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For systems that are in equilibrium, fluctuations can be understood through interactions with external heat reservoirs. For this reason these fluctuations are known as thermal noise, and they usually become vanishingly small in the thermodynamic limit. However, many systems comprising interacting constituents studied by physicists in recent years are both far from equilibrium, and sufficiently small so that they must be considered finite. The finite number of constituents gives rise to an inherent demographic noise in the system, a source of fluctuations that is always present in the stochastic dynamics. This thesis investigates the role of stochastic fluctuations in the macroscopically observable dynamical behaviour of non-equilibrium, finite systems. To facilitate such a study, we construct microscopic models using an individual based modelling approach, allowing the explicit form of the demographic noise to be identified. In many physical systems and theoretical models, absorbing states are a defining feature. Once a system enters one, it cannot leave. We study the dynamics of a system with two symmetric absorbing states, finding that the amplitude of the multiplicative noise can induce a transition between two universal modes of domain coarsening as the system evolves to one of the absorbing states. In biological and ecological systems, cycles are a ubiquitously observed phenomenon, but are di cult to predict analytically from stochastic models. We examine a potential mechanism for cycling behaviour due to the flow of probability currents, induced by the athermal nature of the demographic noise, in a single patch population comprising two competing species. We find that such a current by itself cannot generate macroscopic cycles, but when combined with deterministic dynamics which constrain the system to a closed circular manifold, gives rise to global quasicycles in the population densities. Finally, we examine a spatially extended system comprising many such patch populations, exploring the emergence of synchronisation between the different cycles. By a stability analysis of the global synchronised state, we probe the relationship between the synchronicity of the metapopulation and the magnitude of the coupling between patches due to species migration. In all cases, we conclude that the nature of the demographic noise can play a pivotal role in the macroscopically observed dynamical behaviour of the system.

Many health technologies exhibit some form of learning effect, and this represents a barrier to rigorous assessment by randomised controlled trials. There is reluctance to evaluate while the technique is being learnt, yet unwillingness to admit uncertainty once it has been learnt. In principle, statistical description of a learning curve and subsequent adjustment of an evaluation to take account of learning effects should solve this problem. Exactly how the analyses should be performed has been unclear. This thesis has three components: Systematic review of health technology assessment literature: a systematic description of studies that directly assessed the learning curve effect of health technologies. Systematic search of non-health technology assessment literature: a systematic identification of 'novel' statistical techniques applied to learning curve data in other fields, such as psychology and manufacturing. Testing of statistical methods: testing of these statistical techniques in sets of data describing a variety of health technologies where learning curve effects are known to exist.

M.Sc. / Determining the identity of a person has become vital in today’s world. Emphasis on security has become increasingly more common in the last few decades, not only in Information Technology, but across all industries. One of the main principles of security is that a system only be accessed by a legitimate user. According to the ISO 7498/2 document [1] (an international standard which defines an information security system architecture) there are 5 pillars of information security. These are Identification/Authentication, Confidentiality, Authorization, Integrity and Non Repudiation. The very first line of security in a system is identifying and authenticating a user. This ensures that the user is who he/she claims to be, and allows only authorized individuals to access your system. Technologies have been developed that can automatically recognize a person by his unique physical features. This technology, referred to as ‘biometrics’, allows us to quickly, securely and conveniently identify an individual. Biometrics solutions have already been deployed worldwide, and it is rapidly becoming an acceptable method of identification in the eye of the public. As useful and advanced as unimodal (single biometric sample) biometric technologies are, they have their limits. Some of them aren’t completely accurate; others aren’t as secure and can be easily bypassed. Recently it has been reported to the congress of the U.S.A [2] that about 2 percent of the population in their country do not have a clear enough fingerprint for biometric use, and therefore cannot use their fingerprints for enrollment or verification. This same report recommends using a biometric system with dual (multimodal) biometric inputs, especially for large scale systems, such as airports. In this dissertation we will investigate and compare multimodal biometric techniques, in order to determine how much of an advantage lies in using this technology, over its unimodal equivalent.

Thesis (Ph.D.)--University of the Witwatersrand, Science Faculty (Physics), 2000. / Percolation phenomena are studied in a series of composites, each with a cellular structure (small conductor particles embedded on the surfaces of large insulator particles). The DC and AC conductivities, l/f noise and magnetic properties (in some series) are measured in the systems consisting of Graphite, Graphite-Boron Nitride, Carbon Black, Niobium Carbide, Nickel and Magnetite (Fe304) as the conducting components with Talc-wax (Talc powder coated with 4% wax by volume) being the common insulating component. Compressed discs of 26mm diameter and about 3mm thickness (with various conductor volume fractions covering both the insulating and conducting region) were made from the respective powders at a pressure of 380MPa and all measurements were taken in the axial (pressure) direction. The conductivity (σm) and dielectric constant (εm) of percolation systems obey the equations: σm = σc( ɸ - ɸc)t for ɸ >ɸc; σm = σi( ɸc - ɸ-s and εm = εi( ɸc - ɸ-s' for ɸ < ɸc; outside of the crossover region given by ɸc± (δdc ~=(σi/σc)1/(t+s). Here ɸc is the critical volume fraction of the conductor (with conductivity σ = σc) and cri is the conductivity of the insulator, t and s are the conductivity exponents in the conducting and insulating regions respectively and S’ is the dielectric exponent. The values of s and t are obtained by fitting the DC conductivity results to the combined Percolation or the two exponent phenomenological equations. Both universal and non-universal values of the sand t exponents were obtained. The dielectric exponent S’, obtained from the low frequency AC measurements, is found to be frequency-dependent. The real part of the dielectric constant of the systems, has been studied as a function of the volume fraction (ɸ) of the conducting component. In systems where it is measurable beyond the DC percolation threshold, the dielectric constant has a peak at ɸ > ɸ, which differs from key predictions of the original Percolation Theory. This behaviour of the dielectric constant can be qualitatively modeled by the phenomenological two exponent equation given in Chapter two of this thesis. Even better fits to the data are obtained when the same equation is used in conjunction with ideas from Balberg's extensions to the Random Void model (Balberg 1998a and 1998b). At high frequency and closer to the percolation threshold, the AC conductivity and dielectric constant follow the power laws: σm( ɸ,שּׂ) ~ שּׂX and εm( ɸ,שּׂ) ~ שּׂ-Y respectively. In some of the systems studied, the x and y exponents do not sum up to unity as expected from the relation x + y = 1. Furthermore, the exponent q obtained from שּׂ x σm( ɸ,O)q in all but the Graphite-containing systems is greater than 1, which agrees with the inter-cluster model prediction (q = (s + t)/t). The Niobium Carbide system is the first to give an experimental q exponent greater than the value calculated from the measured DC s and t exponents. l/f or flicker noise (Sv) on the conducting side (ɸ > ɸc) of some of the systems has been measured, which gives the exponents k and w from the well-established relationships Sv/V2 = D(ɸ - ɸc)-k and Sv/V2 = KRw. V is the DC voltage across the sample with resistance R while D and K are constants. A change in the value of the exponent k and w has been observed with k taking the values kl ~ 0.92 - 5.30 close to ɸc and k2 ~ 2.55 - 3.65 further into the conducting region. Values of WI range from 0.36 -1.1 and W2 ~ 1.2 - 1.4. These values of ware generally well within the limits of the noise exponents proposed by Balberg (1998a and 1998b) for the Random Void model. The t exponents calculated from k2 and W2 (using t = k/w) are self-consistent with the t values from DC conductivity measurements. Magnetic measurements in two of the systems (Fe304 and Nickel) show unexpected behaviour of the coercive field and remnant magnetisation plotted as a function of magnetic volume fraction. Fitting the permeability results to the two exponent phenomenological equation gives t values much smaller than the corresponding DC conductivity exponents. A substantial amount of data was obtained and analysed as part of this thesis. Experimental results, mostly in the form of exponents obtained from the various scaling laws of Percolation Theory, are presented in tabular form throughout the relevant chapters. The results have been tested against various models and compare with previous studies. While there is some agreement with previous work, there are some serious discrepancies between the present work and some aspects of the standard or original Percolation Theory, for example the dielectric constant behaviour with conductor volume fraction close to but above ɸc. New results have also emerged from the present work. This includes the change in the noise exponent k with (ɸ - ɸc), the variation of the dielectric exponent s' with frequency and some DC scaling results from the Fe304 system. The present work has dealt with some intriguing aspects of Percolation Theory in real continuum composites and hopefully opened avenues for further theoretical and experimental research. / AC 2016

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