The purpose of this thesis is to predict the lifespan of a battery using a predictive model, utilizing data from early cycles. The goal is to minimize both time and costs for the company by reducing the number of cycles needed for testing. Currently, the company tests a diverse set of batteries, which is both time and resource-consuming. To investigate which data-driven predictive model should be used by the company to predict battery capacity at XX cycles, a thorough literature study has been conducted. In summary, a variety of variables from specific cycles have been calculated based on inspiration from Fei et al. (2021), Severson et al. (2019), Enholm et al. (2022) and an internal project from the company. Following this, two different predictive models, Gaussian Process Regression and Ordinary Least Squared Regression, are applied and compared.  Based on the obtained results, Gaussian Process Regression had a slight better results but a significantly higher complexity compared to Ordinary Least Squared Regression. Therefore, the data-driven model that should be implemented at the company is an Ordinary Least Squared Regression with variables related to different phases during a cycle. This result is primarily based on the varying degrees of complexity of the models. / Syftet med detta examensarbete är att med hjälp av en datadriven prediktionsmodell kunna prediktera livslängden på ett batteri genom att använda data från tidiga cykler. Målet är att minimera både tid och kostnader för företaget genom att minska antalet cykler som behövs för testning. I dagsläget testar företaget en mängd batterier vilket både är tids- samt resurskrävande. För att undersöka vilken datadriven prediktionsmodell som bör användas av företaget för att prediktera batteriekapacitet vid XX cykler har en gedigen litteraturstudie utförts. Sammanfattningsvis har en mängd variabler av de mätningar som finns från specifika cykler beräknats utifrån inspiration från Fei med flera (2021), Severson med flera (2019), Enholm med flera (2022) samt ett internt projekt från företaget. Efter detta applicerades och jämfördes två olika prediktionsmodeller: Gaussian Process Regression och Ordinary Least Squared Regression.  Baserat på de erhållna resultaten hade Gaussian Process Regression något bättre resultat men en betydligt högre komplexitet jämfört med Ordinary Least Squared Regression. Därför är den datadrivna modell som bör implementeras på företaget en Ordinary Least Squared Regression med variabler relaterade till olika faser under en cykel. Detta resultat grundar sig framför allt i olika grad av komplexitet hos modellerna.

The NASA Airborne Topographic Mapper (ATM) is a laser scanning instrument which is used mainly to collect dense topographic data over much of the conterminous US coastline. The inclusion of two digital cameras in consonance with the ATM instrument now gives 3-band (RGB) imagery apart from a very rich topographic data. This imagery, in its crude form, has limited applications due to it being not georeferenced and having a heavy camera lens distortions. As thesis, a processing system - Park-View - is developed to bring this imagery into a more suitable format for the scientists for analytical and interpretational purposes. Park-View utilizes the well gridded elevation data from layer four of another processing system called LaserMap for georeferencing the digital camera images. Camera lens behavior is modeled using a 2D grid image and all of its intrinsic parameters ascertained. These parameters are then incorporated into correcting the lens distortions of georeferenced images. Errors in time-stamping of images and in the mounting angles of the camera are calculated using well known tie-points. Georeferenced images can be stored either in GeoTiff format or jpeg format. Individual images can be georeferenced or put in a mosaic form with the mosaic color equalized for adjoining images. Park-View also provides the main GUI displaying the entire surveyed area, mapper GUI for a batch processing of all the images and a display window for displaying georeferenced images or mosaics. Additional capabilities could be added to the processing system for performing some specific image processing operations on the images such as edge detection and image enhancement.

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利率模型從早期的短期利率模型、遠期利率模型發展到現在的市場模型。在模型的概念上，已經從市場上不存在的瞬間連續利率修正到市場上可觀察的區間連續的遠期利率。而評價方法的進步，使得市場上發展出各式各樣的利率衍生性商品，其中付「提前贖回條款」的債券很常見。為吸引投資人，附提前贖回條款的債券往往伴隨著高配息。本文選用「12年期美金計價『利率區間』連動債券」與「十年期美元計價息滿到期反浮動利率連動債券」做個案分析，在市場模型之下，評價具提前贖回條款的債券。

This project was dedicated to the problem of improving a non-invasive blood glucose monitor being developed by the VivaScan Corporation. The company has made some progress in the non-invasive blood glucose device development and approached WPI for a statistical assistance in the improvement of their model in order to predict the glucose level more accurately. The main goal of this project was to improve the ability of the non-invasive blood glucose monitor to predict the glucose values more precisely. The goal was achieved by finding and implementing the best regression model. The methods included ordinary least squared regression, partial least squares regression, robust regression method, weighted least squares regression, local regression, and ridge regression. VivaScan calibration data for seven patients were analyzed in this project. For each of these patients, the individual regression models were built and compared based on the two factors that evaluate the model prediction ability. It was determined that partial least squares and ridge regressions are two best methods among the others that were considered in this work. Using these two methods gave better glucose prediction. The additional problem of data reduction to minimize the data collection time was also considered in this work.

The initiation, bloom, and bust of harmful Cyanobacteria and algae blooms (HAB) in lakes are controlled by top-down and bottom-up ecological controls. Excess phosphorous and nitrogen inputs from anthropogenic sources are primary to blame, but eukaryotic grazers may also promote or curb Cyanobacteria dominance. We tracked shifts in bacterial composition, lake chemistry, and eukaryotic grazing community weekly or bi-weekly through spring and summer and modeled the causes of specific Cyanobacterial species blooms and busts across three lakes in Utah, USA, with differing lake trophic states. Regardless of trophic status, all three lakes experienced blooms of varying composition and duration. Aphanizomenon strain MDT14a was the most dominant species in every bloom on Utah Lake, comprising up to 44.16% of the bacterial community. Utah Lake experienced a total of 18 blooms across all sites ranging in duration from one to six weeks. Phormidiaceae sp. (8.5  6.1%) and Microcystis sp. (9.7  4.7%) were the most abundant species in the Deer Creek bloom. Deer creek experienced one bloom at the beginning of fall. Nodularia sp. (9.7  2.1) dominated Great Salt Lake bloom. The Great Salt Lake experienced four separate blooms during the summer months that lasted one to three weeks. Phosphorous concentrations on Utah Lake varied across site and season. Nitrate concentrations on Deer Creek increased over season with a ten-fold increase in concentration. We characterized Cyanobacteria blooms as either bloom communities (growing populations of Cyanobacteria) or as bust communities (declining populations of Cyanobacteria). Using these designations, we modeled the growth and decline of the Cyanobacteria populations across season with top-down and bottom up-controls. Based on generalized least-squared modeling, eukaryotic grazing does not affect relative Cyanobacteria abundances as much as nutrient limitations. Aphanizomenom strain MDT14a was positively correlated with temperature (P < 0.028) and the concentration of K (P = 0.007) and negatively correlated with increases in conductivity (P = 0.0088). Microcystis was positively correlated with increasing levels of SRP (P < 0.001) and negatively correlated with higher Ca concentrations (P = 0.008) and PP (P = 0.008). Busts of Microcystis were related to decreases in nitrate (P = 0.06) and lower total lake depths (P = 0.03). Phormidiaceae sp. relative abundance was negatively correlated with higher levels of TDN (P = 0.01-0.001) and Mg (P = 0.01) and positively correlated with higher S concentrations (P = 0.007). Our findings suggest that micronutrients and more bioavailable forms of P may potentially allow Cyanobacteria to break dormancy and proliferate HAB communities.

可轉換公司債是一種在持有期間內，投資人可以在規定的時間內將債券轉換為股票，或是到期時得到債券報酬的一種複合式證券。因此，可轉債除了具有債券性質之外，還包含另一部份可視為一美式選擇權的股票選擇權。 本篇論文將可轉換債券評價結合數值分析中的最小蒙地卡羅法(Least square monte carlo)，使得在評價可轉債時，能夠具有更多的彈性處理發行公司自行設計的贖回條款與其他各種不同的契約情況。 此外，本篇論文針對股價考慮跳躍的性質，使用Compound Poisson 過程模擬發生跳躍的次數，導入Merton的跳躍模型(Jump-diffusion Model)，在Merton的假設下，模擬未來股價的動態變化。 信用風險方面，本文採用Duffie提出的風險CIR模型評價。考慮存活函數(Survival Function)和違約強度(Hazard Rate Function)，使用CIR模型描述信用違約強度在可轉債持有期間的動態變化，最後模擬出違約的時點，結合LSMC下的可轉債評價評價法。 最後利率部份，雖然Brennan and Schwartz(1980)認為隨機利率對於可轉換債券的評價，並沒有明顯的效果，反而會降低評價時的效率，但是為了符合評價過程的合理性，本文使用CIR短期利率模型。