Institutt for matematikk og statistikk
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An Energy Balance Model on an Infinite Line
(Master thesis; Mastergradsoppgave, 20220601)The thesis is an expansion of the work Gerald R. North did in 1975 on an energy balance climate model. By considering a similar model on an infinite line, and allowing the heat diffusion coefficient to vary on the line, more complicated behaviour arose from the model. Much of Norths work was recreated on the infinite lines, but a lot of new discoveries were made. Among what was found were spontaneous ... 
Explainability in subgraphsenhanced Graph Neural Networks
(Journal article; Tidsskriftartikkel; Preprint; Manuskript, 2023)Recently, subgraphsenhanced Graph Neural Networks (SGNNs) have been introduced to enhance the expressive power of Graph Neural Networks (GNNs), which was proved to be not higher than the 1dimensional WeisfeilerLeman isomorphism test. The new paradigm suggests using subgraphs extracted from the input graph to improve the model’s expressiveness, but the additional complexity exacerbates an ... 
Comprehensive uncertainty estimation of the timing of Greenland warmings in the Greenland ice core records
(Journal article; Tidsskriftartikkel; Peer reviewed, 20220620)Paleoclimate proxy records have nonnegligible uncertainties that arise from both the proxy measurement and the dating processes. Knowledge of the dating uncertainties is important for a rigorous propagation to further analyses, for example, for identification and dating of stadial– interstadial transitions in Greenland ice core records during glacial intervals, for comparing the variability in ... 
Weight spectra of Gabidulin rankmetric codes and Betti numbers
(Journal article; Tidsskriftartikkel; Peer reviewed, 20220707)The Helmholtz equation has been used for modeling the sound pressure field under a harmonic load. Computing harmonic sound pressure fields by means of solving Helmholtz equation can quickly become unfeasible if one wants to study many different geometries for ranges of frequencies. We propose a machine learning approach, namely a feedforward dense neural network, for computing the average sound ... 
Kinetic energyfree Hartree–Fock equations: an integral formulation
(Journal article; Tidsskriftartikkel; Peer reviewed, 20220718)We have implemented a selfconsistent feld solver for Hartree–Fock calculations, by making use of Multiwavelets and Multiresolution Analysis. We show how such a solver is inherently a preconditioned steepest descent method and therefore a good starting point for rapid convergence. A distinctive feature of our implementation is the absence of any reference to the kinetic energy operator. This is ... 
Recognition of polar lows in Sentinel1 SAR images with deep learning
(Journal article; Tidsskriftartikkel, 20220906)In this article, we explore the possibility of detecting polar lows in Cband synthetic aperture radar (SAR) images by means of deep learning. Specifically, we introduce a novel dataset consisting of Sentinel1 images divided into two classes, representing the presence and absence of a maritime mesocyclone, respectively. The dataset is constructed using the ECMWF reanalysis version 5 (ERA5) dataset ... 
Identifying dietary patterns across age, educational level and physical activity level in a crosssectional study: the Tromsø Study 2015  2016
(Journal article; Tidsskriftartikkel; Peer reviewed, 20220915)<p><b>Background</b> A healthy diet can decrease the risk of several lifestyle diseases. From studying the health effects of single foods, research now focuses on examining complete diets and dietary patterns reflecting the combined intake of different foods. The main goals of the current study were to identify dietary patterns and then investigate how these differ in terms of sex, age, educational ... 
Personalized optimization of blood glucose regulation: A Diabetes Mellitus case study
(Mastergradsoppgave; Master thesis, 20220713)Type 1 diabetes (T1D) is a chronic autoimmune disease that leads to insulin deficiency. Consequently, the disease will lead to a poor blood glucose (BG) regulation, and in situations of high energy expenditure like exercise, a dysfunctional regulation can cause severe damage or death [5] [14]. Diabetes is responsible for one death every five seconds and financially drains approximately 11% of the ... 
Codes from symmetric polynomials
(Journal article; Tidsskriftartikkel; Peer reviewed, 20221010)We define and study a class of Reed–Muller type errorcorrecting codes obtained from elementary symmetric functions in finitely many variables. We determine the code parameters and higher weight spectra in the simplest cases. 
On structure of linear differential operators, acting on line bundles
(Journal article; Tidsskriftartikkel; Peer reviewed, 20191114)We study differential invariants of linear differential operators and use them to find conditions for equivalence of differential operators acting on line bundles over smooth manifolds with respect to groups of automorphisms. 
On MultiRule and ProbabilityDependant Adaptations of Conway’s Game of Life and Their Character
(Journal article; Tidsskriftartikkel; Peer reviewed, 2022)We introduce some novel adaptations of LifeLike Automata. We focus mainly on some modifications of the original rules where the evolution of the system is depending from the step and the zone of the grid. We study also the properties of some novel nondeterministic adaptations. 
Effects of feedbacks for an energy balance model on a circle
(Mastergradsoppgave; Master thesis, 20220531)A simple, North like, energy balance model on a circle is studied using boundary formulations derived with Green's functions for the stationary case, and a pseudospectral and finite difference solution for the time dependent case. The bifurcation software Auto07p is also applied. The boundary formulation solution can be solved analytically in most cases, and is solved for bifurcation diagrams. ... 
Statistical analysis of locally parameterized shapes
(Journal article; Tidsskriftartikkel; Peer reviewed, 20220829)In statistical shape analysis, the establishment of correspondence and defining shape representation are crucial steps for hypothesis testing to detect and explain local dissimilarities between two groups of objects. Most commonly used shape representations are based on object properties that are either extrinsic or noninvariant to rigid transformation. Shape analysis based on noninvariant properties ... 
Symmetry gaps for higher order ordinary differential equations
(Journal article; Tidsskriftartikkel; Peer reviewed, 20220704)The maximal contact symmetry dimensions for scalar ODEs of order ≥ 4 and vector ODEs of order ≥ 3 are well known. Using a Cartangeometric approach, we determine for these ODEs the next largest realizable (submaximal) symmetry dimension. Moreover, finer curvatureconstrained submaximal symmetry dimensions are also classified. 
DataDriven Robust Control Using Reinforcement Learning
(Journal article; Tidsskriftartikkel; Peer reviewed, 20220221)This paper proposes a robust control design method using reinforcement learning for controlling partiallyunknown dynamical systems under uncertain conditions. The method extends the optimal reinforcement learning algorithm with a new learning technique based on the robust control theory. By learning from the data, the algorithm proposes actions that guarantee the stability of the closedloop system ... 
Symmetries of supergeometries related to nonholonomic superdistributions
(Journal article; Tidsskriftartikkel; Peer reviewed, 20220606)We extend Tanaka theory to the context of supergeometry and obtain an upper bound on the supersymmetry dimension of geometric structures related to strongly regular bracketgenerating distributions on supermanifolds and their structure reductions. 
Probabilistic Wind Power and Electricity Load Forecasting with Echo State Networks
(Mastergradsoppgave; Master thesis, 20220515)With the introduction of distributed generation and the establishment of smart grids, several new challenges in energy analytics arose. These challenges can be solved with a specific type of recurrent neural networks called echo state networks, which can handle the combination of both weather and power consumption or production depending on the dataset to make predictions. Echo state networks ... 
Killing Tensors in KoutrasMcIntosh Spacetimes
(Mastergradsoppgave; Master thesis, 20220515)This thesis is concerned with the (non)existence of Killing Tensors in KoutrasMcIntosh spacetimes. Killing tensors are of particular interest in general relativity, because these correspond to conserved quantities for the geodesic motion. For instance, Carter found such a conserved quantity in the Kerr metric which he used to explicitly integrate the geodesic equations. The equation defining ... 
Wachpress Conjecture Restricted To Arrangements Of Three Conics
(Mastergradsoppgave; Master thesis, 20220515)This thesis discusses Wachpress conjecture restricted to arrangements of three conics. Wachpress conjectured the existence of a set of barycentric coordinates, namely Wachpress coordinates, on all polycons. Barycentric coordinates are very useful in many different fields as they can be used to define a finite element approximation scheme with linear precision. This thesis focuses on the conjecture ... 
On the effects of symmetry in the energy balance on a sphere
(Mastergradsoppgave; Master thesis, 20220515)Simple climate models have gathered much attention as they have suggested the possibility of abrupt climate change associated with tipping points. Several simple climate models are found to have multiple equilibria, but in most cases similar equilibria do not appear or become too difficult to find in complex, fully coupled earth system models. In this thesis, we investigate a simple climate model, ...