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This dissertation develops computational techniques to aid in efficiently studying petrologic systems that would otherwise be challenging. It then focuses on a case study in which the transition from diagenesis to syn-magmatic heating led to a recrystallization and sulfur mobilization. A Markov-chain Montecarlo-based methodology is developed to allow for the assessment of uncertainty in calculated phase assemblage diagrams. Such phase equilibria are ubiquitous in modern petrology, but uncertainties are rarely considered. Methods are discussed for visualizing and quantifying emergent patterns as phase diagrams are re-calculated with input data modified within permitted uncertainty bounds, and these are implemented in a new code. Results show that uncertainty varies significantly across pressure-temperature space and that in some conditions, estimates of stable mineral assemblage are known with very little confidence. A Machine-Learning (ML) based methodology is developed for automatically identifying unknown phases using Electron-dispersion spectra (EDS) in concert with a Random Forest Classification algorithm. This methodology allows for phase identification that it is insensitive to overfitting and noisy spectra. However, this tool is limited by the amount of reference spectra available in the dataset on which the ML algorithm is trained. The approximately 250 EDS spectra in the current training database must be supplemented to make the tool more widely useful, though it currently has an excellent success rate for correctly identifying various sulfide and oxide minerals. An analysis of paragenesis associated with Central Atlantic Magmatic Province (CAMP) intrusions helps to better constrain the dynamics of magma emplacement, while also providing a method for estimating the amount of sedimentary sulfide-sequestered sulfur mobilized as a result of magnetite formation associated with igneous activity. This method demonstrates that dike emplacement can trigger liberation of sedimentary sulfur with no direct cooling impact on climate. / Doctor of Philosophy / Determining how rocks and minerals form is fundamental to the geosciences. Here I present two computer-based techniques that can help address this essential problem. One method involves carefully determining uncertainty in thermodynamic modeling. Knowing the amount of uncertainty ultimately allows us to know the degree of confidence we can have in our model-based conclusions. The second computer-based technique involves using Machine Learning to automate the identification of minerals using an Electron-dispersion spectra (EDS) measured using a Scanning Electron Microscope (SEM). In theory, computers are much better than humans at quickly and repeatedly processing large sets of data such as EDS. This technique works well when the computer is successfully 'trained' on a large set of data but is somewhat limited in this case because there isn't diverse enough data available to train the computer. We therefore need better training data so that we can more fully benefit from this mineral identification tool. A third project I worked on involved assessing the impact of magma intruding into sedimentary rocks of the Culpeper Basin in northern Virginia. This occurred roughly 200 million years ago during the rifting of Pangea. The sedimentary rock around the magma heated up so much that water in the rock boiled and caused the rock to become fractured. After this a hydrothermal system was established that helped convert pyrite to magnetite, removing sulfur from the rocks in the process.

In the present work we study the securitized products of ?financial markets with focus on collateralized debt obligations and the impact of fi?nancial crisis on the markets in the world. First part the thesis is focused on the methodology of the reasons behind launching these products, the portfolio, tranches and further on mechanisms how these structures are working. In the second part the thesis teoretically describes the valuation methods for which the Markov chains and copula functions are used. Further on follows the practical part with output from the quantitative analysis and at the end the thesis describes the impacts on economics of di?fferent countries and practically introduces the stress testing as the precaution tool.

The pandemic scenario caused by COVID-19 is an event with no precedent. Therefore, it<br>is a phenomenon that can be studied to observe how electricity loads have changed during the stayat-home order weeks. The data collection process was done through online surveys and using<br>publicly available data. This study is focusing on analyzing household energy units such as<br>appliances, HVAC, lighting systems. However, collecting this data is expensive and timeconsuming since dwellings would have to be studied individually. As a solution, previous studies<br>have shown success in characterizing residential electricity using surveys with stochastic models.<br>This characterized electricity consumption data allows the researchers to generate a predictive<br>model, make a regression and understand the data. In that way, the data collection process will not<br>be as costly as installing measuring instruments or smart meters. The input data will be the<br>behavioral characteristics of each participant; meanwhile, the output of the analysis will be the<br>estimated electricity consumption "kWh." After generating the "kWh" target, a sensitivity analysis<br>will be done to observe the electricity consumption through time and examine how people evolved<br>their load during and after the stay-at-home order.<br>This research can help understand the change in electricity consumption of people who<br>worked at home during the pandemic and generate energy indicators and costs such as home office<br>electricity cost kWh/year. In addition to utilities and energy, managers can benefit from having a<br>clear understanding of domestic consumers during emergency scenarios as pandemics. <br>