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Similarity Problems: Which Groups Are Unitarizable?
(20240820)This thesis covers some theory on similarity of group representations to unitary representations. We discuss the notion of amenability and give some classes of groups that are amenable. We then prove the DixmierDay ... 
Efficient Implementation of the 3D Helmholtz equation in C++/PETSc
(20240812)The paper describes the comparison of different preconditioners for the solution of the Helmholtz equation with Krylov subspace methods in three dimensions. The solution of this equation has applications in microwave ... 
Prime number races
(20240812)In this thesis we investigate the behaviour of primes in arithmetic progressions, with a focus on the phenomenon known as Chebyshev’s bias. Under the assumption of the Generalized Riemann Hypothesis and the Linear ... 
Point Process Learning estimation of bandwidth selection for the pair correlation function.
(20240812)In this master thesis I use the newly developed method of Point Process Learning (PPL) to select the bandwidth used when estimating the Pair correlation function with kernel estimation. The selection of bandwidth when ... 
Tensor products of Leavitt algebras
(20240812)We outline the construction of the Leavitt algebras Ln, and prove that L2 ⊗L2 is not isomorphic to L2 by using Hochschild homology. 
Entropic Proximal Gradient Method for Generalized Optimal Transport Problems
(20240812)Optimal transport, a fundamental problem in applied mathematics, involves finding the most efficient way to move mass from multiple sources to multiple destinations. Previously known approaches employ entropic regularization ... 
Optimisation and Sampling Strategies for Bayesian MixedEffects Models: A comparative study
(20240812)In this thesis we investigate, and compare, the efficiency of both stochastic optimisation using stochastic automatic differentiation (SAD) and Bayesian sampling using Metropolis Hastings algorithms for parameter ... 
Dilaton Theory and some of its Applications
(20240704)The purpose of this thesis is to explain some results in dilation theory. In this regard, it has been given the principal results and ideas on positive maps and dilation theory such as Nagy’s theorem, von Neumann’s ... 
Quantum Graphs: Different Perspectives
(20240704)In this thesis, we investigate two different notions of quantum graphs. The first approach is through quantum adjacency matrices, while, the second approach is through bimodules over finitedimensional algebras. We ... 
Data Augmentation for Point Process Learning
(20240703)This thesis introduces and evaluates ideas for the use of data augmentation in the area of Point Process Learning. Motivated by the regularizing effect of training with augmented data sets, we create a followup work to ... 
Point Process Learning estimation of bandwidth selection for the pair correlation function
(20240625)In this master thesis I use the newly developed method of Point Process Learning (PPL) to select the bandwidth used when estimating the Pair correlation function with kernel estimation. The selection of bandwidth when ... 
Lowlying zeroes of Lfunctions attached to modular forms
(20240322)We study the family of Lfunctions attached to Hecke newforms of weight k and level N and their lowlying zeroes. First, we recall the Density Conjecture of Katz and Sarnak and how it predicts the behaviour of the lowlying ... 
Reconstructing point patterns from spatially aggregated data
(20240313)In this thesis we explore the ability to reconstruct samples (point configurations) from a point process, based only on the information contained in spatially aggregated data, namely the number of points in the partitions ... 
Do viscous flows slip?
(20231221)In this thesis, the Stokes equation is discussed and solved under different boundary conditions. The Stokes equation governs the flow of viscous liquids, for example honey or syrup. The first chapters in the thesis ... 
Audio Anomaly Detection in Cars
(20230911)Audio anomaly detection in the context of car driving is a crucial task for ensuring vehicle safety and identifying potential faults. This paper aims to investigate and compare different methods for unsupervised audio ... 
Spatiotemporal analysis of COVID19 in Västra Götaland, Sweden
(20230823)Spatiotemporal analysis of COVID19 data with the two different statistical approaches is the main objective of this thesis. The first classical approach, the EndemicEpidemic framework (Held et al., 2005) is a class of ... 
Regulatory Driven Clustering of SingleCell Data; Clustering of singlecell RNA sequencing from glioblastoma with a novel mathematical method
(20230808)Cancer is a leading cause of death worldwide. Singlecell RNA sequencing has arisen as an important method to explore the gene expression of biological cells, including cancer cells. In this study, we deployed a computational ... 
Credit Card Fraud Detection by Nearest Neighbor Algorithms
(20230413)As the usage of internet banking and online purchases have increased dramatically in today’s world, the risk of fraudulent activities and the number of fraud cases are increasing day by day. The most frequent type of ... 
Point process learning for nonparametric intensity estimation with focus on Voronoi estimation
(20230328)Point process learning is a new statistical theory that gives us a way to estimate parameters using crossvalidation for point processes. By thinning a point pattern we are able to create training and validation sets ... 
The lowlying zeros of Lfunctions associated to nonGalois cubic fields
(20230213)We study the lowlying zeros of Artin Lfunctions associated to nonGalois cubic number fields through their one and twolevel densities. In particular, we find new precise estimates for the twolevel density with a ...