4D Flow Magnet Resonance Imaging (4D Flow MRI) is a novel non-invasive technique for imaging of cardiovascular blood flow. However, when utilized as a stand-alone analysis method, 4D Flow MRI has certain limitations including limited spatial resolution and noise artefacts, motivating the application of dedicated post-processing tools. Learning based super-resolution (SR) has here emerged as a promising utility for such work, however, more often than not, these efforts have been constricted to a narrowly defined cardiovascular domain. Rather, there has been limited exploration of how learned super-resolution models perform across \emph{multiple} cardiovascular compartments, with the wide range of hemodynamic compartments covered by the cardiovasculature as an apparent challenge. To address this, we investigate the generalizability of 4D Flow MRI super-resolution using ensemble learning. Our investigation employs ensemble learning techniques, specifically bagging and stacking, with a convolutional neural network (4DFlowNet) serving as the framework for all base learners. To assist in training, synthetic training data was extracted from patient-specific, physics-based velocity fields derived from computational fluid dynamic (CFD) simulations conducted in three key compartments: the aorta, brain and the heart. Varying base and ensemble networks were then trained on pairs of high-resolution and low-resolution synthetic data, with performance quantitatively assessed as a function of cardiovascular domain, and specific architecture. To ensure clinical relevance, we also evaluated model performance on clinically acquired MRI data from the very same three compartments.  We find that ensemble models improve performance, as compared to isolated equivalents. Our ensemble model \textit{Stacking Block-3}, improves in-silico error rate by $16.22$ points across the average domain. Additionally, performance on the aorta, brain and heart improves by $2.66$, $5.81$ and $2.00$ points respectively. Employing both qualitative and quantitative evaluation methods on the in-vivo data, we find that ensemble models produce super-resolved velocity fields that are quantitatively coherent with ground truth reference data and visually pleasing. To conclude, ensemble learning has shown potential in generalizing 4D Flow MRI across multiple cardiovascular compartments.

The nuclear pore complex (NPC) is a proteinaceous gateway embedded in the nuclear envelope (NE) that regulates nucleocytoplasmic transport of molecules in eukaryotes. The NPC is formed by hundreds of proteins that are classified into approximately thirty different types of proteins called nucleoporin (Nup), each presents in multiples of eight copies. These nucleoporins are divided into two categories: the scaffold Nups forming the main structure of the NPC and the phenylalanine-glycine (FG) Nups that contain multiple repeats of intrinsically disordered and hydrophobic FG domains. These FG-Nups constitute the selective permeability barrier in the central channel of the NPC, which mediates the nuclear import of proteins into the nucleus, and the nuclear export of mRNA and pre-ribosomal subunits out of the nucleus. However, the precise copies of these Nups and their specific roles in the nucleocytoplasmic transport mechanism remain largely unknown. Moreover, the dysfunctional nuclear transport and the mutations of Nups have been closely associated with numerous human diseases, such as cancer, tumor and liver cirrhosis. We have developed and employed live-cell high-speed single-molecule microscopy to elucidate these critical questions remained in the nuclear transport and provide the fundamental knowledge for developing therapies. In this dissertation, I will present my major findings for the following three research projects: 1) determine the dynamic components of FG-Nups in native NPCs; 2) track the nucleocytoplasmic transport of transcription factor Smad proteins under ligand-activated conditions; and 3) elucidate the relationship between the nuclear export of mRNA and the presence and absence of specific Nups in live cells.Determination of the dynamic components for FG-Nups in native NPCs. Scaffold Nups have been intensively studied with electron microscopy to reveal their spatial positions and architecture in the past decades. However, the spatial organization of FG-Nups remains obscure due to the challenge of probing these disordered and dynamic polypeptides in live NPCs. By employing high-speed single-molecule microscopy and a live cell HaloTag labeling technique, I have mapped the spatial distribution for all eleven known mammalian FG-Nups within individual NPCs. Results show that all FG-Nups within NPCs are distinct in conformations and organized to form a ~300nm long hourglass shaped toroidal channel through the nuclear envelope. Exceptionally, the two remaining Nups (Nup98 and hCG1) almost extend through the entire NPC and largely overlap with all other FG-Nups in their spatial distributions. These results provide a complete map of FG-Nup organization within the NPC and also offer structural and functional insights into nucleocytoplasmic transport models. Tracking of the nucleocytoplasmic transport of Smad proteins under ligand-activated conditions. The inducement of transforming growth factor β1 (TGF-β1) was reported to cause the nuclear accumulation of Smad2/Smad4 heterocomplexes. However, the relationship between nuclear accumulation and the nucleocytoplasmic transport kinetics of Smad proteins in the presence of TGF-β1 remains obscure. By combining a high-speed single-molecule tracking microscopy technique (FRET), I tracked the entire TGF-β1-induced process of Smad2/Smad4 heterocomplex formation, as well as their transport through nuclear pore complex in live cells. The FRET results have revealed that in TGF-β1-treated cells, Smad2/Smad4 heterocomplexes formed in the cytoplasm, imported through the nuclear pore complexes as entireties, and finally dissociated in the nucleus. Moreover, it was found that basal-state Smad2 or Smad4 cannot accumulate in the nucleus without the presence of TGF-β1, mainly because both of them have an approximately twofold higher nuclear export efficiency compared to their nuclear import. Remarkably and reversely, heterocomplexes of Smad2/Smad4 induced by TGF-β1 can rapidly concentrate in the nucleus because of their almost fourfold higher nuclear import rate in comparison with their nuclear export rate. Thus, these single-molecule tracking data elucidate the basic molecular mechanism to understand nuclear transport and accumulation of Smad protein. Elucidation of the relationship between the nuclear export of mRNA and the presence and absence of specific Nups in live cells. In addition to explore the dynamic organization of NPC, in vivo characterization of the exact copy number and the specific function of each nucleoporin in the nuclear pore complex (NPC) remains desirable and challenging. Using live-cell high-speed super-resolution single-molecule microscopy, we first quantify the native copies of nuclear basket FG-Nups (Nup153, Nup50 and Tpr). Second, with same imaging technique and the auxin-inducible degradation strategies, I track the nuclear export of mRNA through native NPCs in absence of these FG-Nups. I found that these FG-Nups proteins possess the stoichiometric ratio of 1:1:1 and play distinct roles in the nuclear export of mRNAs in live cells. Tpr’s absence in the NPC dominantly reduces nuclear mRNA’s probability of entering the NPC for export. Complete depletion of Nup153 causes mRNA’s successful nuclear export efficiency dropped approximately four folds. Remarkably, the relationship between mRNA’s successful export efficiency and the copy number of Nup153 is not linear but instead follows a sigmoid function, in which mRNA can gain its maximum successful export efficiency as Nup153 increased from zero to around half of their full copies in the NPC. Lastly, the absence of Tpr or Nup153 also alters mRNA’s export routes through the NPC, but the removal of only Nup50 has almost no impact upon mRNA export route and kinetics. / Biology

The investigation of positive steady states to reaction diffusion models in bounded domains with Dirichlet boundary conditions has been of great interest since the 1960’s. We study reaction diffusion models where the reaction term is negative at the origin. In the literature, such problems are referred to as semipositone problems and have been studied for the last 30 years. In this dissertation, we extend the theory of semipositone problems to classes of singular semipositone problems where the reaction term has singularities at certain locations in the domain. In particular, we consider problems where the reaction term approaches negative infinity at these locations. We establish several existence results when the domain is a smooth bounded region or an exterior domain. Some uniqueness results are also obtained. Our existence results are achieved by the method of sub and super solutions, while our uniqueness results are proved by establishing a priori estimates and analyzing structural properties of the solution. We also extend many of our results to systems.

In this dissertation, we establish new existence, multiplicity, and uniqueness results on positive radial solutions for classes of steady state reaction diffusion equations on the exterior of a ball. In particular, for the first time in the literature, this thesis focuses on the study of solutions that satisfy a general class of nonlinear boundary conditions on the interior boundary while they approach zero at infinity (far away from the interior boundary). Such nonlinear boundary conditions occur naturally in various applications including models in the study of combustion theory. We restrict our analysis to reactions terms that grow slower than a linear function for large arguments. However, we allow all types of behavior of the reaction terms at the origin (cases when it is positive, zero, as well as negative). New results are also added to ecological systems with Dirichlet boundary conditions on the interior boundary (this is the case when the boundary is cold). We establish our existence and multiplicity results by the method of sub and super solutions and our uniqueness results via deriving a priori estimates for solutions.

Covariant density functional theory (CDFT) is a modern theoretical tool for the description of nuclear structure physics. Here different physical properties of the ground and excited states in atomic nuclei have been investigated within the CDFT framework employing three major classes of the state-of-the-art covariant energy density functionals. The global performance of CEDFs for even-even nuclei are investigated and the systematic theoretical uncertainties are estimated within the set of four CEDFs in known regions of the nuclear chart and their propagation towards the neutron drip line. Large-scale axial relativistic Hartree-Bogoliubov (RHB) calculations are performed for even-even nuclei to calculate different ground state observabvles. The predictions for the two-neutron drip line are also compared in a systematic way with the non-relativistic results. CDFT has been applied for systematic study of extremely deformed, rotating N ∼ Z nuclei of the A ∼ 40 mass region. At spin zero such structures are located at high energies which prevents their experimental observation. The rotation acts as a tool to bring these exotic shapes down to the yrast line so that their observation could become possible with a future generation detectors such as GRETA or AGATA. The major physical observables of such structures, the underlying single-particle structure and the spins at which they become yrast or near yrast are defined. The search for the fingerprints of clusterization and molecular structures is performed and the configurations with such features are discussed. CDFT has been applied to study fission barriers of superheavy nuclei and related systematic theoretical uncertainties in the predictions of inner fission barrier heights in superheavy elements. Systematic uncertainties are substantial in superheavy elements and their behavior as a function of proton and neutron numbers contains a large random component. The benchmarking of the functionals to the experimental data on fission barriers in the actinides allows reduction of the systematic theoretical uncertainties for the inner fission barriers of unknown superheavy elements. However, even then they on average increase when moving away from the region where benchmarking has been performed.

A process for the use of multihypothesis prediction in the reconstruction of images is proposed for use in both compressed-sensing reconstruction as well as single-image super-resolution. Specifically, for compressed-sensing reconstruction of a single still image, multiple predictions for an image block are drawn from spatially surrounding blocks within an initial non-predicted reconstruction. The predictions are used to generate a residual in the domain of the compressed-sensing random projections. This residual being typically more compressible than the original signal leads to improved compressed-sensing reconstruction quality. To appropriately weight the hypothesis predictions, a Tikhonov regularization to an ill-posed least-squares optimization is proposed. An extension of this framework is applied to the compressed-sensing reconstruction of hyperspectral imagery is also studied. Finally, the multihypothesis paradigm is employed for single-image superresolution wherein each patch of a low-resolution image is represented as a linear combination of spatially surrounding hypothesis patches.

In this thesis we study two reaction-diffusion models that have been used to analyze the existence of alternate stable states in ecosystems. The first model describes the steady states of a logistic growth model with grazing in a spatially homogeneous ecosystem. It also describes the dynamics of the fish population with natural predation. The second model describes phosphorus cycling in stratified lakes. The same equation has also been used to describe the colonization of barren soils in drylands by vegetation. In this study we discuss the existence of multiple positive solutions, leading to the occurrence of S-shaped bifurcation curves. We were able to show that both the models have alternate stable states for certain ranges of parameter values. We also introduce a constant yield harvesting term to the first model and discuss the existence of positive solutions including the occurrence of a Sigma-shaped bifurcation curve in the case of a one-dimensional model. Again we were able to establish that for certain ranges of parameter values the model has alternate stable states. Thus we establish analytically that the above models are capable of describing the phenomena of alternate stable states in ecological systems. We prove our results by the method of sub-super solutions and quadrature method.

No description available.

Game engines such as Unreal Engine 5 are widely used to create photo-realistic renderings. To run these renderings at high quality without experiencing any performance issues,high-performance hardware is often required. In situations where the hardware is lacking,users may be forced to lower the quality and resolution of renderings to maintain goodperformance. While this may be acceptable in some situations, it limits the benefit that apowerful tool like Unreal Engine 5 can provide. This thesis aims to explore the possibilityof using a Real-ESRGAN, fine-tuned on a custom data set, to increase both the resolutionand quality of screenshots taken in Unreal Engine 5. By doing this, users can lower theresolution and quality of their Unreal Engine 5 rendering while still being able to generatehigh quality screenshots similar to those produced when running the rendering at higherresolution and higher quality. To accomplish this, a custom data set was created by randomizing camera positionsand capturing screenshots in an Unreal Engine 5 rendering. This data set was used to finetune a pre-trained Real-ESRGAN model. The fine-tuned model could then generate imagesfrom low resolution and low quality screenshots taken in Unreal Engine 5. The resultingimages were analyzed and evaluated using both quantitative and qualitative methods.The conclusions drawn from this thesis indicate that images generated using the finetuned weights are of high quality. This conclusion is supported by quantitative measurements, demonstrating that the generated images and the ground truth images are similar.Furthermore, visual inspection conducted by the authors confirms that the generated images are similar to the reference images, despite occasional artifacts.

Deeper understanding of character gameplay identity is crucial for designers in an industry where crossover content is more commonplace than ever. Despite its relevance, however, research in the field of game design has yet to be widely conducted on character gameplay identity. Consequently, this study explores how a character’s gameplay identity is preserved across genres through the use of gameplay mechanics. This was achieved by using Pokémon Trainer as a case study, examining how they were adapted from the Pokémon games into the Super Smash Bros. games. By analysing gameplay and select online sources, we conducted a close reading of the Pokémon Trainer, granting insight into the various mechanics that the game designers use to retain the character’s gameplay identity. We have broken these mechanics down into systems, which we then analysed and categorised according to systems theory, giving further insight into the nature of gameplay systems. The results from our analyses show that understanding a character’s gameplay identity can be adapted through multiple different types of gameplay mechanics, and that systems theory is a useful tool to categorise different types of gameplay mechanics.