Random graph coloring:Statistical physics approach

The problem of vertex coloring in random graphs is studied using methods of statistical physics and probability. Our analytical results are compared to those obtained by exact enumeration and Monte Carlo simulations. We critically discuss the merits and shortcomings of the various methods, and interpret the results obtained. We present an exact analytical expression for the two-coloring problem as well as general replica symmetric approximated solutions for the thermodynamics of the graph coloring problem with p colors and K-body edges. ©2002 The American Physical Society.

The application of artificial neural networks to the interpretation and classification of freshwater benthic invertebrate communities

This thesis presents a thorough and principled investigation into the application of artificial neural networks to the biological monitoring of freshwater. It contains original ideas on the classification and interpretation of benthic macroinvertebrates, and aims to demonstrate their superiority over the biotic systems currently used in the UK to report river water quality. The conceptual basis of a new biological classification system is described, and a full review and analysis of a number of river data sets is presented. The biological classification is compared to the common biotic systems using data from the Upper Trent catchment. This data contained 292 expertly classified invertebrate samples identified to mixed taxonomic levels. The neural network experimental work concentrates on the classification of the invertebrate samples into biological class, where only a subset of the sample is used to form the classification. Other experimentation is conducted into the identification of novel input samples, the classification of samples from different biotopes and the use of prior information in the neural network models. The biological classification is shown to provide an intuitive interpretation of a graphical representation, generated without reference to the class labels, of the Upper Trent data. The selection of key indicator taxa is considered using three different approaches; one novel, one from information theory and one from classical statistical methods. Good indicators of quality class based on these analyses are found to be in good agreement with those chosen by a domain expert. The change in information associated with different levels of identification and enumeration of taxa is quantified. The feasibility of using neural network classifiers and predictors to develop numeric criteria for the biological assessment of sediment contamination in the Great Lakes is also investigated.

A dynamic model for the activated sludge treatment of coke oven effluents

This is an Inter-Disciplinary Higher Degree (IHD) thesis about Water Pollution Control in the Iron and Steel Industry. After examining the compositions, and various treatment methods, for the major effluent streams from a typical Integrated Iron and Steel works, it was decided to concentrate investigative work on the activated-sludge treatment of coke-oven effluents. A mathematical model of this process was developed in an attempt to provide a tool for plant management that would enable improved performance, and enhanced control of Works Units. The model differs from conventional models in that allowance is made for the presence of two genera of microorganisms, each of which utilises a particular type of substrate as its energy source. Allowance is also made for the inhibitive effect of phenol on thiocyanate biodegradation, and for the self-toxicity of the bacteria when present in a high substrate concentration environment. The enumeration of the kinetic characteristics of the two groups of micro-organisms was shown to be of major importance. Laboratory experiments were instigated in an attempt to determine accurate values of these coefficients. The use of the Suspended Solids concentration was found to be too insensitive a measure of viable active mass. Other measures were investigated, and Adenosine Triphosphate concentration was chosen as the most effective measure of bacterial populations. Using this measure, a model was developed for phenol biodegradation from experimental results which implicated the possibility of storage of substate prior to metabolism. A model for thiocyanate biodegradation was also developed, although the experimental results indicate that much work is still required in this area.