-world optimization problems. Although it is of- ten sufficient to find a single solution to these problems, there does exist those cases where identifying multiple, diverse solutions can be beneficial or even required. Some of these problems are further complicated by a change in their objective function over time. This type of optimization is referred to as dynamic, multi-modal optimization. Algorithms which exploit multiple optima in a search space are identified as niching algorithms. Although numerous dynamic, niching algorithms have been developed, their performance is often measured solely on their ability to find a single, global optimum. Furthermore, the comparisons often use synthetic benchmarks whose landscape characteristics are generally limited and unknown. This thesis provides a landscape analysis of the dynamic benchmark functions commonly developed for multi-modal optimization. The benchmark analysis results reveal that the mechanisms responsible for dynamism in the current dynamic bench- marks do not significantly affect landscape features, thus suggesting a lack of representation for problems whose landscape features vary over time. This analysis is used in a comparison of current niching algorithms to identify the effects that specific landscape features have on niching performance. Two performance metrics are proposed to measure both the scalability and accuracy of the niching algorithms. The algorithm comparison results demonstrate the algorithms best suited for a variety of dynamic environments. This comparison also examines each of the algorithms in terms of their niching behaviours and analyzing the range and trade-off between scalability and accuracy when tuning the algorithms respective parameters. These results contribute to the understanding of current niching techniques as well as the problem features that ultimately dictate their success.