Data sets of increasing size and complexity require new approaches for prediction as the sheer volume of data from disparate sources inhibits joint processing and modeling. Rather modular segmentation is required, in which a set of models process (potentially overlapping) partitions of the data to independently construct predictions. This framework enables individuals models to be tailored for specific selective superiorities without concern for existing models, which provides utility in cases of segmented expertise. However, a method for fusing predictions from the collection of models is required as models may be correlated. This work details optimal principles for fusing binary predictions from a collection of models to issue a joint prediction. An efficient algorithm is introduced and compared with off the shelf methods for binary prediction. This framework is then implemented in an applied setting to predict instances of civil unrest in Central and South America. Finally, model fusion principles of a spatiotemporal nature are developed to predict civil unrest. A novel multiscale modeling is used for efficient, scalable computation for combining a set of spatiotemporal predictions. / Ph. D.

Multi-modal image fusion is an active research area with many civilian and military applications. Fusion is defined as strategic combination of information collected by various sensors from different locations or different types in order to obtain a better understanding of an observed scene or situation. Fusion of multi-modal images cannot be completed unless these two modalities are spatially aligned. In this research, I consider two important problems. Multi-modal, multi-perspective image registration and decision level fusion of multi-modal images. In particular, LiDAR and visual imagery. Multi-modal image registration is a difficult task due to the different semantic interpretation of features extracted from each modality. This problem is decoupled into three sub-problems. The first step is identification and extraction of common features. The second step is the determination of corresponding points. The third step consists of determining the registration transformation parameters. Traditional registration methods use low level features such as lines and corners. Using these features require an extensive optimization search in order to determine the corresponding points. Many methods use global positioning systems (GPS), and a calibrated camera in order to obtain an initial estimate of the camera parameters. The advantages of our work over the previous works are the following. First, I used high level-features, which significantly reduce the search space for the optimization process. Second, the determination of corresponding points is modeled as an assignment problem between a small numbers of objects. On the other side, fusing LiDAR and visual images is beneficial, due to the different and rich characteristics of both modalities. LiDAR data contain 3D information, while images contain visual information. Developing a fusion technique that uses the characteristics of both modalities is very important. I establish a decision-level fusion technique using manifold models.

Neural networks are being used increasingly often as alternatives to traditional statistical models. As a result, their performance needs to be examined in a statistical framework. Following a brief overview of many types of neural networks, details concerning the implementation of the single hidden layer feedforward neural network (SHLFNN) are presented. The focus of the presentation is on the application of this network in a regression setting. One area where the SHLFNN is being used more frequently is in response surface modeling based on designed experiments. Due to the small sample sizes typically employed by response surface designs, the ability of the SHLFNN to accurately approximate the underlying model is questionable. The results of a simulation which compares the performance of the SHLFNN with that of a second order polynomial model are presented. Finally, methods are explored for combining the SHLFNN model with a linear model. Such a combined model has advantages over each of its components. The combined model will be able to approximate any underlying nonlinear function better than a linear model, and it will allow for easy assessment of the impact of any effects of interest to the researcher, an ability that is lost when only the SHLFNN model is used. / Ph. D.

<p>    </p> <p>Development on instrumentation and algorithms for chemical structure and chemical kinetics are discussed in this thesis. In Chapter 2 and 3, a consensus equilibrium formalism is introduced for the integration of multiple quantum chemical calculations of molecular and electronic structure. In multi-agent consensus equilibrium (MACE), iterative updates in structure optimization are intertwined with the net output, representing an equilibrium balance between multiple computational agents. MACE structure calculations from the integration of multiple low-level electronic structure calculations were compared favorably for small molecules, with results evaluated through comparison with higher level structure (CCSD). Notably, MACE results differed substantially from the average of the independent computational agent outputs, with MACE yielding improved agreement with higher-level CCSD calculations. The primary focus is on the development of the mathematical framework for implementing MACE for molecular and electronic structure determination, these initial preliminary results suggest potential promise for the use of MACE to improve the accuracy of low-level electronic structure calculations through the integration of multiple parallel methods. In Chapter 4 and 5, Fourier- transform fluorescence recovery after photobleaching (FT-FRAP) coupled with periodically comb pattern was demonstrated to monitor the controlled-release mechanisms of microparticles. By monitoring the time-lapse recovery patterns, spatial mobility were decoded in FT domain. Due to the nature of mobility encoded in FT domain, substantial improvements were demonstrated in terms of enhanced signal-to-noise, simplified mathematics, low requirements of sampling, and multiphoton compatibility to probe inside samples. FT-FRAP was able to discriminate and quantify the internal diffusion and exchange to higher mobility in fitting the recovery kinetics within microparticles. Theoretical modeling of exchange and diffusion- controlled release revealed that both RS and RL microparticles exhibited similar exchange decay, with RL having a much higher diffusion decay. The microscopically higher diffusion of RL microparticles is consistent with the dissolution performance of RL microparticles macroscopically. The distinction of controlled release mechanisms provided by FT-FRAP is important to understand and further optimize the design of controlled release systems for GI tract. </p>

Optics are a powerful probe of chemical structure that can often be linked to theoretical predictions, providing robustness as a measurement tool. Not only do optical interactions like second harmonic generation (SHG), single and two-photon excited fluorescence (TPEF), and infrared absorption provide chemical specificity at the molecular and macromolecular scale, but the ability to image enables mapping heterogeneous behavior across complex systems such as biological tissue. This thesis will discuss nonlinear and linear optics, leveraging theoretical predictions to provide frameworks for interpreting analytical measurement. In turn, the causal mechanistic understanding provided by these frameworks will enable structurally specific quantitative tools with a special emphasis on application in biological imaging. The thesis will begin with an introduction to 2nd order nonlinear optics and the polarization analysis thereof, covering both the Jones framework for polarization analysis and the design of experiment. Novel experimental architectures aimed at reducing 1/f noise in polarization analysis will be discussed, leveraging both rapid modulation in time through electro-optic modulators (Chapter 2), as well as fixed-optic spatial modulation approaches (Chapter 3). In addition, challenges in polarization-dependent imaging within turbid systems will be addressed with the discussion of a theoretical framework to model SHG occurring from unpolarized light (Chapter 4). The application of this framework to thick tissue imaging for analysis of collagen local structure can provide a method for characterizing changes in tissue morphology associated with some common cancers (Chapter 5). In addition to discussion of nonlinear optical phenomena, a novel mechanism for electric dipole allowed fluorescence-detected circular dichroism will be introduced (Chapter 6). Tackling challenges associated with label-free chemically specific imaging, the construction of a novel infrared hyperspectral microscope for chemical classification in complex mixtures will be presented (Chapter 7). The thesis will conclude with a discussion of the inherent disadvantages in taking the traditional paradigm of modeling and measuring chemistry separately and provide the multi-agent consensus equilibrium (MACE) framework as an alternative to the classic meet-in-the-middle approach (Chapter 8). Spanning topics from pure theoretical descriptions of light-matter interaction to full experimental work, this thesis aims to unify these two fronts. <br>