The success of Generative Adversarial Networks (GANs) has resulted in unprecedented quality both for image generation and manipulation. Recent state-of-the-art GANs (e.g., the StyleGAN series) have demonstrated outstanding results in photo-realistic image generation. In this dissertation, we explore the latent space properties, including image manipulation, extraction of 3D properties, and performing various weakly supervised and unsupervised downstream tasks using StyleGAN and its derivative architectures. First, we study the images' projection into StyleGAN's latent space and analyze the properties of embedded images in a proposed extended $W+$ latent space. Second, we demonstrate rich semantic interpretations of the images in the latent space, which indirectly creates a compelling semantic understanding of the underlying latent space. Specifically, we combine $W+$ space with Noise space optimization and tensor manipulations to enable high-quality reconstruction and local editing. For example, we can perform image inpainting where these regularized latent spaces reconstruct the image's content, and the details of the missing regions are filled by the GAN prior. Next, we study if a 2D image-based GAN learns a meaningful semantic model and 3D properties in an image. Using our analysis, we can extract a plausible interpretation of 3D geometry, lighting, materials, and other semantic attributes of the source images by modeling the latent space using conditional continuous normalizing flows. As a result, we can perform non-linear sequential edits on the source image without affecting the quality and identity of the image. Furthermore, we propose a technique to extract underlying latent space properties using an unsupervised method to generalize our analysis on unseen datasets where human knowledge is limited. Specifically, we use an information-rich visual-linguistic model, CLIP, trained on internet scale data of image-text pairs. The proposed framework extracts, labels, and projects important directions into the GAN latent space without human supervision. Finally, inspired by the findings of our analysis, we investigate additional related unexplored questions: Can we perform foreground object segmentation? Can an image-based GAN be used to edit videos? Can we generate view-consistent editable 3D animations? Investigating these research questions helps us use GANs to tackle a spectrum of tasks outside the usual image generation task. Specifically, we propose a technique to segment foreground objects from the generated images using the information stored in the StyleGAN feature maps. This framework can be used to create synthetic datasets, which can be used to train existing supervised segmentation networks. Then, we study the regularized $W+$, activation $S$, and Fourier feature $F_f$ spaces to embed and edit videos in the image-based StyleGAN3, a variant of StyleGAN. We can generate high-quality videos at $1024^2$ resolution using a single image and driving videos. Finally, we propose a framework for domain adaptation in 3D-GANs that can link latent spaces of different models together. We build upon EG3D, a 3D-GAN derived from StyleGAN, to enable the generation, editing, and animation of personalized 3D avatars. Technically, we propose a method to align the camera distribution of two domains i.e., faces and avatars. Then we propose a method for domain adaptation in 3D-GANs using texture, geometric, and depth regularization with an option to model more exaggerated geometries. Finally, we propose a method to link and project real faces into the 3D artistic domain. These frameworks allow us to develop tools distilled from an unconditional GAN for unsupervised image segmentation, video editing, and personalized 3D animation generation and manipulation with state-of-the-art performance. We create these tools without needing extra annotated object segmentation, video, or 3D data.

Transportation produces about 25% of the global CO2 emissions, with gasoline and diesel light-duty vehicles being responsible for nearly half the transportation sector energy use. The reduction of emissions from transportation is an enormous challenge. While electrification is on the horizon, around 70% of the world’s vehicles are expected to be non-electric by 2050. One pragmatic way of tackling the emissions is to optimize the systems employed in the over 1 billion vehicles on the road today. In this dissertation, the issue of reducing the transportation emissions is tackled from experimental and simulation points of view. This entails building a stagnation-flow reactor, which reduces the problem to one dimensional and helps attain accurate kinetic data, and employing the state-of-the-art catalytic microkinetic modeling techniques. Gasoline vehicles utilize three-way catalyst systems, where CO, NO and unburned hydrocarbons are simultaneously converted to CO2, N2 and H2O. These systems are based on platinum (Pt), rhodium (Rh) and palladium (Pd) catalysts. Rh is the most expensive metal and estimated to only be 0.0002 ppm of the Earth's crust. Therefore, it is important to understand the detailed chemistry on Rh to better utilize it. First, thorough characterization experiments of a commercial 5 wt. % Rh/Al2O3 catalyst were performed via N2-physisorption, ICP-OES, XRD, H2-TPR, H2--chemisorption, STEM, and EELS. Additionally, the current microkinetic mechanisms for CO oxidation to CO2 over Rh/Al2O3 are limited to stoichiometric conditions and cannot predict the behavior at lean conditions, where gasoline engines are more efficient. An improved understanding of CO oxidation was attained by performing experiments at low-temperature in the stagnation-flow reactor. This includes the effects of temperature, pressure, inlet composition, and flow rate. Then, a microkinetic mechanism that is DFT-parametrized and captures the CO oxidation behavior was developed. The mechanism is versatile and accurately predicts the observed behavior at vastly different temperatures, inlet compositions, and flow rates. The detailed chemistry was examined by performing sensitivity analysis at different compositions. Also, the surface coverage was investigated, and the surface behavior was explained based on thermodynamics. Lastly, the oxidation of dimethyl ether, a potential alternative fuel for diesel engines, was studied at low temperatures in the stagnation-flow reactor. In addition to testing total oxidation, partial oxidation was examined, where the oxidation zone was isolated from the reforming zone. This is of relevance to the after-treatment of DME-powered engines. Additionally, intrinsic activation energy values for DME oxidation are reported for the first time for this catalyst system. Overall, the work advances the current knowledge of existing and alternative transportation systems. It paves the way for accurate modeling of these catalytic process as well as rational design for cheaper and more effective catalysts.

In this dissertation, three different coupled systems of volume integral and hydrodynamic equations are formulated to analyze electromagnetic scattering from composite plasmonic structures consisting of dielectrics, metals, or semiconductors. First coupled system of volume integral and hydrodynamic equations is formulated to describe the electromagnetic interactions on nanostructures consisting of metallic and dielectric parts. The hydrodynamic equation is enforced in metallic parts while the volume integral equation is enforced in both metallic and dielectric parts. This coupled system of equations has two unknowns, electric flux, and hydrodynamic polarization current, and they are expanded using full and half Schaubert-Wilton-Glisson (SWG) basis functions respectively. These basis functions are defined on a mesh of tetrahedrons discretizing the nanostructures. The continuity and the boundary conditions of the hydrodynamic polarization current are ensured via the careful use of half SWG basis functions. Inserting the basis function expansions into the coupled system of equations, and applying Galerkin testing yield a matrix system. An efficient two-level iterative scheme is developed to solve this matrix system for the unknown expansion coefficients. The second method is built upon the first one described above and is formulated to analyze electromagnetic scattering from nanostructures consisting of two different metallic parts. In this formulation, the free electron density velocity is used instead of the hydrodynamic polarization current since the latter is discontinuous while the former is continuous at metal-metal interfaces. Just like the first method, the scatterer is discretized using tetrahedrons but this time both electric flux and free electron velocity are expanded using full SWG basis functions each of which is defined on a pair of tetrahedrons. The matrix system resulting from Galerkin testing is solved using the two-level iterative scheme developed earlier. To model semiconductor plasmon structures the conventional single-fluid hydrodynamic equation is not enough since semiconductors support two charge carriers. Therefore, the third method developed int his dissertation uses a two-fluid hydrodynamic equation to take into account electrons and holes as charge carriers. Adopting this modification, a coupled system of volume integral and two-fluid hydrodynamic equations is formulated and solved to analyze electromagnetic scattering from semiconductor plasmon structures. The two-fluid hydrodynamic equation relates the free electron and the hole polarization currents to the electric flux. Just like the first method, the electric flux and these polarization currents are expanded using full and half SWG basis functions, respectively, and applying Galerkin testing yields a matrix system that is solved using the two-level iterative scheme. Numerical experiments are carried out to demonstrate the accuracy, the efficiency, and the applicability of the proposed methods.

An unmanned aerial vehicle-mounted base station (UAV-BS), also known as an aerial base station (ABS), is a viable technology for the next 6G wireless networks due to its adaptability and affordability. Furthermore, the concept of tethered UAVs (T-UAVs), can be used to circumvent the limited network operating time of UAV-BS networks. T-UAVs are UAVs powered by a ground energy source via a tether that restrain their mobility while providing unlimited power. In this thesis, we propose systems where ABSs are deployed in user hotspots to offload the traffic and assist terrestrial base stations (TBSs). First, we propose three different scenarios based on a model of cluster pairs. We start by determining the optimal locations of T-UAVs that minimize the average pathloss for each scenario. Next, using tools from stochastic geometry and an approach of dividing the space into concentric rings and slices to quantify the locations and orientations of GSs, we analyse both coverage and energy performance for each scenario and compare their performances. We use Monte-Carlo simulations to validate our findings and provide several useful insights. For instance, we show that deploying for each pair of clusters a T-UAV that can be attached and detached from the GS is the best strategy to adopt in terms of both coverage and energy efficiency. Second, we propose a hybrid system composed of tethered and untethered UAVs (T/U-UAVs). We study the coverage performance as a function of some system parameters such as the fraction of T-UAVs that have been used, the U-UAV availability, and the radius of clusters, and we provide useful insights.

Deep generative models are deep learning-based methods that are optimized to synthesize samples of a given distribution. During the past years, they have attracted a lot of interest from the research community, and the developed tools now enjoy many practical applications in content creation and editing. In computer vision, such models are typically built for images, videos, and 3D objects. Recently, there has emerged a paradigm of neural fields, which unifies the representations of such types of data by parametrizing them via neural networks. In this work, we develop generative modeling methods for images, videos, and 3D objects which treat the underlying data in such a form. We show that this perspective can yield state-of-the-art synthesis quality and many useful practical benefits, like interpolation/extrapolation capabilities, geometric inductive biases, and more efficient training and inference.

Fractional diffusion equations have played an increasingly important role in ex- plaining long-range interactions, nonlocal dynamics and anomalous diffusion, pro- viding effective means of describing the memory and hereditary properties of such processes. This dissertation explores the uncertainty propagation in space fractional diffusion equations in one and multiple dimensions with variable diffusivity and order parameters. This is achieved by:(i) deploying accurate numerical schemes of the forward problem, and (ii) employing uncertainty quantifications tools that accelerate the inverse problem. We begin by focusing on parameter calibration of a variable- diffusivity fractional diffusion model. A random, spatially-varying diffusivity field is considered together with an uncertain but spatially homogeneous fractional operator order. Polynomial chaos (PC) techniques are used to express the dependence of the stochastic solution on these random variables. A non-intrusive methodology is used, and a deterministic finite-difference solver of the fractional diffusion model is utilized for this purpose. The surrogates are first used to assess the sensitivity of quantities of interest (QoIs) to uncertain inputs and to examine their statistics. In particular, the analysis indicates that the fractional order has a dominant effect on the variance of the QoIs considered. The PC surrogates are further exploited to calibrate the uncertain parameters using a Bayesian methodology. In the broad range of parameters addressed, the analysis shows that the uncertain parameters having a significant impact on the variance of the solution can be reliably inferred, even from limited observations. Next, we address the numerical challenges when multidimensional space-fractional diffusion equations have spatially varying diffusivity and fractional order. Significant computational challenges arise due to the kernel singularity in the fractional integral operator as well as the resulting dense discretized operators. Hence, we present a singularity-aware discretization scheme that regularizes the singular integrals through a singularity subtraction technique adapted to the spatial variability of diffusivity and fractional order. This regularization strategy is conveniently formulated as a sparse matrix correction that is added to the dense operator, and is applicable to different formulations of fractional diffusion equations. Numerical results show that the singularity treatment is robust, substantially reduces discretization errors, and attains the first-order convergence rate allowed by the regularity of the solutions. In the last part, we explore the application of a Bayesian formalism to detect an anomaly in a fractional medium. Specifically, a computational method is presented for inferring the location and properties of an inclusion inside a two-dimensional domain. The anomaly is assumed to have known shape, but unknown diffusivity and fractional order parameters, and is assumed to be embedded in a fractional medium of known fractional properties. To detect the presence of the anomaly, the medium is forced using a collection of localized sources, and its response is measured at the source locations. To this end, the singularity-aware finite-difference scheme is applied. A non-intrusive regression approach is used to explore the dependence of the computed signals on the properties of the anomaly, and the resulting surrogates are first exploited to characterize the variability of the response, and then used to accelerate the Bayesian inference of the anomaly. In the regime of parameters considered, the computational results indicate that robust estimates of the location and fractional properties of the anomaly can be obtained, and that these estimates become sharper when high contrast ratios prevail between the anomaly and the surrounding matrix.

Aggregation-induced emission (AIE) is a phenomenon with many applications, such as chemical sensors, biological probes, immunoassay markets, and active layers in fabricating organic light-emitting diodes. AIE materials in polymers can enhance the emissivity of such materials while having the benefits of polymeric materials. This thesis examines the use of AIE polymers to study the effect of structure on the properties. This is done by first synthesizing a monomer with AIE characteristics, tetraphenylethylene-methacrylate (TPEMA). Secondly, polymerizing TPEMA using free and controlled radical polymerizations. Finally, the copolymerization of TPEMA with methyl methacrylate (MMA) to understand the effect of spaced-out TPE groups in the polymer chain on the photoluminescence of the polymer. The structures of all intermediates and final products were characterized by nuclear magnetic resonance (NMR) and size exclusion chromatography (SEC). The AIE characteristics were proven and compared using the photoluminescence graphs, showing that the homopolymer had increased emission intensity than its monomer. The copolymer had higher emission intensity than TPEMA and higher normalized emission intensity than that of the homopolymer, showing the effect of structure on the photoluminescence. Both the homopolymer and the copolymer were easier to aggregate than the monomer, making it more effective to utilize the material in applications where it needs to be emissive in diluted solutions. The glass transition temperature and the tacticity of the homopolymer and copolymer were also compared. The thesis is divided into the following five chapters; 1. Introduction, where a brief background along with the scope of the thesis is provided; 2. Literature Review, where a summary of controlled radical polymerization and AIE is given; 3. Experimental Section, where the materials' detailed procedure and characterization are provided; 4. Results and Discussion, where results of successful experiments are discussed; 5. Concluding Remarks, where the results are summarized, and future work is discussed.

Due to the similar nature 3D synthetics share with in vivo cell conditions, peptide-based hydrogels pose an attractive strategy for the culturing of stem cells. One aspect of this unique cell culturing technique is the tunability of the hydrogel’s stiffness, a quality linked to stem cell differentiation. Due to this linkage, a methodology in which specific cell lineages are achieved within IIFK hydrogel cultures is proposed. This work provides an analysis for the peptide scaffold IIFK; it characterizes the effect between different peptide and PBS concentrations over the resulting hydrogel stiffness and develops a mathematical model to further elucidate this interaction. Nine different hydrogel formulations were made (with a minimum of eleven replicates each) and each of its replicate’s stiffness (storage modulus, Pa) was measured through rheological experiments. Then, two different methods of replicate selection were conducted and various models were derived, each using either of the two replicate selection methods and incorporating a specific number of replicates in their creation. Regardless of sample selection and replicate number, the generated models show extremely high significances between IIFK hydrogel stiffness and PBS concentrations over the resulting hydrogel stiffness. Data analysis shows that for IIFK, the hydrogel stiffness bears a strong behavior that can be modeled by a full quadratic equation. However, the data also shows that the dependency of the model is strongly correlated with the datasets chosen to produce it, with number of replicates and replicate values both resulting in differences in each model’s predictive reliability (e.g., 82% vs 91%). Therefore, while this thesis demonstrates the ability to model IIFK hydrogel behaviour with high predictability ratings, it also establishes the necessity of both producing more replicates as well as selecting the best values for IIFK-based hydrogel modelling.

With video data dominating the internet traffic, it is crucial to develop automated models that can analyze and understand what humans do in videos. Such models must solve tasks such as action classification, temporal activity localization, spatiotemporal action detection, and video captioning. This dissertation aims to identify the challenges hindering the progress in human action understanding and propose novel solutions to overcome these challenges. We identify three challenges: (i) the lack of tools to systematically profile algorithms' performance and understand their strengths and weaknesses, (ii) the expensive cost of large-scale video annotation, and (iii) the prohibitively large memory footprint of untrimmed videos, which forces localization algorithms to operate atop precomputed temporally-insensitive clip features. To address the first challenge, we propose a novel diagnostic tool to analyze the performance of action detectors and compare different methods beyond a single scalar metric. We use our tool to analyze the top action localization algorithm and conclude that the most impactful aspects to work on are: devising strategies to handle temporal context around the instances better, improving the robustness with respect to the instance absolute and relative size, and proposing ways to reduce the localization errors. Moreover, our analysis finds that the lack of agreement among annotators is not a significant roadblock to attaining progress in the field. We tackle the second challenge by proposing novel frameworks and algorithms that learn from videos with incomplete annotations (weak supervision) or no labels (self-supervision). In the weakly-supervised scenario, we study the temporal action localization task on untrimmed videos where only a weak video-level label is available. We propose a novel weakly-supervised method that uses an iterative refinement approach by estimating and training on snippet-level pseudo ground truth at every iteration. In the self-supervised setup, we study learning from unlabeled videos by exploiting the strong correlation between the visual frames and the audio signal. We propose a novel self-supervised method that leverages unsupervised clustering in one modality (e.g., audio) as a supervisory signal for the other modality (e.g., video). This cross-modal supervision helps our model utilize the semantic correlation and the differences between the two modalities, resulting in the first self-supervised learning method that outperforms large-scale fully-supervised pretraining for action recognition on the same architecture. Finally, the third challenge stems from localization methods using precomputed clip features extracted from video encoders typically trained for trimmed action classification tasks. Such features tend to be temporally insensitive, i.e., background (no action) segments can have similar representations to foreground (action) segments from the same untrimmed video. These temporally-insensitive features make it harder for the localization algorithm to learn the target task and thus negatively impact the final performance. We propose to mitigate this temporal insensitivity through a novel supervised pretraining paradigm for clip features that not only trains to classify activities but also considers background clips and global video information.

Oxidative coupling of methane (OCM) represents a potentially viable method to convert methane directly into more desirable products such as ethane, and ethylene. In this dissertation, a comprehensive kinetic study of oxidative coupling of methane was performed over La2O3-based catalysts. An accurate and reliable gas-phase model is critical for the entire mechanism. The gas-phase kinetics was first studied using a jet-stirred reactor without catalyst. Both experiments and simulations were conducted under various operating conditions using different gas-phase models. Quantities of interest and rate of production analyses on hydrocarbon products were also performed to evaluate the models. NUIGMech1.1 was selected as the most comprehensive model to describe the OCM gas-phase kinetics and used for the next study. Next, microkinetic analysis on La2O3-based catalysts with different dopants was performed. The Ce addition has the greatest boost over the performance. The kinetics at low conversion regimes were analyzed and correlated to the catalysts’ properties. The activation energy for methane hydrogen abstraction was estimated, with the formation rate of primary products, which suggested that the initiation reaction steps were similar for La2O3-based catalyst. A homogeneous-heterogeneous kinetic model for La2O3/CeO2 catalyst was then constructed. By applying in situ XRD, the doping of CeO2 not only enhanced catalytic performance but also improved catalyst stability from CO2 and H2O. A wide range of operating conditions was investigated experimentally and numerically, where a packed bed reactor model was constructed based on the dimensions of experimental setup and catalyst characterization. The rate of production (ROP) was also performed to identify the important reactions and prove the necessity of surface reactions for the OCM process. Laser-induced fluorescence was implemented to directly observe the presence of formaldehyde. The last section includes the implementation of in situ laser diagnosis techniques at the near-surface region to solve the existing challenges. Raman scattering was implemented to quantitate the concentration profiles of major stable species near the surface and measure the in situ local temperatures at different heights above the catalyst surface, to study the kinetics transiting from the surface edge to the near-surface gas phase and provide a new perspective in OCM kinetic studies.