In metrology, measurement uncertainty is understood as a range in which the true value of the measurement is likely to fall in. The recent years have seen a rapid development in evaluation of measurement uncertainty. ISO Guide to the Expression of Uncertainty in Measurement (GUM 1995) is the primary guiding document for measurement uncertainty. More recently, the Supplement 1 to the "Guide to the expression of uncertainty in measurement" – Propagation of distributions using a Monte Carlo method (GUM SP1) was published in November 2008. A number of software tools for measurement uncertainty have been developed and made available based on these two documents. The current software tools are mainly desktop applications utilising numeric computation with limited mathematical model handling capacity. A novel and generic web-based application, web-based Knowledge-Based Decision Support System (KB-DSS), has been proposed and developed in this research for measurement uncertainty evaluation. A Model-View-Controller architecture pattern is used for the proposed system. Under this general architecture, a web-based KB-DSS is developed based on an integration of the Expert System and Decision Support System approach. In the proposed uncertainty evaluation system, three knowledge bases as sub-systems are developed to implement the evaluation for measurement uncertainty. The first sub-system, the Measurement Modelling Knowledge Base (MMKB), assists the user in establishing the appropriate mathematical model for the measurand, a critical process for uncertainty evaluation. The second sub-system, GUM Framework Knowledge Base, carries out the uncertainty evaluation process based on the GUM Uncertainty Framework using symbolic computation, whilst the third sub-system, GUM SP1 MCM Framework Knowledge Base, conducts the uncertainty calculation according to the GUM SP1 Framework numerically based on Monte Carlo Method. The design and implementation of the proposed system and sub-systems are discussed in the thesis, supported by elaboration of the implementation steps and examples. Discussions and justifications on the technologies and approaches used for the sub-systems and their components are also presented. These include Drools, Oracle database, Java, JSP, Java Transfer Object, AJAX and Matlab. The proposed web-based KB-DSS has been evaluated through case studies and the performance of the system has been validated by the example results. As an established methodology and practical tool, the research will make valuable contributions to the field of measurement uncertainty evaluation.

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This research examines how the Targeted Separation Incentive Program, currently underway by the Navy, is being administered to bring about the voluntary separations of junior officers to meet the requirements of the Navyâ s most recent force reduction. This study evaluates the effects of past separation incentive programs as well as the current compensation package that the service-member may receive which is outlined in the Fiscal Year 2006 National Defense Authorization Act. In addition, an analysis was conducted of the costs associated with retaining the service-member versus the personal costs of that individual of leaving. The objective of this thesis is to evaluate the Department of the Navyâ s (DoN) Targeted Separation Incentive Program in order to see if this program can adequately meet the goals of the current force reduction and whether or not savings can be realized through alternative separation programs.

El fenómeno de ordenación químico en las aleaciones binarias influye directa y fuertemente sobre sus propiedades físicas tales como resistividad eléctrica, capacidad calorífica, constantes elásticas, coeficiente de Hall, etc. Las aleaciones binarias con tendencia a ordenamiento químico a bajas temperaturas, como el sistema Cu-Au y Fe-Al, son interesantes debido a sus importantes propiedades eléctricas y de resistencia a altas temperaturas. El objetivo principal del trabajo es investigar el fenómeno de transición de fases orden¬-desorden en las aleaciones binarias mediante la simulación con el método Monte Carlo y el algoritmo de Metrópolis. Usamos el modelo ABV de la aleación binaria para simular los sistemas AB3 y AB (Cu3AuyFeAl) considerando internaciones atómicas de pares hasta los terceros vecinos más próximos. La dinámica fue introducida por medio de una vacan¬te que intercambia de posición con los átomos vecinos más próximos con cierta probabilidad; además aplicamos condiciones periódicas de frontera para evitar efectos de borde. Una vez logrado el equilibrio térmico a la temperatura requerida se almacenan los datos para calc¬ular la energía del sistema, el calor específico y los parámetros de orden de largo (LRO) y Corto alcance (SRO) de Warren ¬Cowley. En base a los datos obtenidos se han determinado la temperatura crítica de transición orden -desorden para los sistemas estudiados. También hallamos las probabilidades de formación de clústeres (agregados) en la aleación en un amplio rango de temperaturas así como en un rango de concentración de una de las componentes.

The counterparty credit risk is particularly hard to simulate and this thesis is only the second work so far, which considers effective simulation of couterparty risk. There are two new approaches to stochastic modelling, which are useful with respect to ef- ficient simulation of counterparty risk. These are Path-Dependent Simulation (PDS) and Direct-Jump to Simulation date (DJS). It had been show that DJS is far more ef- fective, when it comes counterparty risk simulation of path-independent derivatives. We focus on a portfolio of interest rate swaps, which are effectively path-dependent. DJS approach yields estimates with much lower variance than PDS approach. But as expected, the DJS is also much more computationally intensive. The increase in computing time in majority of cases wipes out any gains in lower variance and PDS approach is shown to be more effective, when computing time is taken into account. We also show that in practice the convergence rate of Monte Carlo method signif- icantly underestimates the true reduction in variance, which can be achieved with increasing number of scenarios. JEL Classification C02, C15, C63, G01, G12, G32 Keywords Monte Carlo, CVA, Exposure, Variance Author's e-mail robberth.cz@gmail.com Supervisor's e-mail boril.sopov@gmail.com

Presenta los modelos estocásticos de los problemas resultantes del tratamiento estadístico dado a los coeficientes, así como algunos métodos de resolución utilizados para calcular los momentos estadísticos de las soluciones. Presenta la discretización de las ecuaciones de las realizaciones en el contexto de Monte Carlo. Realiza simulaciones numéricas.

This course project is made up of two parts. Part one is an investigation and implementation of pricing of financial derivatives using numerical methods for the solution of partial differential equations. Part two is an introduction of Monte Carlo methods in financial engineering. The name of course is MA573:Computational Methods in Financial Mathematics, spring 2009, given by Professor Marcel Blais.

This paper aims to use Monte Carlo methods to price American call options on equities using the variance reduction technique of control variates and to price American put options using the binomial model. We use this information to form option positions. This project was done a part of the masters capstone course Math 573: Computational Methods of Financial Mathematics.

The project investigates the prices of barrier options from the constant underlying volatility in the Black-Scholes model to stochastic volatility model in SABR framework. The constant volatility assumption in derivative pricing is not able to capture the dynamics of volatility. In order to resolve the shortcomings of the Black-Scholes model, it becomes necessary to find a model that reproduces the smile effect of the volatility. To model the volatility more accurately, we look into the recently developed SABR model which is widely used by practitioners in the financial industry. Pricing a barrier option whose payoff to be path dependent intrigued us to find a proper numerical method to approximate its price. We discuss the basic sampling methods of Monte Carlo and several popular variance reduction techniques. Then, we apply Monte Carlo methods to simulate the price of the down-and-out put barrier options under the Black-Scholes model and the SABR model as well as compare the features of these two models.

There is a growing global need for proper access to radiation therapy. This need exists predominantly in low- and middle-income countries but exists in some high-income countries as well. The solution to this problem is complex and requires changes in government policy, education and technology. The objective of the work contained in this dissertation is the development of a novel external beam radiation therapy system capable of treating a variety of cancers. The intent of this system is to provide a cost-effective radiation therapy system, which can primarily be utilized in low- and middle-income countries. This new system uses kilovoltage rather than megavoltage x-rays and is therefore much more cost-effective. The ultimate purpose of this kilovoltage radiation therapy system is to improve access to radiation therapy worldwide by supplementing current radiation therapy technology. As a first step, the kilovoltage x-ray arc therapy or KVAT system was modeled using the EGSnrc BEAMnrc and DOSXYZnrc Monte Carlo software tools. For this initial study 200 kV arc-therapy was simulated on cylindrical water phantoms of two sizes, each of which contained a variety of planning target volume (PTV) sizes and locations. Additionally, prone and supine partial breast irradiation treatment plans were generated using KVAT. The objective of this work was to determine whether or not skin-sparing could be achieved using the KVAT system while also delivering a clinically relevant dose rate to the PTV. The results of the study indicated that skin-sparing is indeed achievable and that the quality of KVAT treatment plans improves for full 360-degree arcs and smaller PTV sizes. The second step of this project involved the Monte Carlo simulation of KVAT treatment plans for breast, lung and prostate cancer. Spherical PTVs of 3-cm diameter were used for the breast and lung treatment plans while a 4-cm diameter PTV was used for prostate. Additionally, inverse optimization was utilized to make full use of the non-conformal irradiation geometry of KVAT. As a means of comparison, megavoltage treatment plans that could be delivered by a clinical linear accelerator were generated for each patient as well. In order to evaluate the safety of KVAT treatment plans, dose constraints were taken from published Radiation Therapy Oncology Group (RTOG) reports. The results of this study indicated that the 200 kV breast and 225 kV lung KVAT treatment plans were within dose constraints and could be delivered in a reasonable length of time. The 225 kV prostate treatment plan, while technically within dose constraints, delivered a large dose to non-critical healthy tissues due to the limited number of beam angles that did not pass through boney anatomy. It was concluded that plans such as prostate with large volumes of bone present might not be feasible for KVAT treatment. The third step aimed to expand upon previous work and simulated more realistic KVAT treatment plans by using PTV volumes contoured by radiation oncologists. Additionally, this study used a completely redesigned KVAT geometry, which employed a stationary reflection anode and a new collimator design. The design modeled in this study was based upon the specifications of the prototype system under construction by PrecisionRT, a commercial partner. Three stereotactic ablative radiotherapy (SABR) lung patients were selected that had received treatment at the Vancouver Island Cancer Centre. In order to fully cover the PTVs of each patient, spherical sub-volumes were placed within the clinically contoured PTV of each patient. Dose constraints for at-risk organs were taken from an RTOG report on stereotactic body radiation therapy and were used to inversely optimize the 200 kV KVAT treatment plans. The calculated KVAT plans were compared with the clinical 6 MV SABR plans delivered to each patient. The results of this study indicated that KVAT lung plans were within dose constraints for all three patients with the exception of the ribs in the second patient who had a tumor directly adjacent to the rib cage. The fourth and last step of this project was the experimental validation of a simple, proof-of-principle KVAT system. Simple geometric methods were used to design a collimator consisting of two slabs of brass separated by ~6 cm, each with 5 apertures, which would create an array of 5 converging beamlets. The collimator was used with a tabletop x-ray tube system. A rectangular solid water phantom and cylindrical TIVAR 1000 phantom were placed on a rotation stage and irradiated using 360-degree arcs. EBT3 gafchromic film was placed in each phantom to measure two-dimensional dose distributions. Film dose distributions were analyzed and compared to Monte Carlo generated dose distributions. Both the rectangular solid water phantom and cylindrical TIVAR phantom showed skin-sparing effects in their dose distributions. The highest degree of skin-sparing was achieved in the larger, 20 cm diameter cylindrical phantom. Furthermore, the measured film data and calculated metrics of the rectangular phantom were within 10% of the MC calculated values for two out of three films. The discrepancy in the third film can be explained by errors in the experimental setup. In conclusion, the work contained in this dissertation has established the feasibility of a cost-effective kilovoltage arc-therapy system designed to treat deep-seated lesions by means of Monte Carlo simulations and experimental dosimetry. The studies performed so far suggest that KVAT is most suitable for smaller lesions in patient anatomy that does not involve large amounts of boney anatomy. Perhaps most importantly, an experimental study has demonstrated the skin-sparing ability of a simple KVAT prototype. / Graduate / 2020-07-10