The Ensemble Kalman Filter (EnKF) is a popular data assimilation method for state-parameter estimation. Following a sequential assimilation strategy, it breaks the problem into alternating cycles of forecast and analysis steps. In the forecast step, the dynamical model is used to integrate a stochastic sample approximating the state analysis distribution (called analysis ensemble) to obtain a forecast ensemble. In the analysis step, the forecast ensemble is updated with the incoming observation using a Kalman-like correction, which is then used for the next forecast step. In realistic large-scale applications, EnKFs are implemented with limited ensembles, and often poorly known model errors statistics, leading to a crude approximation of the forecast covariance. This strongly limits the filter performance. Recently, a new EnKF was proposed in [1] following a one-step-ahead smoothing strategy (EnKF-OSA), which involves an OSA smoothing of the state between two successive analysis. At each time step, EnKF-OSA exploits the observation twice. The incoming observation is first used to smooth the ensemble at the previous time step. The resulting smoothed ensemble is then integrated forward to compute a "pseudo forecast" ensemble, which is again updated with the same observation. The idea of constraining the state with future observations is to add more information in the estimation process in order to mitigate for the sub-optimal character of EnKF-like methods. The second EnKF-OSA "forecast" is computed from the smoothed ensemble and should therefore provide an improved background. In this work, we propose a deterministic variant of the EnKF-OSA, based on the Singular Evolutive Interpolated Ensemble Kalman (SEIK) filter. The motivation behind this is to avoid the observations perturbations of the EnKF in order to improve the scheme's behavior when assimilating big data sets with small ensembles. The new SEIK-OSA scheme is implemented and its efficiency is demonstrated by performing assimilation experiments with the highly nonlinear Lorenz model and a realistic setting of the Advanced Circulation (ADCIRC) model configured for storm surge forecasting in the Gulf of Mexico during Hurricane Ike.

The thesis addresses the influence of compressible effects on the stability of deflagration waves. Due to the quasi-isobaric nature of slow flames, compressible effects in laminar flames are usually neglected. Nevertheless, turbulent deflagrations may propagate at substantially higher speeds, suggesting that compressible effects may play a role in their dynamics. In the present thesis, the stability of diffusion-dominated high-speed deflagrations is addressed. The deflagration is studied in the thickened regime, hence addressing the long wavelength limit of these deflagrations. The deflagrations are modelled by the compressible reactive Navier-Stokes equations with a single-step Arrhenius reaction model. The 2D stability of the steady traveling-wave solution is studied by direct simulation. It is found that, as the flame compressibility becomes significant, not only does the growth rates of the cellular profile of the deflagration waves increase, but the traditional correlation of the burning velocity and the flame surface area become far less strong. Significant compression regions form in front of the nonlinear flames. These compression regions have been found to increase the growth rates by increasing the temperature of the unburned gas in front of the flames, as well as convecting the flame forward. The results show that the flame propagation velocity in references to the unburned gas was significantly faster than the burning velocity. The vorticity was given consideration, as the compressibility of flame increase one can expect the baroclinic source to be of greater significance. The vorticity was show to, in effect, increase as compressibility increases while unexpectedly having a stabilizing direction of rotation on the cellular structure of the flames.

Design and development of novel one-step reactions that produce nitrogen-containing scaffolds is an invaluable area of chemistry due to the abundance of these moieties in natural products and biologically active molecules. Discovering novel methods using uncommon substrates and rare earth metals to access these significant scaffolds present a challenge. Over the course of my doctoral studies, I have designed, developed and optimized novel reactions by using rarely known substrates and rare earth metals that have afforded important nitrogen-containing scaffolds. The products obtained allow access to otherwise long-to-synthesize molecules and expeditious construction of biologically active molecules.

We present two approaches towards a characterization of the complete Pick property. We first discuss the lurking isometry method used in a paper by J.A. Ball, T.T. Trent, and V. Vinnikov. They show that a nondegenerate, positive kernel has the complete Pick property if $1/k$ has one positive square. We also look at the one-point extension approach developed by P. Quiggin which leads to a sufficient and necessary condition for a positive kernel to have the complete Pick property. We conclude by connecting the two characterizations of the complete Pick property. / Master of Science

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Synechocystis PCC 6803 is a photosynthetic bacterium that has the potential to make bioproducts from carbon dioxide and light. Biochemical production from photosynthetic organisms is attractive because it replaces the typical bioprocessing steps of crop growth, milling, and fermentation, with a one-step photosynthetic process. However, low yields and slow growth rates limit the economic potential of such endeavors. Rational metabolic engineering methods are hindered by limited cellular knowledge and inadequate models of Synechocystis. Instead, inverse metabolic engineering, a scheme based on combinatorial gene searches which does not require detailed cellular models, but can exploit sequence data and existing molecular biological techniques, was used to find genes that (1) improve the production of the biopolymer poly-3-hydroxybutyrate (PHB) and (2) increase the growth rate. A fluorescence activated cell sorting assay was developed to screen for high PHB producing clones. Separately, serial sub-culturing was used to select clones that improve growth rate. Novel gene knock-outs were identified that increase PHB production and others that increase the specific growth rate. These improvements make this system more attractive for industrial use and demonstrate the power of inverse metabolic engineering to identify novel phenotype-associated genes in poorly understood systems. / Singapore-MIT Alliance (SMA)

This thesis compares the simple Autoregressive (AR) model against the k- Nearest Neighbor (k-NN) model to make a point forecast of five energy commodity prices. Those commodities are natural gas, heating oil, gasoline, ethanol, and crude oil. The data for the commodities are monthly and, for each commodity, two-thirds of the data are used for an in-sample forecast, and the remaining one-third of the data are used to perform an out-of-sample forecast. Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE) are used to compare the two forecasts. The results showed that one method is superior by one measure but inferior by another. Although the differences of the two models are minimal, it is up to a decision maker as to which model to choose. The Diebold-Mariano (DM) test was performed to test the relative accuracy of the models. For all five commodities, the results failed to reject the null hypothesis indicating that both models are equally accurate.

This thesis discusses development of a future visioning system model that can be adopted to create new product concepts for consumer electronics companies operating in a highly competitive business environment. The research work investigates consumer electronic product companies and their market environment to identify problematic issues and indicates that a proactive new product strategy which opens new markets through developing concept-led products is a strategic priority, thus the concept development stage in new product development process is in need of improvement. An evaluation of existing concept development tools for the purpose of proactive product strategy is presented and concludes that future visioning procedure is the most appropriate tool. To develop a future visioning system model as a concept development tool, the theoretical future visioning system models are analysed and mapped to extract essential structure and contents of future visioning procedure. The consequent future visioning system model is then revised according to the findings and suggestions from the field research work which investigated four major consumer electronics product companies in practice. The findings also validates the necessity of adopting a proactive product strategy and evaluates acceptability of the future visioning system model for practical use. The final future visioning system model is defined after the opinions of the design managers are considered and applied. The major suggestions from the research findings are: (1) Executing proactive product strategy can be a valuable strategic tool (2) A new process is necessary for the companies to create one-step-ahead product (3) Future visioning system is recommended as an advanced approach that creates new product concept. (4) Future visioning system model should consist of eight stages: project initiation, environmental scanning, future visioning, generating product concepts, scenario planning, concept testing, concept visualisation, and finalized concepts. (5) Product concepts can be generated from future vision by applying backcasting. (6) Scenario planning should be used in the future visioning system model as a concept testing tool providing objective validating criteria. (7) Executing a future visioning system model creates new roles for the designer such as information integrator, process moderator, and futurist.

This thesis outlines the dynamic system analysis of a 3D Ultrasonic neuro- navigation system for use in motion capture studies. The work entails the development and implementation of methods for achieving the same. The objective of the project is to come up with an accurate dynamic 3D ultrasonic neuro-navigation system which can deliver up to sub mm accuracy within the operating workspace for use in image guided neuro surgery. The major focus of the work is to come up with a second order Kalman filter which can take out the outliers occurring in a static system in real time, thereby making the system more robust and accurate. Once the filter achieves the requisites, it can be integrated into the current motion tracking software which allows for the real time tracking of transmitters, hence the points of interest.

Predicting and characterizing the state of the ocean is needed for various scientific, industrial, social, management, and recreational activities. Despite the tremendous progress in ocean modeling and simulation capabilities, the ocean models still suffer from different sources of uncertainties. To obtain accurate ocean state predictions, data assimilation (DA) is widely used to constrain the ocean model outputs with available observations. Ensemble Kalman filtering (EnKF) is a sequential DA approach that represents the distribution of the system state through an ensemble of ocean state samples. Different factors may limit the performance of an EnKF in realistic ocean applications, particularly the use of small ensembles and poorly known model error statistics, and also to a lesser extent the strongly nonlinear variations and abrupt regime changes, and unsatisfied underlying assumptions such as the commonly used white observation noise assumption. The objective of this PhD thesis is to develop, implement and test efficient ensemble filtering schemes to enhance the performances of EnKFs in such challenging settings. We resort to the one-step-ahead (OSA) smoothing formulation of the Bayesian filtering problem to introduce EnKFs involving a new update step with future observations (smoothing) between two successive analyses, thereby conditioning the ensemble sampling with more information. We show that this approach enhances the EnKFs performances by providing improved ensemble background statistics, and showcase its performance with realistic ocean DA and forecasting applications, namely a storm surge EnKF forecasting system and the Red Sea ensemble DA and forecasting system. We then derive new EnKF-based schemes accounting for time-correlated observation errors for efficient DA into the class of large dimensional DA problems where observation errors statistics are correlated in time, and further propose a new approach for online estimation of the parameters of the observation error time-correlations model concurrently with the state. We also exploit the OSA-smoothing formulation to propose a new joint EnKF with OSA-smoothing which mitigates for the reported inconsistencies in the joint EnKF update for efficient DA into one-way-coupled systems.