Department of Mathematical Sciences / Institutionen för matematiska vetenskaper
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Enabling mechanistic understanding of cellular dynamics through mathematical modelling and development of efficient methods
(2024-11-13)Cell biology is complex, but unravelling this complexity is important. For example, the recent COVID-19 pandemic highlighted the need to understand how cells function in order to develop efficient vaccines and treatments. ... -
Yeast at the Crossroads: Nutrient Signalling Paths and Stressful Turns
(2024-11-11)Nutrients serve essential functions as building blocks for cellular components. Intriguingly, they serve as signalling elements that control basic cellular functions. In microorganisms such as Saccharomyces cerevisiae, ... -
Hodge Theory in Combinatorics and Mirror Symmetry
(2024-10-22)Hodge theory, in its broadest sense, encompasses the study of the decomposition of cohomology groups of complex manifolds, as well as related fields such as periods, motives, and algebraic cycles. In this thesis, ideas ... -
Extreme rainfall modelling under climate change and proper scoring rules for extremes and inference
(2024-09-06)Model development, model inference and model evaluation are three important cornerstones of statistical analysis. This thesis touches on all these through modelling extremes under climate change and evaluating extreme ... -
Unsupervised methods for integrative data analysis
(2024-05-17)Unsupervised data analysis methods are important for data exploration to introduce structure, reduce data dimensions, or extract interpretable knowledge. Integrative analysis of two or more data sets is crucial to gain ... -
Sharp bounds on the height of some arithmetic Fano varieties
(2023)In the framework of Arakelov geometry one can define the height of a polarized arithmetic variety equipped with an hermitian metric over its complexification. When the arithmetic variety is Fano, the complexification is ... -
New AI-based methods for studying antibiotic-resistant bacteria
(2023-11-03)Antibiotic resistance is a growing challenge for human health, causing millions of deaths worldwide annually. Antibiotic resistance genes (ARGs), acquired through mutations in existing genes or horizontal gene transfer, ... -
Efficient training of interpretable, non-linear regression models
(2023-06-30)Regression, the process of estimating functions from data, comes in many flavors. One of the most commonly used regression models is linear regression, which is computationally efficient and easy to interpret, but lacks ... -
The influence of numbers when students solve equations
(2023)Is it possible that some students’ primary difficulty with equation-solving is neither handling the literal symbols nor the equality, but the numbers used as coefficients? It is well known that many students find algebra ... -
Numerical approximation of mixed dimensional partial differential equations
(2023)In this thesis, we explore numerical approximation of elliptic partial differential equations posed on domains with a high number of interfaces running through. The finite element method is a well-studied numerical method ... -
Limit Theorems for Lattices and L-functions
This PhD thesis investigates distributional questions related to three types of objects: Unimodular lattices, symplectic lattices, and Hecke L-functions of imaginary quadratic number fields of class number 1. In Paper ... -
Sketches of Noncommutative Topology
(2022-11-07)This thesis thematically divided into two parts. In the first part we are mastering C*-isomorphism problem by using various techniques applied to different examples of noncommutative algebraic varieties. In the second part ... -
Global residue currents and the Ext functors
(2022-09-09)This thesis concerns developments in multivariable residue theory. In particular we consider global constructions of residue currents related to work by Andersson and Wulcan. In the first paper of this thesis, we consider ... -
Mathematical Modelling of Cellular Ageing: a Multi-Scale Perspective
(2022-04-19)In a growing and increasingly older population, we are progressively challenged by the impact of ageing on individuals and society. The UN declared the years 2021-2030 as the Decade of Healthy Ageing, highlighting the ... -
On the mathematics of the one-dimensional Hegselmann-Krause model
(2022-01-19)This thesis contains three papers, which all in different ways concern the asymptotics of the Hegselmann-Krause model in opinion dynamics. In this model a set of conformist agents repeatedly and synchronously replace their ... -
Combinatorics of solvable lattice models with a reflecting end
(2021-04-21)I den här avhandlingen studerar vi några exakt lösbara, kvantintegrerbara gittermodeller. Izergin bevisade en determinantformel för partitionsfunktionen till sexvertexmodellen på ett gitter av storlek n × n med Korepins ... -
Network modeling and integrative analysis of high-dimensional genomic data
(2020-05-07)Genomic data describe biological systems on the molecular level and are, due to the immense diversity of life, high-dimensional. Network modeling and integrative analysis are powerful methods to interpret genomic data. ... -
The construction, analysis and validation of mechanistic mathematical models of protein kinetics in the context of replicative ageing in budding yeast
(2020-05-04)Mathematical modelling constitutes a forceful tool for elucidating properties of biological systems. Using theoretical approaches in combination with experimental techniques it is possible to study specific molecular aspects ... -
Geometrical and percolative properties of spatially correlated models
(2020-03-10)This thesis consists of four papers dealing with phase transitions in various models of continuum percolation. These models exhibit complicated dependencies and are generated by different Poisson processes. For each such ...
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