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- PostThe low-lying zeros of L-functions associated to non-Galois cubic fields(2023) Ahlquist, Victor; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Brandes, Julia; Södergren, AndersWe study the low-lying zeros of Artin L-functions associated to non-Galois cubic number fields through their one- and two-level densities. In particular, we find new precise estimates for the two-level density with a power-saving error term. We apply the L-functions Ratios Conjecture to study these densities for a larger class of test functions than unconditional computations allow. By reviewing a known Ratios Conjecture prediction, due to Cho, Fiorilli, Lee, and Södergren, for the one-level density, we isolate a phase transition in the lower-order terms, which reveals a striking symmetry. Our computations show that the same symmetry exists in the one-level density of several other families, that have previously been studied in the literature, and this motivates us to formulate a conjecture extending one part of the Katz–Sarnak prediction for families of symplectic symmetry type. Moreover, we isolate several phase transitions in the lower-order terms of the two-level density. To the best of our knowledge, this is the first time such phase transitions have been observed in any n-level density with n ≥ 2.
- PostPrediction of mass transport properties in 3D microstructures using 2D CNNs(2022) Valdimarsson, Sævar Óli; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Särkkä, Aila; Röding, MagnusPorous materials and the relationship between their 3D microstructure and their mass transport properties is of interest in multiple fields. To analyse this relationship and build an understanding of it requires a great quantity of data, but obtaining experimental 3D data is difficult and expensive. An alternative is to generate virtual microstructures and simulate their mass transports, which can then be used to estimate the relationship. 2D experimental data is easier to obtain and work with than 3D experimental data, e.g. it requires less storage space and memory. It is of interest to investigate models that can estimate mass transport properties of 3D microstructures from 2D data. In this work, 2D data is extracted from a pre-existing 3D virtual microstructure dataset and the viability of using 2D convolutional neural networks (CNNs) to predict the mass transport properties is explored. Keywords:
- PostClifford algebras and examples of Dirac operators in two dimensions(2023) Klyver, Markus; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Rosén, Andreas
- PostSolving Problems, One Role at a Time(2023) Dunér, Felix; Johansson, Eric; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Axelson-Fisk, Marina; Dannélls, Dana; Musial, MariuszFor large companies, leveraging internal knowledge and existing information within the organization has proved to be difficult for several reasons. In this thesis, which is conducted in collaboration with Ericsson, an attempt to facilitate the extraction of internal knowledge is made, more specifically by matching new issues that employees face with pre-existing, solved ones. The issues are represented by so-called ‘support tickets’ and partly consist of manually entered text where the user describes the problem. The support process could be optimized by automatically identifying what kind of issue the user experience. This study aims to investigate if it is possible to extract semantic information from the text contained in support tickets through semantic role labeling (SRL), and leverage that information to match similar issues related to Ericsson’s cloud infrastructure branch. SRL is often used for information extraction and question-answering, but not in a technical domain. Two pre-trained SRL models were tested: one based on FrameNet and the other based on PropBank. Eventually, the FrameNet model was used throughout the thesis. After initial preprocessing and standardization of technical jargon, pre-trained stateof- the-art (SOTA) models were used to extract semantic information, and visual analysis and overall statistics supported the idea that they could identify relevant targets in sentences and populate frames with roles accordingly. The information yielded through SRL allowed for new ways of representing the support tickets. However, further experiments with topic modeling and classification indicated that the information produced by the FrameNet SRL model was not useful for grouping support tickets according to the categorizations provided by Ericsson. It is suggested that the FrameNet model may be too general for the specific context and that customization of the semantic framework may be a possible solution. It is also noted that the categorizations used as similarity proxies for the support tickets may be based on information outside of the text used to represent the support tickets. Even though the semantic information yielded through SRL did not improve the ability to match similar support tickets in this case, we firmly believe that these features can be helpful. Since the semantic frames provide information otherwise not present in the text, they should be able to enrich the representation.
- PostChange point detection in financial time series in connection to purchase behaviours(2022) Skytt, Hanna; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Picchini, Umberto; Schauer, MoritzUnderstanding purchase behaviours of individuals is of interest when the goal is to inspire people to make more environmentally friendly choices. A company with these aspirations is Svalna AB. They have created an app that uses a carbon calculator to give an insight into greenhouse gas emissions based on financial transactions. The aim of this thesis has been to investigate purchase behaviours by comparing the underlying distributions before and after a change point has occurred. This thesis has focused on change point detection in time series using the Metropolis-Hastings algorithm. The model, which has been implemented from scratch, has been tested on well-behaved simulated time series and can accurately find a change point. It has then been used to investigate some specific cases in financial time series provided by Svalna. The results from testing on the simulated time series show a promising start and it is concluded that the overall method is a possibility to investigate the underlying distributions of financial time series.