16 resultados para Computer Algebra

em Brock University, Canada


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Relation algebras is one of the state-of-the-art means used by mathematicians and computer scientists for solving very complex problems. As a result, a computer algebra system for relation algebras called RelView has been developed at Kiel University. RelView works within the standard model of relation algebras. On the other hand, relation algebras do have other models which may have different properties. For example, in the standard model we always have L;L=L (the composition of two (heterogeneous) universal relations yields a universal relation). This is not true in some non-standard models. Therefore, any example in RelView will always satisfy this property even though it is not true in general. On the other hand, it has been shown that every relation algebra with relational sums and subobjects can be seen as matrix algebra similar to the correspondence of binary relations between sets and Boolean matrices. The aim of my research is to develop a new system that works with both standard and non-standard models for arbitrary relations using multiple-valued decision diagrams (MDDs). This system will implement relations as matrix algebras. The proposed structure is a library written in C which can be imported by other languages such as Java or Haskell.

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The effects oftwo types of small-group communication, synchronous computer-mediated and face-to-face, on the quantity and quality of verbal output were con^ared. Quantity was deiSned as the number of turns taken per minute, the number of Analysis-of-Speech units (AS-units) produced per minute, and the number ofwords produced per minute. Quality was defined as the number of words produced per AS-unit. In addition, the interaction of gender and type of communication was explored for any differences that existed in the output produced. Questionnaires were also given to participants to determine attitudes toward computer-mediated and face-to-face communication. Thirty intermediate-level students fi-om the Intensive English Language Program (lELP) at Brock University participated in the study, including 15 females and 15 males. Nonparametric tests, including the Wilcoxon matched-pairs test, Mann-Whitney U test, and Friedman test were used to test for significance at the p < .05 level. No significant differences were found in the effects of computer-mediated and face-to-face communication on the output produced during follow-up speaking sessions. However, the quantity and quality of interaction was significantly higher during face-to-face sessions than computer-mediated sessions. No significant differences were found in the output produced by males and females in these 2 conditions. While participants felt that the use of computer-mediated communication may aid in the development of certain language skills, they generally preferred face-to-face communication. These results differed fi-om previous studies that found a greater quantity and quality of output in addition to a greater equality of interaction produced during computer-mediated sessions in comparison to face-to-face sessions (Kern, 1995; Warschauer, 1996).

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The quantitative component of this study examined the effect of computerassisted instruction (CAI) on science problem-solving performance, as well as the significance of logical reasoning ability to this relationship. I had the dual role of researcher and teacher, as I conducted the study with 84 grade seven students to whom I simultaneously taught science on a rotary-basis. A two-treatment research design using this sample of convenience allowed for a comparison between the problem-solving performance of a CAI treatment group (n = 46) versus a laboratory-based control group (n = 38). Science problem-solving performance was measured by a pretest and posttest that I developed for this study. The validity of these tests was addressed through critical discussions with faculty members, colleagues, as well as through feedback gained in a pilot study. High reliability was revealed between the pretest and the posttest; in this way, students who tended to score high on the pretest also tended to score high on the posttest. Interrater reliability was found to be high for 30 randomly-selected test responses which were scored independently by two raters (i.e., myself and my faculty advisor). Results indicated that the form of computer-assisted instruction (CAI) used in this study did not significantly improve students' problem-solving performance. Logical reasoning ability was measured by an abbreviated version of the Group Assessment of Lx)gical Thinking (GALT). Logical reasoning ability was found to be correlated to problem-solving performance in that, students with high logical reasoning ability tended to do better on the problem-solving tests and vice versa. However, no significant difference was observed in problem-solving improvement, in the laboratory-based instruction group versus the CAI group, for students varying in level of logical reasoning ability.Insignificant trends were noted in results obtained from students of high logical reasoning ability, but require further study. It was acknowledged that conclusions drawn from the quantitative component of this study were limited, as further modifications of the tests were recommended, as well as the use of a larger sample size. The purpose of the qualitative component of the study was to provide a detailed description ofmy thesis research process as a Brock University Master of Education student. My research journal notes served as the data base for open coding analysis. This analysis revealed six main themes which best described my research experience: research interests, practical considerations, research design, research analysis, development of the problem-solving tests, and scoring scheme development. These important areas ofmy thesis research experience were recounted in the form of a personal narrative. It was noted that the research process was a form of problem solving in itself, as I made use of several problem-solving strategies to achieve desired thesis outcomes.

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The study examined coaches' usage of text-based computer-mediated communication (CMC) media (e.g., text-messaging, email) in the coach-player relationship. Data were collected by surveying Ontario-based male baseball coaches (n = 86) who coached players between 15 and 18 years old. Predictions were made regarding how demographic factors such as age and coaching experience affected coaches' CMC use and opinions. Results indicated that over 76% of respondents never used any CMC media other than email and team websites in their interactions with players. Results also revealed that coaches' usage rates contrasted with their opinion of the usefulness of the media, and their perception of players' use of the media. Coaches characterized most CMC media as limited, unnecessary, and sometimes inappropriate. Additional research should explore players' CMC usage rates and possible guidelines for use of the new media in authority relationships. Academia needs to keep pace with the developments in this area.

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This study compared the relative effectiveness of two computerized remedial reading programs in improving the reading word recognition, rate, and comprehension of adolescent readers demonstrating significant and longstanding reading difficulties. One of the programs involved was Autoskill Component Reading Subskills Program, which provides instruction in isolated letters, syllables, and words, to a point of rapid automatic responding. This program also incorporates reading disability subtypes in its approach. The second program, Read It Again. Sam, delivers a repeated reading strategy. The study also examined the feasibility of using peer tutors in association with these two programs. Grade 9 students at a secondary vocational school who satisfied specific criteria with respect to cognitive and reading ability participated. Eighteen students were randomly assigned to three matched groups, based on prior screening on a battery of reading achievement tests. Two I I groups received training with one of the computer programs; the third group acted as a control and received the remedial reading program offered within the regular classroom. The groups met daily with a trained tutor for approximately 35 minutes, and were required to accumulate twenty hours of instruction. At the conclusion of the program, the pretest battery was repeated. No significant differences were found in the treatment effects of the two computer groups. Each of the two treatment groups was able to effect significantly improved reading word recognition and rate, relative to the control group. Comprehension gains were modest. The treatment groups demonstrated a significant gain, relative to the control group, on one of the three comprehension measures; only trends toward a gain were noted on the remaining two measures. The tutoring partnership appeared to be a viable alternative for the teacher seeking to provide individualized computerized remedial programs for adolescent unskilled readers. Both programs took advantage of computer technology in providing individualized drill and practice, instant feedback, and ongoing recordkeeping. With limited cautions, each of these programs was considered effective and practical for use with adolescent unskilled readers.

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This paper presents two studies, both examining the efficacy of a computer programme (Captain's Log) in training attentional skills. The population of interest is the traumatically brain injured. Study #1 is a single-case design that offers recommendations for the second, .larger (N=5) inquiry. Study #2 is an eight-week hierarchical treatment programme with a multi-based testing component. Attention, memory, listening comprehension, locus-of-control, self-esteem, visuo-spatial, and general outcome measures are employed within the testing schedule. Results suggest that any improvement was a result of practice effects. With a few single-case exceptions, the participants showed little improvement in the dependent measures.

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This study had three purposes related to the effective implem,entation and practice of computer-mediated online distance education (C-MODE) at the elementary level: (a) To identify a preliminary framework of criteria 'or guidelines for effective implementation and practice, (b) to identify areas ofC-MODE for which criteria or guidelines of effectiveness have not yet been developed, and (c) to develop an implementation and practice criteria questionnaire based on a review of the distance education literature, and to use the questionnaire in an exploratory survey of elementary C-MODE practitioners. Using the survey instrument, the beliefs and attitudes of 16 elementary C'- MODE practitioners about what constitutes effective implementation and practice principles were investigated. Respondents, who included both administrators and instructors, provided information about themselves and the program in which they worked. They rated 101 individual criteria statenlents on a 5 point Likert scale with a \. point range that included the values: 1 (Strongly Disagree), 2 (Disagree), 3 (Neutral or Undecided), 4 (Agree), 5 (Strongly Agree). Respondents also provided qualitative data by commenting on the individual statements, or suggesting other statements they considered important. Eighty-two different statements or guidelines related to the successful implementation and practice of computer-mediated online education at the elementary level were endorsed. Response to a small number of statements differed significantly by gender and years of experience. A new area for investigation, namely, the role ofparents, which has received little attention in the online distance education literature, emerged from the findings. The study also identified a number of other areas within an elementary context where additional research is necessary. These included: (a) differences in the factors that determine learning in a distance education setting and traditional settings, (b) elementary students' ability to function in an online setting, (c) the role and workload of instructors, (d) the importance of effective, timely communication with students and parents, and (e) the use of a variety of media.

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This case study examines the impact of a computer information system as it was being implemented in one Ontario hospital. The attitudes of a cross section of the hospital staff acted as a barometer to measure their perceptions of the implementation process. With The Mississauga Hospital in the early stages of an extensive computer implementation project, the opportunity existed to identify staff attitudes about the computer system, overall knowledge and compare the findings with the literature. The goal of the study was to develop a greater base about the affective domain in the relationship between people and the computer system. Eight exploratory questions shaped the focus of the investigation. Data were collected from three sources: a survey questionnaire, focused interviews, and internal hospital documents. Both quantitative and qualitative data were analyzed. Instrumentation in the study consisted of a survey distributed at two points in time to randomly selected hospital employees who represented all staff levels.Other sources of data included hospital documents, and twenty-five focused interviews with staff who replied to both surveys. Leavitt's socio-technical system, with its four subsystems: task, structure, technology, and people was used to classify staff responses to the research questions. The study findings revealed that the majority of respondents felt positive about using the computer as part of their jobs. No apparent correlations were found between sex, age, or staff group and feelings about using the computer. Differences in attitudes, and attitude changes were found in potential relationship to the element of time. Another difference was found in staff group and perception of being involved in the decision making process. These findings and other evidence about the role of change agents in this change process help to emphasize that planning change is one thing, managing the transition is another.

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This study investigated the effectiveness of a computer program, PERSONAL CAREER DIRECTIONS (PC DIRECTIONS) (Anderson, Welborn, & Wright, 1983) on career planning and exploration for twenty-four Brock University students (18 women and 6 men) who requested career planning assistance at the Career/Placement Services of the Counselling Centre. A one-group pretest/posttest design was used in the study_ Progress in career planning and exploration was measured by Career Planning (CP) and Career Exploration (CE) scales of the Career Development Inventory (College and University Form) (Super, Thompson, Lindeman, Jordaan, & Myers, 1981). A paired samples 2-tailed t test for Career Development Attitudes (CDA) , the combined CP and CE scales, revealed the posttest scores were significantly higher than the pretest scores, t(23) = 3.74, 2 < .001. Student progress was also assessed by self-report lists of job titles which reflected positive changes after students used PC DIRECTIONS. In response to several questions, students' attitudes were more positive than negative toward the program. Implications are that PC DIRECTIONS is an effective component in promoting career planning for university students. Further studies may reveal that different types of students may benefit from different interventions in the career planning process.

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This study was undertaken in order to determine the effects of playing computer based text adventure games on the reading comprehension gains of students. Forty-five grade five students from one elementary school were randomly assigned to experimental and control groups, and were tested with regard to ability, achievement and reading skills. An experimental treatment, consisting of playing computer based interactive fiction games of the student's choice for fifteen minutes each day over an eight-week period, was administered. A comparison treatment engaged the control group in sustained silent reading of materials of the student's choice for an equal period of time. Following the experimental period all students were post-tested with an alternate form of the pre-test in reading skills, and gain scores were analysed. It was found that there were no significant differences in the gain scores of the experimental and control groups for overall reading comprehenSion, but the experimental group showed greater gains than the control group in the structural analysis reading sub-skill. Extreme variance in the data made generalization very difficult, but the findings indicated a potential for computer based interactive fiction as a useful tool for developing reading sl

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Given a heterogeneous relation algebra R, it is well known that the algebra of matrices with coefficient from R is relation algebra with relational sums that is not necessarily finite. When a relational product exists or the point axiom is given, we can represent the relation algebra by concrete binary relations between sets, which means the algebra may be seen as an algebra of Boolean matrices. However, it is not possible to represent every relation algebra. It is well known that the smallest relation algebra that is not representable has only 16 elements. Such an algebra can not be put in a Boolean matrix form.[15] In [15, 16] it was shown that every relation algebra R with relational sums and sub-objects is equivalent to an algebra of matrices over a suitable basis. This basis is given by the integral objects of R, and is, compared to R, much smaller. Aim of my thesis is to develop a system called ReAlM - Relation Algebra Manipulator - that is capable of visualizing computations in arbitrary relation algebras using the matrix approach.

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Relation algebras and categories of relations in particular have proven to be extremely useful as a fundamental tool in mathematics and computer science. Since relation algebras are Boolean algebras with some well-behaved operations, every such algebra provides an atom structure, i.e., a relational structure on its set of atoms. In the case of complete and atomic structure (e.g. finite algebras), the original algebra can be recovered from its atom structure by using the complex algebra construction. This gives a representation of relation algebras as the complex algebra of a certain relational structure. This property is of particular interest because storing the atom structure requires less space than the entire algebra. In this thesis I want to introduce and implement three structures representing atom structures of integral heterogeneous relation algebras, i.e., categorical versions of relation algebras. The first structure will simply embed a homogeneous atom structure of a relation algebra into the heterogeneous context. The second structure is obtained by splitting all symmetric idempotent relations. This new algebra is in almost all cases an heterogeneous structure having more objects than the original one. Finally, I will define two different union operations to combine two algebras into a single one.

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Please consult the paper edition of this thesis to read. It is available on the 5th Floor of the Library at Call Number: Z 9999 E38 D56 1992

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Qualitative spatial reasoning (QSR) is an important field of AI that deals with qualitative aspects of spatial entities. Regions and their relationships are described in qualitative terms instead of numerical values. This approach models human based reasoning about such entities closer than other approaches. Any relationships between regions that we encounter in our daily life situations are normally formulated in natural language. For example, one can outline one's room plan to an expert by indicating which rooms should be connected to each other. Mereotopology as an area of QSR combines mereology, topology and algebraic methods. As mereotopology plays an important role in region based theories of space, our focus is on one of the most widely referenced formalisms for QSR, the region connection calculus (RCC). RCC is a first order theory based on a primitive connectedness relation, which is a binary symmetric relation satisfying some additional properties. By using this relation we can define a set of basic binary relations which have the property of being jointly exhaustive and pairwise disjoint (JEPD), which means that between any two spatial entities exactly one of the basic relations hold. Basic reasoning can now be done by using the composition operation on relations whose results are stored in a composition table. Relation algebras (RAs) have become a main entity for spatial reasoning in the area of QSR. These algebras are based on equational reasoning which can be used to derive further relations between regions in a certain situation. Any of those algebras describe the relation between regions up to a certain degree of detail. In this thesis we will use the method of splitting atoms in a RA in order to reproduce known algebras such as RCC15 and RCC25 systematically and to generate new algebras, and hence a more detailed description of regions, beyond RCC25.