We are developing theoretical and computational methods to study two related three-body processes in ultracold quantum gases: three-body resonances and three-body recombination. Three-body recombination causes the ultracold gas to heat up and atoms to leave the trap where they are confined. Therefore, it is an undesirable effect in the process of forming ultracold quantum gases. Metastable three-body states (resonances) are formed in the ultracold gas. When decaying they also give additional kinetic energy to the gas, that leads to the heating too. In addition, a reliable method to obtain three-body resonances would be useful in a number of problems in other fields of physics, for example, in models of metastable nuclei or to study dissociative recombination of H3 +. Our project consists of employing computer modeling to develop a method to obtain three-body resonances. The method uses a novel two-step diagonalization approach to solve the three-body Schrödinger equation. The approach employs the SVD method of Tolstikhin et al. coupled with a complex absorbing potential. We tested this method on a model system of three identical bosons with nucleon mass and compared it to the results of a previous study. This model can be employed to understand the 3He nucleus . We found one three-body bound state and four resonances. We are also studying Efimov resonances using a 4He-based model. In a system of identical spinless bosons, Efimov states are a series of loosely bound three-body states which begin to appear as the energy of the two-body bound state approaches zero . Although they were predicted 35 years ago, recent evidence of Efimov states found by Kraemer et al. in a gas of ultracold Cs atoms has sparked great interest by theorists and experimentalists. Efimov resonances are a kind of pre-dissociated Efimov trimer. To search for Efimov resonances we tune the diatom interaction potential, V(r): V(r) → λV(r) as Esry et al. did . We calculated the first two values of λ for which there is a "condensation" (infinite number) of Efimov states. They are λEfimov1 = 0.9765 and λEfimov2 = 6.834. We performed calculations for λ = 2.4, but found no evidence of Efimov resonances. For future work we plan to work with λ ≈ 4 and λ ≈ λEfimov2 where we might see d-wave and higher l-wave Efimov resonances. There is also a many-body project that forms part of this thesis and consists of a direct diagonalization of the Bogolyubov Hamiltonian, which describes elementary excitations of a gas of bosons interacting through a pairwise interaction. We would like to reproduce the corresponding energy spectrum. So far we have performed several convergence tests, but have not observed the desired energy spectrum. We show preliminary results.

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The goal of this project is to find a suitable Few-Shot Learning (FSL) model that can be used in a fault detection system for use in an industrial setting. A dataset of Printed Circuit Board (PCB) images has been created to train different FSL models. This dataset is meant for evaluating FSL models in the specialized setting of fault detection in PCB manufacturing. FSL is a part of deep learning that has seen a large amount of development recently. Few-shot learning allows neural networks to learn on small datasets. In this thesis, various state-of-the-art FSL algorithms are implemented and tested on the custom PCB dataset. Different backbones are used to establish a benchmark for the tested FSL algorithms on three different datasets. Those datasets are ImageNet, PCB Defects, and the created PCB dataset. Our results show that ProtoNets combined with ResNet12 backbone achieved the highest accuracy in two test scenarios. In those tests, the model combination achieved 87.20%and 92.27% in 1-shot and 5-shot test scenarios, respectively. This thesis presents a Few-Shot Anomaly Detection (FSAD) model based on Vision Transformers (ViT). The model is compared to the state-of-the-art FSAD model DevNet on the MVTec-AD dataset. DevNet and ViT are chosen for comparison because they both approach the problem by dividing images into patches. How the models handle the image patches is however very different. The results indicate that ViT Deviation does not obtain as high AUC-ROC and AUC-PR scores as DevNet. This is because of the use of the very deep ViT architecture in the ViT Deviation model. A shallower transformer-based model is believed to be better suited for FSAD. Improvements for ViT Deviation are suggested for future work. The most notable suggested improvement is the use of the FS-CT architecture as a FSAD model because of the high accuracy it achieves in classification. / Målet med detta projekt är att hitta en lämplig Few-Shot Learning(FSL) modell som kan användas i ett feldetekteringssystem för användning i en industriell miljö. Ett dataset av Printed Circuit Board(PCB) bilder har skapats för att träna olika FSL-modeller. Detta datasetär avsedd för att utvärdera FSL-modeller i det specialiserade områdetfeldetektering vid PCB-tillverkning. FSL är en del av djupinlärningsom har utvecklats mycket den senaste tiden. FSL tillåter neuralanätverk att lära sig på små datamängder.I detta examensarbete implementeras och testas olika state-of-theart FSL algoritmer på det anpassade PCB-datasetet. Olika ryggradsmodeller används för att upprätta ett riktmärke för de testade FSL-algoritmernapå tre olika dataset. Dessa dataset är ImageNet[6], PCB Defects[14]och det skapade PCB-datasetet. Våra resultat visar att ProtoNets ikombination med ResNet12-ryggraden uppnådde den högsta noggrannheten i två testscenarier. I dessa tester uppnådde modellkombinationen 87,20% och 92,27% i testscenarier med 1-shot respektive5-shot.Detta examensarbete presenterar en Few-Shot Anomaly Detectionmodell (FSAD) baserad på Vision Transformers (ViT). Modellen jämförs med FSAD-modellen DevNet på MVTec-AD-datasetet. DevNetoch ViT väljs för jämförelse eftersom de båda angriper problemetgenom att dela upp bilder i mindre lappar. Hur modellerna hanterarlapparna är dock väldigt olika. Resultaten indikerar att ViT-Deviationinte får lika hög AUC-ROC och AUC-PR som DevNet. Detta beror påanvändningen av den mycket djupa ViT-arkitekturen i ViT Deviationmodellen. En grundare ViT-baserad modell tros vara bättre lämpadför FSAD. Förbättringar för ViT-Deviation föreslås för framtida arbete.Den mest anmärkningsvärda föreslagna förbättringen är användningen av FS-CT-arkitekturen som en FSAD-modell på grund av de lovande resultaten den uppnår i klassificering.

This thesis investigates the possibility of efficiently adapting self-supervised representation learning on visual domains beyond natural scenes, e.g., medical imagining and non-RGB sensory images. The thesis contributes to i) formalizing the self-supervised representation learning paradigm in a unified conceptual framework and ii) proposing the hypothesis based on supervision signal from data, called data-prior. Method adaptations following the hypothesis demonstrate significant progress in downstream tasks performance on microscopic histopathology and 3-dimensional particle management (3DPM) mining material non-RGB image domains. Supervised learning has proven to be obtaining higher performance than unsupervised learning on computer vision downstream tasks, e.g., image classification, object detection, etc. However, it imposes limitations due to human supervision. To reduce human supervision, end-to-end learning, i.e., transfer learning, remains proven for fine-tuning tasks but does not leverage unlabeled data. Representation learning in a self-supervised manner has successfully reduced the need for labelled data in the natural language processing and vision domain. Advances in learning effective visual representations without human supervision through a self-supervised learning approach are thought-provoking. This thesis performs a detailed conceptual analysis, method formalization, and literature study on the recent paradigm of self-supervised representation learning. The study’s primary goal is to identify the common methodological limitations across the various approaches for adaptation to the visual domain beyond natural scenes. The study finds a common component in transformations that generate distorted views for invariant representation learning. A significant outcome of the study suggests this component is closely dependent on human knowledge of the real world around the natural scene, which fits well the visual domain of the natural scenes but remains sub-optimal for other visual domains that are conceptually different. A hypothesis is proposed to use the supervision signal from data (data-prior) to replace the human-knowledge-driven transformations in self-supervised pretraining to overcome the stated challenge. Two separate visual domains beyond the natural scene are considered to explore the mentioned hypothesis, which is breast cancer microscopic histopathology and 3-dimensional particle management (3DPM) mining material non-RGB image. The first research paper explores the breast cancer microscopic histopathology images by actualizing the data-prior hypothesis in terms of multiple magnification factors as supervision signal from data, which is available in the microscopic histopathology images public dataset BreakHis. It proposes a self-supervised representation learning method, Magnification Prior Contrastive Similarity, which adapts the contrastive learning approach by replacing the standard image view transformations (augmentations) by utilizing magnification factors. The contributions to the work are multi-folded. It achieves significant performance improvement in the downstream task of malignancy classification during label efficiency and fully supervised settings. Pretrained models show efficient knowledge transfer on two additional public datasets supported by qualitative analysis on representation learning. The second research paper investigates the 3DPM mining material non-RGB image domain where the material’s pixel-mapped reflectance image and height (depth map) are captured. It actualizes the data-prior hypothesis by using depth maps of mining material on the conveyor belt. The proposed method, Depth Contrast, also adapts the contrastive learning method while replacing standard augmentations with depth maps for mining materials. It outperforms material classification over ImageNet transfer learning performance in fully supervised learning settings in fine-tuning and linear evaluation. It also shows consistent improvement in performance during label efficiency. In summary, the data-prior hypothesis shows one promising direction for optimal adaptations of contrastive learning methods in self-supervision for the visual domain beyond the natural scene. Although, a detailed study on the data-prior hypothesis is required to explore other non-contrastive approaches of recent self-supervised representation learning, including knowledge distillation and information maximization.

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The higher-order modes (HOMs) of an optical fiber has been demonstrated as a new dimension to transmitting signals with the development of mode-division multiplexing (MDM) technique. This dissertation aims to explore the HOMs as an extra degree of freedom for device innovation. In particular, with femtosecond (FS) laser point-by-point (PbP) inscription technique which opens up a unique possibility to explore the HOMs for device innovation, we design, fabricate, and characterize novel-structured fiber Bragg gratings (FBGs) written in the step-index two-mode fibers. We also develop a numerical model for the PbP gratings which has the potential for inverse design problem. Chapter 2 begins with a general framework of MDM with adaptive wavefront shaping in few-mode fibers (FMFs) and multimode fibers (MMFs), followed by two examples in slightly more detail. The fabrication setup and an short overview of the FS laser system will also be covered. In Chapter 3, we show the design, fabrication, and characterization of off-axis Bragg gratings in a step-index two-mode fiber (TMF). Through measuring the transmission and reflection spectra along with the associated reflected mode intensity profiles under different input polarization, we experimentally investigate the off-axis TM-FBGs (FBGs in a TMF) with multiple characteristics reported for the first time to our best knowledge. To highlight, we report the laser-induced birefringence exhibits strong offset dependence, the reflectivity heavily depends on the offset and polarization, and particularly the mode pattern can be controlled solely through polarization. The design and characterization of cross-axis TM-FBGs are presented in Chapter 4. Specifically, these gratings show six primary reflection peaks, which are identified through mode-decomposition based on the intensity profiles through nonlinear optimization problem. We also show in this chapter the development of a numerical model for the general PbP gratings, implementation of this model into standard coupled-wave analysis shows reasonable agreement to the experimental findings. In Chapter 5, discussions and suggestions for future studies are given. / Doctor of Philosophy / The higher-order modes (HOMs) of an optical fiber has been demonstrated as a new space for signal transmission, in the ``mode space'' one can use the modes as distinct multiplexing channel and therefore increase the data capacity of a single fiber. This work aims to explore if the the higher-order modes can also add some extra degree of freedom for device innovation. In particular, we use femtosecond (FS) laser point-by-point (PbP) technique for device fabrication, since the structural change induced by this fabrication methods is highly localized, typically ranging from a few hundred nanometers to a few micrometers. Hence this particular fabrication technique offers a unique possibility of exploiting the HOMs for device innovation. In this work, we fabricate, and characterize fiber Bragg gratings (FBGs) with novel structural designs written within the step-index two-mode fibers, with multiple characteristics reported for the first time as far as we know. We also develop a numerical model for the PbP gratings which has the potential for inverse design problem.

High-resolution micro computed tomography (micro-CT) offers 3D image resolution of 1 um for non-destructive evaluation of various samples. However, the micro-CT performance is limited by several factors. Primarily, scan time is extremely long, and sample dimension is restricted by the x-ray beam and the detector size. The latter is the cause for the well-known interior problem. Recent advancement in image reconstruction, spurred by the advent of compressed sensing (CS) theory in 2006 and interior tomography theory since 2007, offers great reduction in the number of views and an increment in the volume of samples, while maintaining reconstruction accuracy. Yet, for a number of reasons, traditional filtered back-projection based reconstruction methods remain the de facto standard on all manufactured scanners. This work demonstrates that CS based global and interior reconstruction methods can enhance the imaging capability of micro-CT scanners. First, CS based few-view reconstruction methods have been developed for use with data from a real micro-CT scanner. By achieving high quality few-view reconstruction, the new approach is able to reduce micro-CT scan time to up to 1/8th of the time required by the conventional protocol. Next, two new reconstruction techniques have been developed that allow accurate interior reconstruction using just a limited number of global scout views as additional information. The techniques represent a significant progress relative to the previous methods that assume a fully sampled global scan. Of the two methods, the second method uses CS techniques and does not place any restrictions on scanning geometry. Finally, analytic and iterative reconstruction methods have been developed for enlargement of the field of view for the interior scan with a small detector. The idea is that truncated projections are acquired in an offset detector geometry, and the reconstruction procedure is performed through the use of a weighting function / weighted iteration updates, and projection completion. The CS based reconstruction yields the highest image quality in the numerical simulation. Yet, some limitations of the CS based techniques are observed in case of real data with various imperfect properties. In all the studies, physical micro-CT phantoms have been designed and utilized for performance analysis. Also, important guidelines are suggested for future improvements. / Ph. D.

Electromagnetic processes induced by electron scattering off few-nucleon systems are theoretically investigated in the non-relativistic formalism. Non-relativistic one-body nuclear current operators are used with a parametrization of nucleon electromagnetic form factors based on recent experimental nucleon scattering data. Electromagnetic form factors of three-nucleon and four-nucleon systems are calculated from elastic electron-nucleus scattering information. Nuclear response functions used in the determination of differential cross sections for inclusive and exclusive quasi-elastic electron-nucleon scattering from the 4He nucleus are also calculated. Final-state interactions in the quasi-elastic nucleon knockout process are explicitly taken into account using the Glauber approximation. The sensitivity of the response functions to the final-state interactions is investigated. The Antisymmetrized Molecular Dynamics approach with angular momentum and parity projection is employed to construct ground state wave functions for the nuclei. A reduced form of the realistic Argonne V18 nucleon-nucleon potential is used to describe nuclear Hamiltonian. A convenient numerical technique of approximating expectation values of nuclear Hamiltonian operators is employed. The constructed wave functions are used to calculate ground-state energies, root-mean-square radii and magnetic dipole moments of selected light nuclei. The theoretical predictions of the nuclear properties for the selected nuclei give a satisfactory description of experimental values. The Glauber approximation is combined with the Antisymmetrized Molecular Dynamics to generate wave functions for scattering states in quasi-elastic scattering processes. The wave functions are then used to study proton knockout reactions in the 4He nucleus. The theoretical predictions of the model reproduce experimental observation quite well. / Physics / Ph D. (Physics)