Institutt for matematikk og statistikk: Recent submissions
Now showing items 101-120 of 426
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Seasonality, density dependence, and spatial population synchrony
(Journal article; Tidsskriftartikkel; Peer reviewed, 2022-12-15)Studies of spatial population synchrony constitute a central approach for understanding the drivers of ecological dynamics. Recently, identifying the ecological impacts of climate change has emerged as a new important focus in population synchrony studies. However, while it is well known that climatic seasonality and sequential density dependence influences local population dynamics, the role of ... -
Differential invariants of curves in G2 flag varieties
(Journal article; Tidsskriftartikkel; Peer reviewed, 2022-05-10)We compute the algebra of differential invariants of unparametrized curves in the homogeneous G<sub>2</sub> flag varieties, namely in G<sub>2</sub>/P. This gives a solution to the equivalence problem for such curves. We consider the cases of integral and generic curves and relate the equivalence problems for all three choices of the parabolic subgroup P. -
Power Flow Balancing With Decentralized Graph Neural Networks
(Journal article; Tidsskriftartikkel; Peer reviewed, 2022-08-01)We propose an end-to-end framework based on a Graph Neural Network (GNN) to balance the power flows in energy grids. The balancing is framed as a supervised vertex regression task, where the GNN is trained to predict the current and power injections at each grid branch that yield a power flow balance. By representing the power grid as a line graph with branches as vertices, we can train a GNN that ... -
Understanding Pooling in Graph Neural Networks
(Journal article; Tidsskriftartikkel; Peer reviewed, 2022-07-21)Many recent works in the field of graph machine learning have introduced pooling operators to reduce the size of graphs. In this article, we present an operational framework to unify this vast and diverse literature by describing pooling operators as the combination of three functions: selection, reduction, and connection (SRC). We then introduce a taxonomy of pooling operators, based on some of ... -
An Energy Balance Model on an Infinite Line
(Master thesis; Mastergradsoppgave, 2022-06-01)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 subgraphs-enhanced Graph Neural Networks
(Journal article; Tidsskriftartikkel, 2023)Recently, subgraphs-enhanced 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 1-dimensional Weisfeiler-Leman 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, 2022-06-20)Paleoclimate proxy records have non-negligible 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 rank-metric codes and Betti numbers
(Journal article; Tidsskriftartikkel; Peer reviewed, 2022-07-07)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 energy-free Hartree–Fock equations: an integral formulation
(Journal article; Tidsskriftartikkel; Peer reviewed, 2022-07-18)We have implemented a self-consistent 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 Sentinel-1 SAR images with deep learning
(Journal article; Tidsskriftartikkel, 2022-09-06)In this article, we explore the possibility of detecting polar lows in C-band synthetic aperture radar (SAR) images by means of deep learning. Specifically, we introduce a novel dataset consisting of Sentinel-1 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 cross-sectional study: the Tromsø Study 2015 - 2016
(Journal article; Tidsskriftartikkel; Peer reviewed, 2022-09-15)<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, 2022-07-13)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, 2022-10-10)We define and study a class of Reed–Muller type error-correcting 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, 2019-11-14)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 Multi-Rule and Probability-Dependant Adaptations of Conway’s Game of Life and Their Character
(Journal article; Tidsskriftartikkel; Peer reviewed, 2022)We introduce some novel adaptations of Life-Like 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 non-deterministic adaptations. -
Effects of feedbacks for an energy balance model on a circle
(Mastergradsoppgave; Master thesis, 2022-05-31)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 pseudo-spectral and finite difference solution for the time dependent case. The bifurcation software Auto-07p is also applied. The boundary formulation solution can be solved analytically in most cases, and is solved for bifurcation diagrams. ... -
Symmetry gaps for higher order ordinary differential equations
(Journal article; Tidsskriftartikkel; Peer reviewed, 2022-07-04)The maximal contact symmetry dimensions for scalar ODEs of order ≥ 4 and vector ODEs of order ≥ 3 are well known. Using a Cartan-geometric approach, we determine for these ODEs the next largest realizable (submaximal) symmetry dimension. Moreover, finer curvature-constrained submaximal symmetry dimensions are also classified. -
Data-Driven Robust Control Using Reinforcement Learning
(Journal article; Tidsskriftartikkel; Peer reviewed, 2022-02-21)This paper proposes a robust control design method using reinforcement learning for controlling partially-unknown 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 closed-loop system ... -
Symmetries of supergeometries related to nonholonomic superdistributions
(Journal article; Tidsskriftartikkel; Peer reviewed, 2022-06-06)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 bracket-generating distributions on supermanifolds and their structure reductions. -
Probabilistic Wind Power and Electricity Load Forecasting with Echo State Networks
(Mastergradsoppgave; Master thesis, 2022-05-15)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 ...