Description:
In the 1990s, two major issues emerged globally for tertiary mathematics educators: declining standards in the mathematical proficiency of students at tertiary-entry level and the advocates for the incorporation of IT into the processes of teaching and learning. Addressing these issues required significant reform of both curriculum content and classroom practice to ensure that the technology was used appropriately and effectively. These reforms were largely implemented by staff from tertiary Schools of Mathematics. Rather than leading the reform, the Education community lagged behind and in some instances has taken research into the use of IT in Mathematics Education in a questionable direction. In this paper, we outline what we contend has been a failure on the behalf of the Education community to tackle and address problems experienced by mathematics educators (particularly at the tertiary level) and make some suggestions for the directions of future research in Mathematics Education.
Description:
In the 1990s, two major issues emerged globally for tertiary mathematics educators: declining standards in the mathematical proficiency of students at tertiary-entry level and the advocates for the incorporation of IT into the processes of teaching and learning. Addressing these issues required significant reform of both curriculum content and classroom practice to ensure that the technology was used appropriately and effectively. These reforms were largely implemented by staff from tertiary Schools of Mathematics. Rather than leading the reform, the Education community lagged behind and in some instances has taken research into the use of IT in Mathematics Education in a questionable direction. In this paper, we outline what we contend has been a failure on the behalf of the Education community to tackle and address problems experienced by mathematics educators (particularly at the tertiary level) and make some suggestions for the directions of future research in Mathematics Education.
Description:
Abstract: Ontologies in a web setting, particularly those used in a group context (such as a virtual community), need to be flexible and open to changes that reflect the evolution of knowledge. OWL the ontology language of the semantic web provides very little for facilitating the description of evolutionary changes in an ontology. We propose a dynamic web ontology language (dOWL), an extension to OWL, which consists of a set of elements that can be used to model these evolutionary changes in an ontology.
Description:
Abstract: Ontologies in a web setting, particularly those used in a group context (such as a virtual community), need to be flexible and open to changes that reflect the evolution of knowledge. OWL the ontology language of the semantic web provides very little for facilitating the description of evolutionary changes in an ontology. We propose a dynamic web ontology language (dOWL), an extension to OWL, which consists of a set of elements that can be used to model these evolutionary changes in an ontology.
Description:
Objectives: This paper presents preliminary findings from the first 10 case studies of Consumers who each suspect they have experienced an adverse drug reaction (ADR). These case studies are part of a larger study involving Consumer/Doctor decisions surrounding adverse drug reactions and prescribing, which is captured in Diagram 1. The key problem identified from our preliminary background work is that there appear to be gaps in our knowledge about the nature of the decisions being made that relate to ADRs, who these decisions are made by, the information required to make these decisions, the completeness of knowledge that is being used and the impact these factors have on the prevention, early detection or management of ADRs. Further investigation will assist in the development of decision support software in this area.
Description:
Motivation: The increasing use of DNA microarray-based tumor gene expression profiles for cancer diagnosis requires mathematical methods with high accuracy for solving clustering, feature selection and classification problems of gene expression data. Results: New algorithms are developed for solving clustering, feature selection and classification problems of gene expression data. The clustering algorithm is based on optimization techniques and allows the calculation of clusters step-by-step. This approach allows us to find as many clusters as a data set contains with respect to some tolerance. Feature selection is crucial for a gene expression database. Our feature selection algorithm is based on calculating overlaps of different genes. The database used, contains over 16 000 genes and this number is considerably reduced by feature selection. We propose a classification algorithm where each tissue sample is considered as the center of a cluster which is a ball. The results of numerical experiments confirm that the classification algorithm in combination with the feature selection algorithm perform slightly better than the published results for multi-class classifiers based on support vector machines for this data set.
Description:
Motivation: The increasing use of DNA microarray-based tumor gene expression profiles for cancer diagnosis requires mathematical methods with high accuracy for solving clustering, feature selection and classification problems of gene expression data. Results: New algorithms are developed for solving clustering, feature selection and classification problems of gene expression data. The clustering algorithm is based on optimization techniques and allows the calculation of clusters step-by-step. This approach allows us to find as many clusters as a data set contains with respect to some tolerance. Feature selection is crucial for a gene expression database. Our feature selection algorithm is based on calculating overlaps of different genes. The database used, contains over 16 000 genes and this number is considerably reduced by feature selection. We propose a classification algorithm where each tissue sample is considered as the center of a cluster which is a ball. The results of numerical experiments confirm that the classification algorithm in combination with the feature selection algorithm perform slightly better than the published results for multi-class classifiers based on support vector machines for this data set.
Description:
This paper presents a computational approach for predicting the Australian stock market index - AORD using multi-layer feed-forward neural networks from the time series data of AORD and various interrelated markets. This effort aims to discover an optimal neural network or a set of adaptive neural networks for this prediction purpose, which can exploit or model various dynamical swings and intermarket influences discovered from professional technical analysis and quantitative analysis. Four dimensions for optimality on data selection are considered: the optimal inputs from the target market (AORD) itself, the optimal set of interrelated markets, the optimal inputs from the optimal interrelated markets, and the optimal outputs. Two traditional dimensions of the neural network architecture are also considered: the optimal number of hidden layers, and the optimal number of hidden neurons for each hidden layer. Three important results were obtained: A 6-day cycle was discovered in the Australian stock market; the time signature used as additional inputs provides useful information; and a minimal neural network using 6 daily returns of AORD and 1 daily returns of SP500 plus the day of the week as inputs exhibits up to 80% directional prediction correctness.
Description:
We examine various methods for data clustering and data classification that are based on the minimization of the so-called cluster function and its modications. These functions are nonsmooth and nonconvex. We use Discrete Gradient methods for their local minimization. We consider also a combination of this method with the cutting angle method for global minimization. We present and discuss results of numerical experiments.
Description:
We examine various methods for data clustering and data classification that are based on the minimization of the so-called cluster function and its modications. These functions are nonsmooth and nonconvex. We use Discrete Gradient methods for their local minimization. We consider also a combination of this method with the cutting angle method for global minimization. We present and discuss results of numerical experiments.
Description:
Knowledge discovery from databases (KDD) exercises in law have typically attempted to derive knowledge about decision making processes in the legal domain automatically from datasets. This is made difficult in that real data that represents aspects of a decision process in law is commonly stored as text and rarely stored in structured databases. The central claim advanced here is that KDD processes can be usefully applied to existing datasets of client and demographic data in order to provide feedback for the effective operation of organizations within the legal system. However, the cost of data mining suites and the scarcity of specialized personnel for these tools mitigates against their use. In this study data mining with Association Rules (AR) has been performed on a data-set of over 380,000 records from a legal aid agency. Methods to visualise patterns in order to suggest and test plausible hypotheses from the data have been developed. The tool, called WebAssociate is entirely web based. Domain experts using the tool report favorable responses.
Description:
In this paper is presented an hybrid algorithm for finding the absolute extreme point of a multimodal scalar function of many variables. The algorithm is suitable when the objective function is expensive to compute, the computation can be affected by noise and/or partial derivatives cannot be calculated. The method used is a genetic modification of a previous algorithm based on the Prices method. All information about behavior of objective function collected on previous iterates are used to chose new evaluation points. The genetic part of the algorithm is very effective to escape from local attractors of the algorithm and assures convergence in probability to the global optimum. The proposed algorithm has been tested on a large set of multimodal test problems outperforming both the modified Prices algorithm and classical genetic approach.
Description:
This article describes an argumentation shell to support the formulation, representation and drafting of legal arguments. The shell can be used to capture generic arguments in many legal domains as well as to assist decision-makers in constructing their own actual arguments . The shell demonstrates that knowledge represented using the generic/actual argument model (GAAM) (a variant of Toulmin's argument structure) can be used to: (a) support the development of complex arguments, (b) add context and increase specificity for the retrieval of relevant documents, (c) incorporate background knowledge, (d) assist in the drafting of documents that represent arguments made, and (e) provide a structure for complex inferences requiring a range of mechanisms. The shell can be used to support decision making in a range of legal domains, including discretionary domains.
Description:
The Knowledge Discovery from Databases (KDD) technique called 'association rules' is applied to a large data set representing applicants for government-funded legal aid. Results indicate that KDD can be an invaluable tool for legal analysts. Association rules discovered identify associations between variables that are present in the data set though are not necessarily causal. Interesting rules can prompt analysts to formulate hypotheses for further investigation. The identification of interesting rules is typically performed using an objective measure of 'interesting' although this measure is often not sufficiently accurate to eliminate all uninteresting rules. In this article, a subjective measure of interestingness is adopted in conjunction with the objective measures. This leads to the ability to focus more accurately on those rules that surprise the analyst and are therefore more likely to be interesting. In general, KDD techniques have not been applied to law despite possible benefits because data is often stored in narrative form rather than in structured databases. However, the impending introduction of data warehouses that collect data from a number of organizations across a legal system presents invaluable opportunities for analysts using KDD.
Description:
The Knowledge Discovery from Databases (KDD) technique called 'association rules' is applied to a large data set representing applicants for government-funded legal aid. Results indicate that KDD can be an invaluable tool for legal analysts. Association rules discovered identify associations between variables that are present in the data set though are not necessarily causal. Interesting rules can prompt analysts to formulate hypotheses for further investigation. The identification of interesting rules is typically performed using an objective measure of 'interesting' although this measure is often not sufficiently accurate to eliminate all uninteresting rules. In this article, a subjective measure of interestingness is adopted in conjunction with the objective measures. This leads to the ability to focus more accurately on those rules that surprise the analyst and are therefore more likely to be interesting. In general, KDD techniques have not been applied to law despite possible benefits because data is often stored in narrative form rather than in structured databases. However, the impending introduction of data warehouses that collect data from a number of organizations across a legal system presents invaluable opportunities for analysts using KDD.
Description:
In this paper we propose a framework based on argumentation that can be used to support deliberative discourse on line. Online communities have several distinct advantages as very open forums but they also have some deep disadvantages. We argue that the proposed framework and web application GAAMtalk permits and encourages the positive elements of online deliberation that will enhance discussions.
Description:
In this paper we propose a framework based on argumentation that can be used to support deliberative discourse on line. Online communities have several distinct advantages as very open forums but they also have some deep disadvantages. We argue that the proposed framework and web application GAAMtalk permits and encourages the positive elements of online deliberation that will enhance discussions.
Description:
In this paper global optimisation-based techniques are studied in order to increase the accuracy of medical diagnosis and prognosis with FNA image data from the Wisconsin Diagnostic and Prognostic Breast Cancer databases. First we discuss the problem of determining the most informative features for the classification of cancerous cases in the databases under consideration. Then we apply a technique based on convex and global optimisation to breast cancer diagnosis. It allows the classification of benign cases and malignant ones and the subsequent diagnosis of patients with very high accuracy. The third application of this technique is a method that calculates centres of clusters to predict when breast cancer is likely to recur in patients for which cancer has been removed. The technique achieves higher accuracy with these databases than reported elsewhere in the literature.
Description:
In this paper global optimisation-based techniques are studied in order to increase the accuracy of medical diagnosis and prognosis with FNA image data from the Wisconsin Diagnostic and Prognostic Breast Cancer databases. First we discuss the problem of determining the most informative features for the classification of cancerous cases in the databases under consideration. Then we apply a technique based on convex and global optimisation to breast cancer diagnosis. It allows the classification of benign cases and malignant ones and the subsequent diagnosis of patients with very high accuracy. The third application of this technique is a method that calculates centres of clusters to predict when breast cancer is likely to recur in patients for which cancer has been removed. The technique achieves higher accuracy with these databases than reported elsewhere in the literature.
Description:
Argumentation concepts have been applied to numerous knowledge engineering endeavours in recent years. For example, a variety of logics have been developed to represent argumentation in the context of a dialectical situation such as a dialogue. In contrast to the dialectical approach, argumentation has also been used to structure knowledge. This can be seen as a non-dialectical approach. The Toulmin argument structure has often been used to structure knowledge non-dialectically yet most studies that apply the Toulmin structure do not use the original structure but vary one or more components. Variations to the Toulmin structure can be understood as different ways to integrate a dialectical perspective with a non-dialectical one. Drawing the dialectical/non-dialectical distinction enables the specification of a framework called the generic actual argument model that is expressly non-dialectical. The framework enables the development of knowledge-based systems that integrate a variety of inference procedures, combine information retrieval with reasoning and facilitate automated document drafting. Furthermore, the non-dialectical framework provides the foundation for simple dialectical models. Systems based on our approach have been developed in family law, refugee law, determining eligibility for government legal aid, copyright law and e-tourism.
Description:
Argumentation concepts have been applied to numerous knowledge engineering endeavours in recent years. For example, a variety of logics have been developed to represent argumentation in the context of a dialectical situation such as a dialogue. In contrast to the dialectical approach, argumentation has also been used to structure knowledge. This can be seen as a non-dialectical approach. The Toulmin argument structure has often been used to structure knowledge non-dialectically yet most studies that apply the Toulmin structure do not use the original structure but vary one or more components. Variations to the Toulmin structure can be understood as different ways to integrate a dialectical perspective with a non-dialectical one. Drawing the dialectical/non-dialectical distinction enables the specification of a framework called the generic actual argument model that is expressly non-dialectical. The framework enables the development of knowledge-based systems that integrate a variety of inference procedures, combine information retrieval with reasoning and facilitate automated document drafting. Furthermore, the non-dialectical framework provides the foundation for simple dialectical models. Systems based on our approach have been developed in family law, refugee law, determining eligibility for government legal aid, copyright law and e-tourism.
Description:
This paper describes the MODDE (Model of Decision support system Design and Evaluation) framework in some detail. The work is in progress and is being currently applied to the EMBRACE project being developed for the Refugee Review Tribunal (RRT) of Australia. Refugee law is the general legal area we are working in, while the specific domain under investigation is that of the decision makers at the RRT. EMBRACE is a decision support system being designed to assist the RRT in maintaining consistency of decisions, and preserve discretion of decision makers as well as making it easier to cope with high volumes of work in decreasing time frames. The use of the MODDE framework is intended to facilitate systematic attention to important features of decision making in our specific legal domain and to provide a sound basis upon which to evaluate a part of the system intrinsic to user acceptance. Copyright 2001 ACM.
Description:
Global optimization-based techniques are studied in order to increase the accuracy of medical diagnosis and prognosis with data from various databases. First, we discuss feature selection, the problem of determining the most informative features for classification in the databases under consideration. Then, we apply a technique based on convex and global optimization for classification in these databases. The third application of this technique is a method that calculates centers of clusters to predict when breast cancer is likely to recur in patients for which cancer has been removed. The technique achieves high accuracy with these databases. Better classifiers will lead to improved assistance in making medical diagnostic and prognostic decisions.