Department of Mathematical Sciences / Institutionen för matematiska vetenskaper
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Similarity Problems: Which Groups Are Unitarizable?
(2024-08-20)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 Dixmier-Day ... -
Efficient Implementation of the 3D Helmholtz equation in C++/PETSc
(2024-08-12)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
(2024-08-12)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.
(2024-08-12)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
(2024-08-12)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
(2024-08-12)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 Mixed-Effects Models: A comparative study
(2024-08-12)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
(2024-07-04)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
(2024-07-04)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 finite-dimensional algebras. We ... -
Data Augmentation for Point Process Learning
(2024-07-03)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 follow-up work to ... -
Point Process Learning estimation of bandwidth selection for the pair correlation function
(2024-06-25)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 ... -
Low-lying zeroes of L-functions attached to modular forms
(2024-03-22)We study the family of L-functions attached to Hecke newforms of weight k and level N and their low-lying zeroes. First, we recall the Density Conjecture of Katz and Sarnak and how it predicts the behaviour of the low-lying ... -
Reconstructing point patterns from spatially aggregated data
(2024-03-13)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?
(2023-12-21)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 ... -
Lås upp konstens hemligheter: En jämförelse av intensitetsytor från olika tidsintervall med hjälp av blickspårning och spatiala punktprocesser
(2023-11-28)Ögonrörelser består av fixeringar, korta perioder där ögonen är relativt stilla och tar in eller bearbetar information. Genom att registrera ögonrörelserna av en person som tittar på en tavla kan positioner av fixeringar ... -
Stokastiska modeller för evolution: En studie av fixeringsannolikhet i cancermodeller
(2023-11-28)Cancer är en välkänd och förödande sjukdom som drabbar många personer varje år. Denna sjukdom är svårbehandlad då cancerbehandling främjar evolution av resistens hos cancercellerna, vilket leder till allt mer svårbehandlad ... -
Simuleringsdriven inferens av stokastiska dynamiska system
(2023-11-28)Stokastiska modeller, som ger tillförlitlig och användbar information om ett systems beteende, består ofta av stokastiska differentialekvationer (SDE) vars likelihoodfunktion inte är analytiskt tillgänglig. Mer traditionella ... -
Matematiska modeller och datorberäkningar för ytdiffusion
(2023-11-28)I detta arbete undersöks geometriska flöden och hur dessa kan implementeras numeriskt med fasfältsmodeller. Speciellt ligger fokus på ytdiffusion, som är ett geometriskt flöde där ändliga ytor i andra dimensionen konvergerar ... -
Sfäriska polynom och deras nollställen på sfären
(2023-11-28)Bérard och Helffer visar i artikeln A. Stern’s analysis of the nodal sets of some families of spherical harmonics revisited [BH] på existensen av sfäriska polynom med en känd mängd nodaldomäner, områden som omsluts av ... -
Haarmåttet på en lokalkompakt grupp: Ett bevis från grunden av dess existens och entydighet
(2023-11-28)Syftet med denna rapport är att bevisa att det på varje lokalkompakt grupp finns ett så kallat vänster-Haarmått, och att detta är unikt upp till en multiplikativ konstant. Läsaren antas inte vara förtrogen med varken ...
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