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.

Geological image processing of petrographic thin sections using the rotating polarizer stage

One of the fundamental problems with image processing of petrographic thin sections is that the appearance (colour I intensity) of a mineral grain will vary with the orientation of the crystal lattice to the preferred direction of the polarizing filters on a petrographic microscope. This makes it very difficult to determine grain boundaries, grain orientation and mineral species from a single captured image. To overcome this problem, the Rotating Polarizer Stage was used to replace the fixed polarizer and analyzer on a standard petrographic microscope. The Rotating Polarizer Stage rotates the polarizers while the thin section remains stationary, allowing for better data gathering possibilities. Instead of capturing a single image of a thin section, six composite data sets are created by rotating the polarizers through 900 (or 1800 if quartz c-axes measurements need to be taken) in both plane and cross polarized light. The composite data sets can be viewed as separate images and consist of the average intensity image, the maximum intensity image, the minimum intensity image, the maximum position image, the minimum position image and the gradient image. The overall strategy used by the image processing system is to gather the composite data sets, determine the grain boundaries using the gradient image, classify the different mineral species present using the minimum and maximum intensity images and then perform measurements of grain shape and, where possible, partial crystallographic orientation using the maximum intensity and maximum position images.

A Study of Ordered Gene Problems Featuring DNA Error Correction and DNA Fragment Assembly with a Variety of Heuristics, Genetic Algorithm Variations, and Dynamic Representations

Ordered gene problems are a very common classification of optimization problems. Because of their popularity countless algorithms have been developed in an attempt to find high quality solutions to the problems. It is also common to see many different types of problems reduced to ordered gene style problems as there are many popular heuristics and metaheuristics for them due to their popularity. Multiple ordered gene problems are studied, namely, the travelling salesman problem, bin packing problem, and graph colouring problem. In addition, two bioinformatics problems not traditionally seen as ordered gene problems are studied: DNA error correction and DNA fragment assembly. These problems are studied with multiple variations and combinations of heuristics and metaheuristics with two distinct types or representations. The majority of the algorithms are built around the Recentering- Restarting Genetic Algorithm. The algorithm variations were successful on all problems studied, and particularly for the two bioinformatics problems. For DNA Error Correction multiple cases were found with 100% of the codes being corrected. The algorithm variations were also able to beat all other state-of-the-art DNA Fragment Assemblers on 13 out of 16 benchmark problem instances.

Calculation of nondifferential properties for atomic ground states /

A new method for sampling the exact (within the nodal error) ground state distribution and nondiflPerential properties of multielectron systems is developed and applied to firstrow atoms. Calculated properties are the distribution moments and the electronic density at the nucleus (the 6 operator). For this purpose, new simple trial functions are developed and optimized. First, using Hydrogen as a test case, we demonstrate the accuracy of our algorithm and its sensitivity to error in the trial function. Applications to first row atoms are then described. We obtain results which are more satisfactory than the ones obtained previously using Monte Carlo methods, despite the relative crudeness of our trial functions. Also, a comparison is made with results of highly accurate post-Hartree Fock calculations, thereby illuminating the nodal error in our estimates. Taking into account the CPU time spent, our results, particularly for the 8 operator, have a relatively large variance. Several ways of improving the eflSciency together with some extensions of the algorithm are suggested.

Evaluation of a stage II screening protocol for prostate cancer

In 2003, prostate cancer (PCa) is estimated to be the most commonly diagnosed cancer and third leading cause of cancer death in Canada. During PCa population screening, approximately 25% of patients with a normal digital rectal examination (DRE) and intermediate serum prostate specific antigen (PSA) level have PCa. Since all patients typically undergo biopsy, it is expected that approximately 75% of these procedures are unnecessary. The purpose of this study was to compare the degree of efficacy of clinical tests and algorithms in stage II screening for PCa while preventing unnecessary biopsies from occurring. The sample consisted of 201 consecutive men who were suspected of PCa based on the results of a DRE and serum PSA. These men were referred for venipuncture and transrectal ultrasound (TRUS). Clinical tests included TRUS, agespecific reference range PSA (Age-PSA), prostate specific antigen density (PSAD), and free-to-total prostate specific antigen ratio (%fPSA). Clinical results were evaluated individually and within algorithms. Cutoffs of 0.12 and 0.15 ng/ml/cc were employed for PSAD. Cutoffs that would provide a minimum sensitivity of 0.90 and 0.95, respectively were utilized for %fPSA. Statistical analysis included ROC curve analysis, calculated sensitivity (Sens), specificity (Spec), and positive likelihood ratio (LR), with corresponding confidence intervals (Cl). The %fPSA, at a 23% cutoff ({ Sens=0.92; CI, 0.06}, {Spec=0.4l; CI, 0.09}, {LR=1.56; CI, O.ll}), proved to be the most efficacious independent clinical test. The combination of PSAD (cutoff 0.15 ng/ml/cc) and %fPSA (cutoff 23%) ({Sens=0.93; CI, 0.06}, {Spec=0.38; CI, 0.08}, {LR=1.50; CI, 0.10}) was the most efficacious clinical algorithm. This study advocates the use of %fPSA at a cutoff of 23% when screening patients with an intermediate serum PSA and benign DRE.