South African schools face many challenges as they are inundated with dysfunctional behaviour. The research on South African schools indicates that behavioural challenges such as disobedience, swearing, truancy violence and bullying are evident in many school contexts. From a reductionist, individualist approach, the focus when addressing these challenges is often on causal factors and dysfunctional individuals rather than on ways in which people relate and interact in schools. It is however evident from a social ecological perspective, that in order to facilitate social change, we need to understand people’s experiences of social interaction in schools as an important context for the enhancement of wellbeing. The first phase of the PhD project is a base‐line exploration of the learners’, educators’ and parents’ experiences of relating and interacting in school communities. A qualitative phenomenological investigation was applied in combination with a cross‐sectional descriptive survey design. 1170 learners, ages ranging from 11 to 18 years, 150 parents and 85 educators, from 12 South African schools, participated in the research. The participants completed written assignments that were analysed through the application of global analysis followed by thematic analysis. The findings indicated that enabling ways of relating and interacting were patterned by active engagement and acknowledgement of people. Disenabling social interaction was patterned by disengagement and disregard for people. The findings indicated that both enabling and disenabling ways of relating and interacting, play a crucial role in the enhancement of mental wellbeing in schools, and suggest that schools need to focus more seriously on the ways in which people in schools relate and interact on the everyday micro‐levels of social interaction, as suggested by complexity theory. The second phase of the study comprised a more in‐depth investigation into nurturing and restraining relationships between parents, learners and educators in a school community. A single instrumental case study design was applied to gain an indepth understanding of the complex dynamic interactions between the members of the school community. All the learners and educators in the school were involved during the work sessions. Nominal group technique was applied to obtain information about their perceptions of relationships in the school community. The work sessions were followed by focus group interviews with 18 educators, 40 learners, the management team, six members of the administrative and terrain staff and two parents. A thematic analysis of the data indicated that nurturing relationships could be understood with reference to connectedness: respect, care and transparent communication; whilst restrained relationships could be understood with reference to limited connectedness between people: abuse of power, shifting of responsibility and disrespect for one another. The findings indicated the need for a sensitive, empathic and non‐patronising approach to people in school communities that acknowledge that restrained relationships are inevitably part of the human interaction and understand schools in terms of inter‐subjective recursive processes that pattern the relationships between the members of the school community. In the third phase, the findings of the first two stages of the study were integrated with theoretical perspectives and critical reflections on the findings to conceptualise a relationship‐focused approach to the co‐construction of an enabling school community. The approach encompasses the facilitation of continuous conversations using identified facets of interrelatedness as focal points for the understanding of being together in school communities on a meta‐level. It is recommended that the implementation of a relationship‐focused approach conceptualised in this study, should be considered as an alternative approach for dealing with the challenges associated with human behaviour that currently prevail in schools. Further research on the implementation of the approach in schools is recommended. / Thesis (Ph.D. (Psychology))--North-West University, Potchefstroom Campus, 2011

With an abundance of social network data being released, the need to protect sensitive information within these networks has become an important concern of data publishers. In this thesis we focus on the popular notion of k-anonymization as applied to social network graphs. Given such a network N, the problem we study is to transform N to N', such that some property P of each node in N' is attained by at least k-1 other nodes in N'. We study edge-labeled, vertex-labeled and unlabeled graphs, since instances of each occur in real-world social networks. Our main contributions are as follows 1. When looking at edge additions, we show that k-label sequence anonymity of arbitrary edge-labeled graphs is NP-complete, and use this fact to prove hardness results for many other recently introduced notions of anonymity. We also present interesting hardness results and algorithms for labeled and unlabeled bipartite graphs. 2. When looking at node additions, we show that on vertex-labeled graphs, the problem is NP-complete. For unlabeled graphs, we give an efficient (near-linear) algorithm and show that it gives solutions that are optimal modulo k, a guarantee that is novel in the literature. We examine anonymization both from its theoretical foundations and empirically, showing that our proposed algorithms for anonymization maintain structural properties shown to be necessary for graph analysis. / Graduate

Given graphs G,H, is it possible to find a matching which, when deleted from G, destroys all copies of H? The answer is obvious for some inputs—notably, when G is a large complete graph the answer is “no”—but in general this can be a very difficult question. In this thesis, we study this decision problem when H is a fixed tree or cycle; our aim is to identify those H for which it can be solved efficiently. The H-transverse matching problem, TM(H) for short, asks whether an input graph admits a matching M such that no subgraph of G − M is isomorphic to H. The main goal of this thesis is the following dichotomy. When H is a triangle or one of a few small-diameter trees, there is a polynomial-time algorithm to find an H-transverse matching if one exists. However, TM(H) is NP-complete when H is any longer cycle or a tree of diameter ≥ 4. In addition, we study the restriction of these problems to structured graph classes. / Graduate

The final Chapter concerns a problem of partitioning graphs subject to certain restrictions. We prove that several subproblems are NP-complete.

High-Frequency Surface Wave Radar (HFSWR) is a radar technology that offers numerous advantages for surveillance of coastal waters beyond the exclusive economic zone. However, target detection and tracking is primarily limited by ionospheric interference. Ionospheric clutter is characterized by a high degree of nonhomogeneity and nonstationarity, which makes its suppression difficult using conventional processing techniques. Space-time adaptive processing techniques have enjoyed great success in airborne radar, but have not yet been investigated in the context of HFSWR. This thesis is primarily concerned with the evaluation of existing STAP techniques in the HFSWR scenario and the development of a new multistage adaptive processing approach, dubbed the Fast Fully Adaptive (FFA) scheme, which was developed with the particular constraints of the HFSWR interference environment in mind. Three different spatio-temporal partitioning schemes are introduced and a thorough investigation of the performance of the FFA is conducted.

High-Frequency Surface Wave Radar (HFSWR) is a radar technology that offers numerous advantages for surveillance of coastal waters beyond the exclusive economic zone. However, target detection and tracking is primarily limited by ionospheric interference. Ionospheric clutter is characterized by a high degree of nonhomogeneity and nonstationarity, which makes its suppression difficult using conventional processing techniques. Space-time adaptive processing techniques have enjoyed great success in airborne radar, but have not yet been investigated in the context of HFSWR. This thesis is primarily concerned with the evaluation of existing STAP techniques in the HFSWR scenario and the development of a new multistage adaptive processing approach, dubbed the Fast Fully Adaptive (FFA) scheme, which was developed with the particular constraints of the HFSWR interference environment in mind. Three different spatio-temporal partitioning schemes are introduced and a thorough investigation of the performance of the FFA is conducted.

We study the geometry of immanants, which are polynomials on n^2 variables that are defined by irreducible representations of the symmetric group Sn. We compute stabilizers of immanants in most cases by computing Lie algebras of stabilizers of immanants. We also study tensor network states, which are special tensors defined by contractions. We answer a question about tensor network states asked by Grasedyck. Both immanants and tensor network states are related to the Geometric Complexity Theory program, in which one attempts to use representation theory and algebraic geometry to solve an algebraic analogue of the P versus N P problem. We introduce the Geometric Complexity Theory (GCT) program in Section one and we introduce the background for the study of immanants and tensor network states. We also explain the relation between the study of immanants and tensor network states and the GCT program. Mathematical preliminaries for this dissertation are in Section two, including multilinear algebra, representation theory, and complex algebraic geometry. In Section three, we first give a description of immanants as trivial (SL(E) x SL(F )) ><| delta(Sn)-modules contained in the space S^n(E X F ) of polynomials of degree n on the vector space E X F , where E and F are n dimensional complex vectorspaces equipped with fixed bases and the action of Sn on E (resp. F ) is induced by permuting elements in the basis of E (resp. F ). Then we prove that the stabilizer of an immanant for any non-symmetric partition is T (GL(E) x GL(F )) ><| delta(Sn) ><| Z2, where T (GL(E) x GL(F )) is the group of pairs of n x n diagonal matrices with the product of determinants equal to 1, delta(Sn) is the diagonal subgroup of Sn x Sn. We also prove that the identity component of the stabilizer of any immanant is T (GL(E) x GL(F )). In Section four, we prove that the set of tensor network states associated to a triangle is not Zariski closed and we give two reductions of tensor network states from complicated cases to simple cases. In Section five, we calculate the dimension of the tangent space and weight zero subspace of the second osculating space of GL_(n^2) .[perm_n] at the point [perm_n] and determine the Sn x Sn-module structure of this space. We also determine some lines on the hyper-surface determined by the permanent polynomial. In Section six, we give a summary of this dissertation.

Biodiversity is a concept that plays a key role in both scientific theories such as the species-area law and conservation politics. Currently, however, little agreement exists on how biodiversity should be defined, let alone measured. This has led to suggestions that biodiversity is not a metaphysically robust concept, with major implications for its usefulness in formulating scientific theories and making conservation decisions. A general discussion of biodiversity is presented, highlighting its application both in scientific and conservation contexts, its relationship with environmental ethics, and existing approaches to its measurement. To overcome the limitations of existing biodiversity concepts, a new concept of biocomplexity is proposed. This concept equates the biodiversity of any biological system with its effective complexity. Biocomplexity is shown to be the only feasible measure of biodiversity that captures the essential features desired of a general biodiversity concept. In particular, it is a well-defined, measurable and strongly intrinsic property of any biological system. Finally, the practical application of biocomplexity is discussed.

Thesis (Ph. D.)--University of Texas at El Paso, 2007. / Title from title screen. Vita. CD-ROM. Includes bibliographical references. Also available online.

Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 78-80).