School Mathematics, Statistics and Computer Science
https://researchspace.ukzn.ac.za/handle/10413/6526
2020-08-12T04:27:23ZSelf-adaptive inertial algorithms for approximating solutions of split feasilbility, monotone inclusion, variational inequality and fixed point problems.
https://researchspace.ukzn.ac.za/handle/10413/18529
Self-adaptive inertial algorithms for approximating solutions of split feasilbility, monotone inclusion, variational inequality and fixed point problems.
In this dissertation, we introduce a self-adaptive hybrid inertial algorithm for approximating
a solution of split feasibility problem which also solves a monotone inclusion problem
and a fixed point problem in p-uniformly convex and uniformly smooth Banach spaces.
We prove a strong convergence theorem for the sequence generated by our algorithm which
does not require a prior knowledge of the norm of the bounded linear operator. Numerical
examples are given to compare the computational performance of our algorithm with other
existing algorithms.
Moreover, we present a new iterative algorithm of inertial form for solving Monotone Inclusion
Problem (MIP) and common Fixed Point Problem (FPP) of a finite family of
demimetric mappings in a real Hilbert space. Motivated by the Armijo line search technique,
we incorporate the inertial technique to accelerate the convergence of the proposed
method. Under standard and mild assumptions of monotonicity and Lipschitz continuity
of the MIP associated mappings, we establish the strong convergence of the iterative
algorithm. Some numerical examples are presented to illustrate the performance of our
method as well as comparing it with the non-inertial version and some related methods in
the literature.
Furthermore, we propose a new modified self-adaptive inertial subgradient extragradient
algorithm in which the two projections are made onto some half spaces. Moreover, under
mild conditions, we obtain a strong convergence of the sequence generated by our proposed
algorithm for approximating a common solution of variational inequality problems
and common fixed points of a finite family of demicontractive mappings in a real Hilbert
space. The main advantages of our algorithm are: strong convergence result obtained
without prior knowledge of the Lipschitz constant of the the related monotone operator,
the two projections made onto some half-spaces and the inertial technique which speeds
up rate of convergence. Finally, we present an application and a numerical example to
illustrate the usefulness and applicability of our algorithm.
Masters Degree. University of KwaZulu-Natal, Durban.
2020-01-01T00:00:00ZThe adoption of Web 2.0 tools in teaching and learning by in-service secondary school teachers: the Mauritian context.
https://researchspace.ukzn.ac.za/handle/10413/18465
The adoption of Web 2.0 tools in teaching and learning by in-service secondary school teachers: the Mauritian context.
With the current rapid increase in use of Web 2.0 tools by students, it is becoming
necessary for teachers to understand what is happening in this social networking
phenomenon, so that they can better understand the new spaces that students inhabit and
the implications for students’ learning and investigate the wealth of available Web 2.0 tools,
and work to incorporate some into their pedagogical and learning practices. Teachers are
using the Internet and social networking tools in their personal lives. However, there is little
empirical evidence on teachers’ viewpoints and usage of social media and other online
technologies to support their classroom practice. This study stemmed from the urgent need
to address this gap by exploring teachers’ perceptions, and experience of the integration
of online technologies, social media, in their personal lives and for professional practice to
find the best predictors of the possibility of teachers’ using Web 2.0 tools in their
professional practice.
Underpinning the study is a conceptual framework consisting of core ideas found in the
unified theory of acceptance and use of technology (UTAUT) and technology pedagogy
and content knowledge (TPACK) models. The conceptual framework, together with a
review of relevant literature, enabled the formulation of a theoretical model for
understanding teachers’ intention to exploit the potential of Web 2.0 tools. The model was
then further developed using a mixed-method, two-phase methodology. In the first phase,
a survey instrument was designed and distributed to in-service teachers following a
Postgraduate Certificate in Education course at the institution where the researcher works.
Using the data collected from the survey, exploratory factor analysis, correlational analysis
and multiple regression analysis were used to refine the theoretical model. Other statistical
methods were also used to gain further insights into teachers’ perceptions of use of Web
2.0 tools in their practices. In the second phase of the study, survey respondents were
purposefully selected, based on quantitative results, to participate in interviews. The
qualitative data yielded from the interviews was used to support and enrich understanding
of the quantitative findings.
The constructs teacher knowledge and technology pedagogy knowledge from the TPACK
model and the constructs effort expectancy, facilitating conditions and performance
expectancy are the best predictors of teachers’ intentions to use Web 2.0 tools in their
professional practice. There was an interesting finding on the relationship between UTAUT
and TPACK constructs. The constructs performance expectancy and effort expectancy had
a significant relationship with all the TPACK constructs – technology knowledge,
technology pedagogy knowledge, pedagogical content knowledge (PCK), technology and
content knowledge and TPACK – except for content knowledge and pedagogical
knowledge. The association between the TPACK construct PCK with the UTAUT
constructs performance expectancy and effort expectancy was an unexpected finding
because PCK is only about PCK and has no technology component.
The theoretical contribution of this study is the model, which is teachers’ intention of future
use of Web 2.0 tools in their professional practice. The predictive model, together with
other findings, enhances understanding of the nature of teachers’ intention to utilise Web
2.0 tools in their professional practice. Findings from this study have implications for school
infrastructure, professional development of teachers and an ICT learning environment to
support the adoption of Web 2.0 tools in teaching practices and are presented as guiding
principles at the end of the study.
Doctoral Degree. University of KwaZulu-Natal, Durban.
2018-01-01T00:00:00ZNetwork intrusion detection using genetic programming.
https://researchspace.ukzn.ac.za/handle/10413/18422
Network intrusion detection using genetic programming.
Network intrusion detection is a real-world problem that involves detecting intrusions on a computer network. Detecting whether a network connection is intrusive or non-intrusive is essentially a binary classification problem. However, the type of intrusive connections can be categorised into a number of network attack classes and the task of associating an intrusion to a particular network type is multiclass classification.
A number of artificial intelligence techniques have been used for network intrusion detection including Evolutionary Algorithms. This thesis investigates the application of evolutionary algorithms namely, Genetic Programming (GP), Grammatical Evolution (GE) and Multi-Expression Programming (MEP) in the network intrusion detection domain. Grammatical evolution and multi-expression programming are considered to be variants of GP. In this thesis, a comparison of the effectiveness of classifiers evolved by the three EAs within the network intrusion detection domain is performed. The comparison is performed on the publicly available KDD99 dataset. Furthermore, the effectiveness of a number of fitness functions is evaluated.
From the results obtained, standard genetic programming performs better than grammatical evolution and multi-expression programming. The findings indicate that binary classifiers evolved using standard genetic programming outperformed classifiers evolved using grammatical evolution and multi-expression programming. For evolving multiclass classifiers different fitness functions used produced classifiers with different characteristics resulting in some classifiers achieving higher detection rates for specific network intrusion attacks as compared to other intrusion attacks. The findings indicate that classifiers evolved using multi-expression programming and genetic programming achieved high detection rates as compared to classifiers evolved using grammatical evolution.
Masters Degree. University of KwaZulu-Natal, Pietermaritzburg.
2018-01-01T00:00:00ZMeta-analysis with application to estimating combined estimators of effect sizes in biomedical research.
https://researchspace.ukzn.ac.za/handle/10413/18257
Meta-analysis with application to estimating combined estimators of effect sizes in biomedical research.
Meta-analysis is a statistical analysis that combines results from different independent
studies. In meta-analysis a number of statistical methods are currently used for
combining effect sizes of different studies. The simplest of these methods is based
on a fixed-effects model, which assumes that all studies in the meta-analysis share
a common true effect size and that the effect sizes in our meta-analysis differ only
because of sampling error. Another statistical method that is used in meta-analysis,
is the random-effects model, which assumes sampling variation due to fixed-effects
model assumptions and random variation because the effect sizes themselves are
sampled from a population of effect sizes. These models are compared to determine
which model is appropriate and under what circumstances is the model appropriate.
We illustrate these models by applying each model to a collection of 3 studies examining
the effectiveness of new drug versus placebo to treat patients with duodenal
ulcers and meta-analysis of 9 studies of the use of diuretics during pregnancy to prevent
the development of pre-eclampsia. Results indicated that the choice between
the two model depends on the question of which model fits the distribution of effect
sizes better and takes account of the relevant source(s) of error. We further study
the meta-analysis of longitudinal studies where effect sizes are reported at multiple
time points. Univariate meta-analysis is a statistical approach which may be used to
study effect sizes reported at multiple time point. The problem with this approach
is that it ignores correlation between the effect sizes, which might increase the standard
error of the point estimates. We used the linear mixed-effects model, which
borrows ideas from multivariate meta-analysis. One of the advantages of the linear
mixed-effects model is that it accounts for correlation between effect sizes both
within and between studies. The independence model where separate univariate
meta-analysis is done at each of the time points was compared against models where
correlation was accounted for different alternatives; including random study effects,
correlated random time effects and/or correlated within-study errors, or unstructured
covariance structures. We implemented these methods through an example
of meta-analysis of 16 randomized clinical trials of radiotherapy and chemotherapy
versus radiotherapy alone for the post-operative treatment of patients with malignant gliomas, where in each trial, survival is evaluated at 6, 12, 18 and 24 months post randomization. The results revealed that models that accounted for correlations had better fit.
Keywords: meta-analysis, fixed-effects model, random-effects model, heterogeneity,
publication bias, linear mixed-effects model.
Masters Degree. University of KwaZulu-Natal, Pietermaritzburg.
2018-01-01T00:00:00Z