Notes on Elementary Spectral Graph Theory Applications to Graph Clustering Using Normalized Cuts

These are notes on the method of normalized graph cuts and its applications to graph clustering. I provide a fairly thorough treatment of this deeply original method due to Shi and Malik, including complete proofs. I include the necessary background on graphs and graph Laplacians. I then explain in detail how the eigenvectors of the graph Laplacian can be used to draw a graph. This is an attractive application of graph Laplacians. The main thrust of this paper is the method of normalized cuts. I give a detailed account for K = 2 clusters, and also for K \u3e 2 clusters, based on the work of Yu and Shi. Three points that do not appear to have been clearly articulated before are elaborated: 1. The solutions of the main optimization problem should be viewed as tuples in the K-fold cartesian product of projective space RP^{N-1}. 2. When K \u3e 2 , the solutions of the relaxed problem should be viewed as elements of the Grassmannian G(K,N)

Towards the development of an organisation development model for the mining industry

D. Litt. et Phil.(Leadership in Performance and Change)The aim of this study was to develop an organisation development model to support organisational change and transformation in a dynamic, continuously changing business environment, specifically for the mining industry in South Africa. Literature revealed that there is a tendency to employ universal and generic models to challenges of organisational change, whereas successful 00 needs a situation specific or contextualised approach. The field of OD reflects a paucity of empirical research, necessitating a greater research competence and more in-depth, robust empirical 00 studies to answer to 'contemporary contextual and environmental challenges. A further call is voiced towards OD to resolve organisational change challenges from a systemic perspective, which has been a central tenet of the field. A number of research participants from a South African company that has been implementing organisational change and transformation interventions in the mining sector, were selected by means of purposive sampling. A modernist qualitative approach with the case study as research strategy was utilised during the development of the model. Various data collection techniques were utilised with grounded theory as a data analysis technique to explore and systematically develop the concepts and categories of the model. Atlas.ti, together with manual coding procedures were utilised to systematically organise and analyse the rich descriptive data. Credibility, transferability, dependability and confirmability were ensured by following the guidelines presented in the literature. In the literature study, the sample's narrative was critically contrasted against the established scientific knowledge base of OD, considering specifically taxonomies, models and theories related to the emergent OD model. The resulting model deviates from the established perspectives on OD, in that it reflects a hybrid of several fields of study endeavour. The latter is consistent with a business practice perspective that integrates and deal with a single application domain, compared to a science-informed perspective which conducts research largely within defined (and confined) disciplinary boundaries. The OD model has implications for the mining industry in South Africa, and the development of grounded theory should facilitate the application thereof in future research

Risk management for build, operate and transfer projects within Kuwait

Infrastructure projects, based on the Build-Operate-Transfer, (BOT), method, have been of interest to governments of developed and developing countries for some time, resulting in their worldwide use. Using the BOT method enables governments to reallocate risks and rewards to the private sector for larger infrastructure projects throughout the projects' operating life. In order to implement a BOT infrastructure project successfully, one of the essential requirements is to carry out a thorough analysis of risks relating to the project including the social, economic, environmental, political, legal, and the financial aspects. Due to the fact that the type of risk study required for large-scale projects is so sophisticated, and therefore expensive and time consuming, the government, due to lack of expertise and time, often obtains a project viability study from the private sector. This can cause problems in that the private sector may incur financial losses or even bankruptcy, unless the host government guarantees compensation to the losers of the bid. Because all parties have different targets which they wish to achieve from the project, a may conflict arise and cause lengthy negotiations, sometimes lasting for years which often result in the death of the project. The greatest opportunity for a successful outcome for a BOT project is obtained when the extensive efforts and costs involved in the risk study process are shared by all parties. The responsibility of the decision maker is to identify, understand and analyze the many risk factors both, qualitative, (linguistic in nature) and quantitative, that will affect funding, procurement, developing, construction and operation, before proceeding with the build stage of the project. Firstly, it is necessary to evaluate the quantitative Risk Factors subjectively, and list them in order of importance. Secondly, conduct an evaluation of the qualitative factors and since the consideration of qualitative factors is subjective, the decision maker will often limit the number of factors being evaluated possibly resulting in inconsistent results. This study proposes a decision framework, which would be useful in determining the influence of the qualitative Risk Factors on the project management of BOT infrastructure projects. A methodology is provided to enable the identification of interrelationships between the Risk Factors and their influence on the project. Using Analytical Hierarchy Process (AHP) techniques, which model the relationships between the Risk Factors, a validation of this approach will be sought using a decomposed evaluation method and also information obtained from three existing case studies, (the Channel Tunnel, Sulaibiya Wastewater Treatment and Reclamation Plant and Marsa Allam Airport). The results of the decomposed approach were compared to experts' holistic evaluations for the same case studies mentioned above. The findings indicate that the decomposed approach showed a strong correlation to the holistic approach. An evaluation of the risks for the Sulaibiya Wastewater Treatment and Reclamation Plant study is provided and suggestions made to highlight risks attached to such a project before it is actually undertaken. Using the decomposed approach enables the decision maker to see the contribution of each risk compared to all of the risks in the total project and will help to determine and subsequently minimize or preventing any risk factors and so considerably improving the risk management of the project