Obtaining online ecological colourings by generalizing first-fit

A colouring of a graph is ecological if every pair of vertices that have the same set of colours in their neighbourhood are coloured alike. We consider the following problem: if a graph G and an ecological colouring c of G are given, can further vertices added to G, one at a time, be coloured using colours from some finite set C so that at each stage the current graph is ecologically coloured? If the answer is yes, then we say that the pair (G,c) is ecologically online extendible. By generalizing the well-known First-Fit algorithm, we are able to characterize when (G,c) is ecologically online extendible. For the case where c is a colouring of G in which each vertex is coloured distinctly, we give a simple characterization of when (G,c) is ecologically online extendible using only the colours of c, and we also show that (G,c) is always online extendible if we permit ourselves to use one extra colour. We also study (off-line) ecological H-colourings where the colouring must satisfy further restrictions imposed by some fixed pattern graph H. We characterize the computational complexity of this problem. This solves an open question posed by Crescenzi et al

Obtaining Online Ecological Colourings by Generalizing First-Fit

A colouring of a graph is ecological if every pair of vertices that have the same set of colours in their neighbourhood are coloured alike. We consider the following problem: if a graph G and an ecological colouring c of G are given, can further vertices added to G, one at a time, be coloured so that at each stage the current graph is ecologically coloured? If the answer is yes, then we say that the pair (G,c) is ecologically online extendible. By generalizing the well-known First-Fit algorithm, we are able to characterize when (G,c) is ecologically online extendible, and to show that deciding whether (G,c) is ecologically extendible can be done in polynomial time. We also describe when the extension is possible using only colours from a given finite set C. For the case where c is a colouring of G in which each vertex is coloured distinctly, we give a simple characterization of when (G,c) is ecologically online extendible using only the colours of c, and we also show that (G,c) is always online extendible using the colours of c plus one extra colour. We also study (off-line) ecological H-colourings (an H-colouring of G is a homomorphism from G to H). We study the problem of deciding whether G has an ecological H-colouring for some fixed H and give a characterization of its computational complexity in terms of the structure of H

Obtaining online ecological colourings by generalizing first-fit

A colouring of a graph is ecological if every pair of vertices that have the same set of colours in their neighbourhood are coloured alike. We consider the following problem: if a graph G and an ecological colouring c of G are given, can further vertices added to G, one at a time, be coloured using colours from some finite set C so that at each stage the current graph is ecologically coloured? If the answer is yes, then we say that the pair (G,c) is ecologically online extendible. By generalizing the well-known First-Fit algorithm, we are able to characterize when (G,c) is ecologically online extendible. For the case where c is a colouring of G in which each vertex is coloured distinctly, we give a simple characterization of when (G,c) is ecologically online extendible using only the colours of c, and we also show that (G,c) is always online extendible if we permit ourselves to use one extra colour. We also study (off-line) ecological H-colourings where the colouring must satisfy further restrictions imposed by some fixed pattern graph H. We characterize the computational complexity of this problem. This solves an open question posed by Crescenzi et al

Re-connecting landscape : roles for spatial planning

The thesis sets out the candidate’s contribution to the field of landscape planning in relation to themes such as sustainability, multifunctionality and resilience. It contextualises the candidate’s work in terms of the literature linking spatial planning, natural resource management and sustainable development, and shows how these have, most recently, led to a concern for ‘re-connection’. It then considers more specifically the influence of ten published outputs concerning interventions on behalf of the cultural landscape. Substantially, the candidate’s contribution is viewed as a way of ‘designing with nature’, within the legacy of Ian McHarg. The first part of the thesis explains how the candidate contributed broadly to a gradual acceptance of natural resource management as a legitimate concern for spatial planning, and how this was subsequently re-interpreted within a discourse of sustainable development. A set of ten published outputs is then critically reviewed in terms of: a synoptic overview; a contribution to the theory of landscape planning; an exploration of aspects of practical implementation; and a consideration of future prospects for promoting social-environmental resilience through the medium of multifunctional landscape. The thesis concludes by anticipating further development of the themes of multifunctionality, sustainability, resilience and re-connection within a ‘Neo-McHargian’ context

Impulsivity and eating behaviour: an examination of subtypes of impulsive behaviour and overeating in healthy females

A wealth of support has shown higher levels of state and trait impulsivity can be found among those individuals prone to developing problematic eating behaviors and obesity. Thus, upon commencing the investigations in this thesis, it was hypothesized that impulsivity is an individual difference implicated in overeating behaviour. Increasing information indicates that there are divisions within impulsivity subtypes. Prior to this thesis, studies in the field of eating behaviour had not distinguished between subtypes of impulsivity. This was problematic because it limited researchers ability to describe how impulsivity is specifically involved in the perpetuation of overeating behaviour. The purpose of this Thesis was to provide a methodical inquiry into the relationship between impulsivity, and its relation with overeating behaviour. This objective was achieved by separating three prioritites, first to determine if impulsivity was higher in women who self report overeating, second to define differences between impulsivity classifications and determine if there was a consistnent pattern between self reported overeating and a relation to a subtype of overeating behaviour, and third to designate a specific impulsivity subtype to individuals who self report overeating behaviour. Six Experimental Chapters explored these three priorities. Two exploratory correlational/regression analysis were used to refine our ability to operationalize measures of self reported overeating and impulsivity (Chapters 2 and 5). Chapter 3 and Chapter 5 were devoted to assess the impact that ingestion of palatable food, and the violation of cognitive boundaries of restraint, have on subsequent impulsivity. The two remaining investigations were structured to assess the impact that environmental factors have on impulsive behaviour. In Chapter 4, a Controlled versus Unrestricted eating environment were manipulated to determine whether overeaters benefit from a structured breakfast meal prior to completing a battery of impulsivity tasks. In Chapter 7, anticipation for a rewarding food item was manipulated in two conditions. In this final Chapter, the impact that anticipation for rewarding food in self reported overeaters was assessed. The battery of impulsivity tasks in this thesis include the Balloon Analogue Risk Task (BART), The Go No Go task, the Matching Familiar Figures task (MFFT), and two versions of the Delay Discounting Task (DDT). Impulsivity was classified along a spectrum of Reward Reactivity versus Inhibition subtypes, based on Evenden´s (1999) classification of impulsive behaviour. Participants tendency to overeat was based on a dual classification of tendency to restrain eating (Three Factor Eating Questionnaire- Restraint) with tendency to overeat (Three Factor Eating Questionnaire-Disinhibition subscale). The outcomes of the five experimental investigations in this thesis demonstrated a reliable pattern by which participants with high Disinhibition scores had significantly more impulsive responses on the MFFT task. These results indicated that inhibition impulsivity is the clearest individual difference to be found between healthy volunteers who self-report overeating. The role that Inhibition Impulsivity plays in the perpetuation of overeating behaviour is illustrated and discussed in each Experimental Chapter

Incremental inference on higher-order probabilistic graphical models applied to constraint satisfaction problems

Thesis (PhD)--Stellenbosch University, 2022.ENGLISH ABSTRACT: Probabilistic graphical models (PGMs) are used extensively in the probabilistic reasoning domain. They are powerful tools for solving systems of complex relationships over a variety of probability distributions, such as medical and fault diagnosis, predictive modelling, object recognition, localisation and mapping, speech recognition, and language processing [5, 6, 7, 8, 9, 10, 11]. Furthermore, constraint satisfaction problems (CSPs) can be formulated as PGMs and solved with PGM inference techniques. However, the prevalent literature on PGMs shows that suboptimal PGM structures are primarily used in practice and a suboptimal formulation for constraint satisfaction PGMs. This dissertation aimed to improve the PGM literature through accessible algorithms and tools for improved PGM structures and inference procedures, specifically focusing on constraint satisfaction. To this end, this dissertation presents three published contributions to the current literature: a comparative study to compare cluster graph topologies to the prevalent factor graphs [1], an application of cluster graphs in land cover classification in the field of cartography [2], and a comprehensive integration of various aspects required to formulate CSPs as PGMs and an algorithm to solve this formulation for problems too complex for traditional PGM tools [3]. First, we present a means of formulating and solving graph colouring problems with probabilistic graphical models. In contrast to the prevailing literature that mostly uses factor graph configurations, we approach it from a cluster graph perspective, using the general-purpose cluster graph construction algorithm, LTRIP. Our experiments indicate a significant advantage for preferring cluster graphs over factor graphs, both in terms of accuracy as well as computational efficiency. Secondly, we use these tools to solve a practical problem: land cover classification. This process is complex due to measuring errors, inefficient algorithms, and low-quality data. We proposed a PGM approach to boost geospatial classifications from different sources and consider the effects of spatial distribution and inter-class dependencies (similarly to graph colouring). Our PGM tools were shown to be robust and were able to produce a diverse, feasible, and spatially-consistent land cover classification even in areas of incomplete and conflicting evidence. Lastly, in our third publication, we investigated and improved the PGM structures used for constraint satisfaction. It is known that tree-structured PGMs always result in an exact solution [12, p355], but is usually impractical for interesting problems due to exponential blow-up. We, therefore, developed the “purge-and merge” algorithm to incrementally approximate a tree-structured PGM. This algorithm iteratively nudges a malleable graph structure towards a tree structure by selectively merging factors. The merging process is designed to avoid exponential blow-up through sparse data structures from which redundancy is purged as the algorithm progresses. This algorithm is tested on constraint satisfaction puzzles such as Sudoku, Fill-a-pix, and Kakuro and manages to outperform other PGM-based approaches reported in the literature [13, 14, 15]. Overall, the research reported in this dissertation contributed to developing a more optimised approach for higher order probabilistic graphical models. Further studies should concentrate on applying purge-and-merge on problems closer to probabilistic reasoning than constraint satisfaction and report its effectiveness in that domain.AFRIKAANSE OPSOMMING: Grafiese waarskynlikheidsmodelle (PGM) word wyd gebruik vir komplekse waarskynlikheidsprobleme. Dit is kragtige gereedskap om sisteme van komplekse verhoudings oor ‘n versameling waarskynlikheidsverspreidings op te los, soos die mediese en foutdiagnoses, voorspellingsmodelle, objekherkenning, lokalisering en kartering, spraakherkenning en taalprosessering [5, 6, 7, 8, 9, 10, 11]. Voorts kan beperkingvoldoeningsprobleme (CSP) as PGM’s geformuleer word en met PGM gevolgtrekkingtegnieke opgelos word. Die heersende literatuur oor PGM’s toon egter dat sub-optimale PGM-strukture hoofsaaklik in die praktyk gebruik word en ‘n sub-optimale PGM-formulering vir CSP’s. Die doel met die verhandeling is om die PGM-literatuur deur toeganklike algoritmes en gereedskap vir verbeterde PGM-strukture en gevolgtrekking-prosedures te verbeter deur op CSP toepassings te fokus. Na aanleiding hiervan voeg die verhandeling drie gepubliseerde bydraes by die huidige literatuur: ‘n vergelykende studie om bundelgrafieke tot die heersende faktorgrafieke te vergelyk [1], ‘n praktiese toepassing vir die gebruik van bundelgrafieke in “land-cover”- klassifikasie in die kartografieveld [2] en ‘n omvattende integrasie van verskeie aspekte om CSP’s as PGM’s te formuleer en ‘n algoritme vir die formulering van probleme te kompleks vir tradisionele PGM-gereedskap [3] Eerstens bied ons ‘n wyse van formulering en die oplos van grafiekkleurprobleme met PGM’s. In teenstelling met die huidige literatuur wat meestal faktorgrafieke gebruik, benader ons dit van ‘n bundelgrafiek-perspektief deur die gebruik van die automatiese bundelgrafiekkonstruksie-algoritme, LTRIP. Ons eksperimente toon ‘n beduidende voorkeur vir bundelgrafieke teenoor faktorgrafieke, wat akku raatheid asook berekende doeltreffendheid betref. Tweedens gebruik ons die gereedskap om ‘n praktiese probleem op te los: “landcover”-klassifikasie. Die proses is kompleks weens metingsfoute, ondoeltreffende algoritmes en lae-gehalte data. Ons stel ‘n PGM-benadering voor om die georuimtelike klassifikasies van verskillende bronne te versterk, asook die uitwerking van ruimtelike verspreiding en interklas-afhanklikhede (soortgelyk aan grafiekkleurprobleme). Ons PGM-gereedskap is robuus en kon ‘n diverse, uitvoerbare en ruimtelik-konsekwente “land-cover”-klassifikasie selfs in gebiede van onvoltooide en konflikterende inligting bewys. Ten slotte het ons in ons derde publikasie die PGM-strukture vir CSP’s ondersoek en verbeter. Dit is bekend dat boomstrukture altyd tot ‘n eksakte oplossing lei [12, p355], maar is weens eksponensiële uitbreiding gewoonlik onprakties vir interessante probleme. Ons het gevolglik die algoritme, purge-and-merge, ontwikkel om inkrementeel ‘n boomstruktuur na te doen. Die algoritme hervorm ‘n bundelgrafiek stapsgewys in ‘n boomstruktuur deur faktore selektief te “merge”. Die saamsmeltproses is ontwerp om eksponensiële uitbreiding te vermy deur van yl datastrukture gebruik te maak waarvan die waarskeinlikheidsruimte ge-“purge” word namate die algoritme vorder. Die algoritme is getoets op CSP-speletjies soos Sudoku, Fill-a-pix en Kakuro en oortref ander PGM-gegronde benaderings waaroor in die literatuur verslag gedoen word [13, 14, 15]. In die geheel gesien, het die navorsing bygedra tot die ontwikkeling van ‘n meer geoptimaliseerde benadering vir hoër-orde PGM’s. Verdere studies behoort te fokus op die toepassing van purge-and-merge op probleme nader aan waarskynlikheidsredenasie-probleme as aan CSP’s en moet sy effektiwiteit in daar die domein rapporteer.Doctora

Looking for alternatives risk, reflexivity and complementary Therapies

This thesis explores individuals' motivations for using complementary and alternative medicines (CAM). More specifically, the thesis explores the relationship between the use of CAM and wider social and cultural changes which have altered individuals’ expectations about their health and their understanding of risk and embodiment. The thesis draws on data from 24 in-depth interviews with individuals using a range of complementary and alternative health practices. Building on previous literature in this field this thesis not only explores individuals' initial motivations for using CAM, but also the reasons why they remain engaged with such practices and how their motives change over the course of time. I argue that the use of complementary and alternative medicines should be understood in terms of a career. As individuals progress along the CAM career trajectory their motives for using any given therapy not only change, but they also acquire further justifications and rationalizations for using CAM. One of the main motivations for using complementary therapies, amongst the participants of this study, was because of concerns over the safety of Western medicines, which were associated with potential risks to the health of the body. In contrast, so-called 'natural' remedies or other types of complementary therapies were seen to represent a relatively 'risk-free’ alternative. In this sense I argue that complementary therapies are adopted as part of a strategy of risk avoidance and as a means of coping with the anxieties associated with caring for health and body within late modem society. The thesis also explores individuals' use of complementary and alternative medicines for self-care purposes. I argue that such practices should be viewed as a form of resistance to medical control and an attempt to regain control over the self. The thesis not only adds to our current understanding of complementary therapies within contemporary society, but also makes a significant contribution to key sociological debates