The use of particle counters in potable water treatment is achieving higher levels of acceptance on an ongoing basis. This is due to its superior sensitivity in terms of water clarity determination in comparison to turbidity meters. However, the ability of the particle counter to distinguish between various particle sizes, arguably its biggest advantage over turbidity measurement, is not being utilised fully, due to the large volumes of data generated and the amount of post-measurement data processing required to unlock some of the information. In many cases it is being used purely as a substitute or parallel measurement for turbidity. Furthermore, in the South African context, where data is being generated, the particle count data holds little value as it cannot be compared to generally available data sets to reveal the entire message contained in the count. No record of counts is available to rate new measurements against. / Prof. J. Haarhoff

Perfect slice sampling is a method to turn Markov Chain Monte Carlo (MCMC) samplers into exact generators for independent random variates. We show that the simplest version of the perfect slice sampler suggested in the literature does not always sample from the target distribution. (author's abstract) / Series: Research Report Series / Department of Statistics and Mathematics

This thesis focuses on the non-arbitrage (fair) pricing of interest rate derivatives, in particular caplets and swaptions using the LIBOR market model (LMM) developed by Brace, Gatarek, and Musiela (1997) and Swap market model (SMM) developed Jamshidan (1997), respectively. Today, in most financial markets, interest rate derivatives are priced using the renowned Black-Scholes formula developed by Black and Scholes (1973). We present new pricing models for caplets and swaptions, which can be implemented in the financial market other than the Black-Scholes model. We theoretically construct these "new market models" and then test their practical aspects. We show that the dynamics of the LMM imply a pricing formula for caplets that has the same structure as the Black-Scholes pricing formula for a caplet that is used by market practitioners. For the SMM we also theoretically construct an arbitrage-free interest rate model that implies a pricing formula for swaptions that has the same structure as the Black-Scholes pricing formula for swaptions. We empirically compare the pricing performance of the LMM against the Black-Scholes for pricing caplets using Monte Carlo methods.

Submitted in fulfilment of the Degree of Master of Engineering in Chemical Engineering, Durban University of Technology, Durban, South Africa, 2017. / A pertinent issue facing the materials industry is that of the lifespan of materials when exposed to certain solvents/ environments. Limitations to the applications of materials require further research into understanding their failure mechanisms and how such problems can be addressed in terms of re-engineering such materials to be more durable. PVC and HDPE are two common polymers used extensively in industrial applications. Gibbs ensemble Monte Carlo simulations were used to simulate systems of PVC and HDPE with methanol, respectively. The temperatures used in this work were 25, 30 and 40 oC and all systems were at atmospheric pressure. Laboratory tests were used to complement simulations for analysis purposes. Results showed an increase in temperature resulted in a decrease in the overall clustering in both polymers although PVC displayed a greater decrease than HDPE. Linear clustering dominated over other forms of clustering with increases in temperature, with dimers being the most prevalent topology type. The results of this study suggest that the presence of chlorine atoms in PVC may not directly affect clustering of absorbed methanol, and their effect may instead be indirect by means of altering the accessible free volume within the polymer. Swelling was also investigated in the simulated systems and it was found that PVC displayed a greater degree of swelling than HDPE despite its lower rate of clustering. The effect of cluster radius on the cluster analysis was also considered. / M

D.Phil. / We propose solutions to two statistical problems using the frequency domain approach to time series analysis. In both problems the data at hand can be described by the well known signal plus noise model. The first problem addressed is the estimation of the underlying variance of a process for the use in a Shewhart or CUSUM control chart when the mean of the process may be changing. We propose an estimator for the underlying variance based on the periodogram of the observed data. Such estimators have properties which make them superior to some estimators currently used in Statistical Quality Control. We also present a CUSUM chart for monitoring the variance which is based upon the periodogram-based estimator for the variance. The second problem, stimulated by a specific problem in Variable Star Astronomy, is to test whether or not the mean of a bivariate time series is constant over the span of observations. We consider two periodogram-based tests for constancy of the mean, derive their asymptotic distributions under the null hypothesis and under local alternatives and show how consistent estimators for the unknown parameters in the proposed model can be found

This document demonstrates the use of the C++ programming language as a simulation tool in the efficient pricing of exotic European options. Extensions to the basic problem of simulation pricing are undertaken including variance reduction by conditional expectation, control and antithetic variates. Ultimately we were able to produce a modularized, easily extend-able program which effectively makes use of Monte Carlo simulation techniques to price lookback, Asian and barrier exotic options. Theories of variance reduction were validated except in cases where we used control variates in combination with the other variance reduction techniques in which case we observed increased variance. Again, the main aim of this half thesis was to produce a C++ program which would produce stable pricings of exotic options.

M.Phil. (Energy Studies) / This dissertation details the radiation shielding analysis and optimization performed to design a shield for the mineral-PET (Positron Emission Tomography) facility. PET is a nuclear imaging technique currently used in diagnostic medicine. The technique is based on the detection of 511 keV coincident and co-linear photons produced from the annihilation of a positron (produced by a positron emitter) and a nearby electron. The technique is now being considered for the detection of diamonds in Kimberlite rock, in which mineral-PET technology aims to improve diamond mining through the early detection of diamond bearing rocks. High energy photons are produced via Bremsstrahlung (which occurs when electrons from an accelerator, impinge on a high density target)...

M.Ing. / The Graphics Processor Unit (GPU) has been in the gaming industry for several years now. Of late though programmers and scientists have started to use the parallel processing or stream processing capabilities of the GPU in general numerical applications. The Monte Carlo method is a processing intensive methods, as it evaluates systems with stochastic components. The stochastic components require several iterations of the systems to develop an idea of how the systems reacts to the stochastic inputs. The stream processing capabilities of GPUs are used for the analysis of such systems. Evaluating low-cost Inertial Measurement Units (IMU) for utilisation in Inertial Navigation Systems (INS) is a processing intensive process. The non-deterministic or stochastic error components of the IMUs output signal requires multiple simulation runs to properly evaluate the IMUs performance when applied as input to an INS. The GPU makes use of stream processing, which allows simultaneous execution of the same algorithm on multiple data sets. Accordingly Monte Carlo techniques are applied to create trajectories for multiple possible outputs of the INS based on stochastically varying inputs from the IMU. The processing power of the GPU allows simultaneous Monte Carlo analysis of several IMUs. Each IMU requires a sensor error model, which entails calibration of each IMU to obtain numerical values for the main error sources of lowcost IMUs namely scale factor, non-orthogonality, bias, random walk and white noise. Three low-cost MEMS IMUs was calibrated to obtain numerical values for their sensor error models. Simultaneous Monte Carlo analysis of each of the IMUs is then done on the GPU with a resulting circular error probability plot. The circular error probability indicates the accuracy and precision of each IMU relative to a reference trajectory and the other IMUs trajectories. Results obtained indicate the GPU to be an alternative processing platform, for large amounts of data, to that of the CPU. Monte Carlo simulations on the GPU was performed 200 % faster than Monte Carlo simulations on the CPU. Results obtained from the Monte Carlo simulations, indicated the Random Walk error to be the main source of error in low-cost IMUs. The CEP results was used to determine the e ect of the various error sources on the INS output.

Please read the abstract in the section 00front of this document / Dissertation (MEng (Mechanical Engineering))--University of Pretoria, 2007. / Mechanical and Aeronautical Engineering / MEng / unrestricted

Orientadores: Vera Lúcia da Silveira Nantes Button, Marcio Aparecido Müller / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação / Made available in DSpace on 2018-08-18T16:48:44Z (GMT). No. of bitstreams: 1 Malthez_AnnaLuizaMetidieriCruz_M.pdf: 1404598 bytes, checksum: 6c50e1c9d0a46804d7c8ac36de121a04 (MD5) Previous issue date: 2011 / Resumo: Devido ao crescimento do uso de radiação ionizante em aplicações médicas, nas últimas décadas, os códigos para simulações de radiação interagindo com a matéria, baseados no Método de Monte Carlo, têm sido constantemente adaptados para aplicações em física médica. O método de Monte Carlo é um método estatístico de simulação numérica de problemas utilizando essencialmente uma sequência de números aleatórios. Atualmente, o método pode ser aplicado em simulações físicas, matemáticas e biológicas; o comportamento dos sistemas é descrito por amostragens aleatórias de funções de densidade de probabilidade e os acúmulos dos valores observados das amostragens produzem o resultado final da simulação. No caso de transporte de radiação, o valor esperado de grandezas de interesse, como, por exemplo, energia depositada ou dose em determinado meio ou volume de interesse simulado, pode ser estimado. Na maior parte das aplicações do método, o processo físico é simulado diretamente, necessitando somente da descrição matemática do processo físico, ou seja, da função densidade de probabilidade. Dentre os códigos mais utilizados para transporte de radiação, destacam-se: o EGS (Electron Gamma Shower); MCNP (Monte Carlo Neutron Photon Transport Code); ITS (Integrated Tiger Serie); PENELOPE (Penetration and Energy Loss of Positrons and Electrons) e o GEANT4 (Geometry and Tracking) disponibilizado pelo CERN (European Organization for Nuclear Research). O GEANT4 é um conjunto de ferramentas computacionais (toolkit) que utiliza programação orientada a objeto em C++, criado através de um projeto internacional e inicialmente utilizado para aplicações em física de altas energias; porém, atualmente é utilizado em áreas que compreendem desde astrofísica até física médica, com energias de 250 eV até 100 TeV. No toolkit do GEANT4 têm sido incorporados diversos processos físicos e partículas que permitem seu uso em física médica. Este código apresenta diversas vantagens em relação aos outros códigos, como, por exemplo, lidar com todos os tipos de partículas, geometrias complexas e estar em C++. Com o uso crescente dos códigos de Monte Carlo e das diversas aplicações do GEANT4 em física médica, publicadas recentemente, este código se apresentou como uma ferramenta promissora para aplicações na área de radioterapia, na qual vêm sendo utilizados diversos tipos de simulações. Considerando as vantagens deste código e suas aplicações em física médica, nesta dissertação de mestrado, foram desenvolvidas diversas simulações para verificar a aplicabilidade e validar o GEANT4 para aplicações em radioterapia. Por exemplo, foi estudada a dependência da energia depositada com parâmetros não-físicos do algoritmo de transporte de elétrons; o transporte de elétrons para energias de 1 a 20 MeV, que no G4 e em diversos outros códigos, apresentou problemas de grande relevância; e a influência do número de eventos nos resultados simulados. Também, foi avaliada a aplicação do G4 no transporte de radiação, através de simulações de elétrons e fótons emitidos por equipamentos e fontes usados em radioterapia, como acelerador linear e fontes de Co-60 e Ir-192, e através de cálculos de algumas grandezas, como dose, alcance e Stopping Power de elétrons monoenergéticos transportados em água. Os resultados em todas as simulações desenvolvidas apresentaram uma exatidão dentro de 2%, indicando que o GEANT4 pode ser utilizado, em simulações de fótons e elétrons, para aplicações em radioterapia / Abstract: Due to the increasing use of ionizing radiation in medical applications, in recent decades, the simulation codes for radiation interacting with matter, based on Monte Carlo Method, have been constantly adapted to applications in medical physics. TheMonte Carlo method is a statisticalmethod of numerical simulation of problems using essentially a sequence of random numbers. Currently, the method can be applied in physical, mathematical and biological simulations, the behavior of systems is described by random sampling of probability density functions and accumulation of the observed values of the samples producing the final result of the simulation. In the case of radiation transport, the expected value of quantities of interest such as, for example, dose or energy deposited in a medium or interest volume simulated, can be estimated. In most applications of the method, the physical process is simulated directly, requiring only the mathematical description of the physical process, ie the probability density function. Among the most commonly used codes for radiation transport are: the EGS (Electron Gamma Shower), MCNP (Monte Carlo Neutron Photon Transport Code), ITS (Integrated Tiger Series), PENELOPE (Penetration and Energy Loss of Electrons and Positrons) and Geant4 (Geometry and Tracking) released by CERN (European Organization for Nuclear Research). The GEANT4 is a set of computational tools (toolkit) that uses object-oriented programming in C++, created through an international project and initially used for applications in high energy physics, but is now used in areas that include from astrophysics to medical physics, with energies of 250 eV to 100 TeV. In the GEANT4 toolkit have been incorporated several physical processes and particles that allow its use in medical physics. This code has several advantages over other codes, for example, dealing with all types of particles and complex geometries and to be in C++. With the increasing use of Monte Carlo codes and the various applications of GEANT4 in medical physics, published recently, this code is presented as a promising tool for applications in radiotherapy, which have been used in various types of simulations. Considering the advantages of this code and its applications in medical physics in this dissertation, it was developed various simulations to verify the GEANT4 applicability and validation for radiotherapy applications. For example, it was study various aspects of implementation of the code, for example, the dependence of the energy deposited with non-physical parameters of the electrons transport algorithm, the transport of electrons to energies 1 to 20 MeV, in which GEANT4 and various other codes, presented problems of great relevance, and the influence of number of events in the simulated results. Also, it was evaluated the application of G4 in the transport of radiation through simulations of photons and electrons emitted by equipment and sources used in radiotherapy, as linear accelerator and sources of Co-60 and Ir-192, and by calculation of some quantities such as dose range and Stopping Power of monoenergetic electrons transported in water. The results in all simulations developed present a accuracy within 2%, indicating that Geant4 can be used, in simulations of photons and electrons, for applications in radiotherapy / Mestrado / Engenharia Biomedica / Mestre em Engenharia Elétrica