Institutt for matematikk og statistikk
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Beyond the OberbeckBoussinesq and long wavelength approximation
(Journal article; Tidsskriftartikkel, 20221222)We present the first simulations of a reduced magnetized plasma model that incorporates both arbitrary wavelength polarization and nonOberbeck–Boussinesq effects. Significant influence of these two effects on the density, electric potential and <i><b>E</i></b> × <i><b>B</i></b> vorticity and nonlinear dynamics of interchange blobs are reported. Arbitrary wavelength polarization implicates socalled ... 
On uniqueness of submaximally symmetric parabolic geometries
(Journal article; Tidsskriftartikkel; Peer reviewed, 20240124)Among (regular, normal) parabolic geometries of type (<i>G,P</i>), there is a locally unique maximally symmetric structure and it has symmetry dimension dim(<i>G</i>). The symmetry gap problem concerns the determination of the next realizable (submaximal) symmetry dimension. When <i>G</i> is a complex or splitreal simple Lie group of rank at least three or when (<i>G,P</i>) = (<i>G<sub>2</sub></i>, ... 
Preservice and inservice teachers’ views on digital tools for diverse learners in mathematics education
(Journal article; Tidsskriftartikkel; Peer reviewed, 2023)Although teachers are expected to use digital tools in their mathematics teaching in many countries, little is known about preservice and inservice teachers’ digital competence, especially in relationship to specific groups of school students. Results from a survey of 394 preservice teachers and 61 inservice teachers, at three Norwegian institutions, provide information on how they considered different ... 
Biogeographic gradients of picoplankton diversity indicate increasing dominance of prokaryotes in warmer Arctic fjords
(Journal article; Tidsskriftartikkel; Peer reviewed, 20240302)limate change is opening the Arctic Ocean to increasing human impact and ecosystem changes. Arctic fjords, the region’s most productive ecosystems, are sustained by a diverse microbial community at the base of the food web. Here we show that Arctic fjords become more prokaryotic in the picoplankton (0.2–3 µm) with increasing water temperatures. Across 21 fjords, we found that Arctic fjords had ... 
Linear codes associated to symmetric determinantal varieties: Even rank case
(Journal article; Tidsskriftartikkel; Peer reviewed, 20230620)We consider linear codes over a finite field Fq, for odd q, derived from determinantal varieties, obtained from symmetric matrices of bounded ranks. A formula for the weight of a codeword is derived. Using this formula, we have computed the minimum distance for the codes corresponding to matrices upperbounded by any fixed, even rank. A conjecture is proposed for the cases where the upper bound is ... 
Exceptionally simple superPDE for F (4)
(Journal article; Tidsskriftartikkel; Peer reviewed, 20240201)For the largest exceptional simple Lie superalgebra F(4), having dimension (2416), we provide two explicit geometric realizations as supersymmetries, namely as the symmetry superalgebra of superPDE systems of second and third order respectively. 
ODEs whose Symmetry Groups are not FiberPreserving
(Journal article; Tidsskriftartikkel; Peer reviewed, 2023)We observe that, up to conjugation, a majority of higher order ODEs (ordinary differential equations) and ODE systems have only fiberpreserving point symmetries. By exploiting Lie's classification of Lie algebras of vector fields, we describe all exceptions to this in the case of scalar ODEs and systems of ODEs on a pair of functions. The scalar ODEs whose symmetry algebras are not fiber preserving ... 
Deep Learning Based Automatic Segmentation of Gas Flares in Single Beam Echo Sounder Data
(Mastergradsoppgave; Master thesis, 20240118)This thesis introduces the first study of instance segmentation applied to gas flares in single beam echo sounder data. We develop a comprehensive dataset consisting of 1,414 images, featuring 5,142 segmented objects identified as gas flare. A key contribution is the adaptation of the Brier score specifically for instance segmentation. Further, we show how to adapt the Weighted Box Fusion (WBF) ... 
Decomposable (5, 6)solutions in elevendimensional supergravity
(Journal article; Tidsskriftartikkel; Peer reviewed, 20230608)We present decomposable (5, 6)solutions M<sup>1,4</sup>×M<sup>6</sup> in elevendimensional supergravity by solving the bosonic supergravity equations for a variety of nontrivial flux forms. Many of the bosonic backgrounds presented here are induced by various types of null flux forms on products of certain totally Ricciisotropic Lorentzian Walker manifolds and Ricciflat Riemannian manifolds. ... 
Power availability of PV plus thermal batteries in realworld electric power grids
(Journal article; Tidsskriftartikkel; Peer reviewed, 20230725)As variable renewable energy sources comprise a growing share of total electricity generation, energy storage technologies are becoming increasingly critical for balancing energy generation and demand.<p> <p>In this study, a realworld electricity system was modeled rather than modeling hypothetical future electric power systems where the existing electricity infrastructure are neglected. In ... 
The expressive power of pooling in Graph Neural Networks
(Journal article; Tidsskriftartikkel; Peer reviewed, 2023)In Graph Neural Networks (GNNs), hierarchical pooling operators generate local summaries of the data by coarsening the graph structure and the vertex features. While considerable attention has been devoted to analyzing the expressive power of messagepassing (MP) layers in GNNs, a study on how graph pooling affects the expressiveness of a GNN is still lacking. Additionally, despite the recent advances ... 
Total Variation Graph Neural Networks
(Journal article; Tidsskriftartikkel, 202307)Recently proposed Graph Neural Networks (GNNs) for vertex clustering are trained with an unsupervised minimum cut objective, approximated by a Spectral Clustering (SC) relaxation. However, the SC relaxation is loose and, while it offers a closedform solution, it also yields overly smooth cluster assignments that poorly separate the vertices. In this paper, we propose a GNN model that computes cluster ... 
On Cclass equations
(Journal article; Tidsskriftartikkel; Peer reviewed, 20230929)The concept of a Cclass of differential equations goes back to E. Cartan with the upshot that generic equations in a Cclass can be solved without integration. While Cartan’s definition was in terms of differential invariants being first integrals, all results exhibiting Cclasses that we are aware of are based on the fact that a canonical Cartan geometry associated to the equations in the class ... 
Double Schubert polynomials do have saturated Newton polytopes
(Journal article; Tidsskriftartikkel; Peer reviewed, 20231103)We prove that double Schubert polynomials have the saturated Newton polytope property. This settles a conjecture by Monical, Tokcan and Yong. Our ideas are motivated by the theory of multidegrees. We introduce a notion of standardization of ideals that enables us to study nonstandard multigradings. This allows us to show that the support of the multidegree polynomial of each Cohen–Macaulay prime ... 
Bianchi type cosmological models in f(T) teleparallel gravity
(Journal article; Tidsskriftartikkel; Peer reviewed, 20231012)Symmetry assumptions on the geometrical framework have provided successful mechanisms to develop physically meaningful solutions to many problems. In teleparallel gravity, invariance of the frame and spinconnection under a group of motions defines an affine symmetry group. Here, we assume there exists a threedimensional group of affine symmetries acting simply transitively on a spatial hypersurface ... 
Associations and predictive power of dietary patterns on metabolic syndrome and its components
(Journal article; Tidsskriftartikkel; Peer reviewed, 20231031)Background and aims: Metabolic syndrome (MetS) defines important risk factors in the development of cardiovascular diseases and other serious health conditions. This study aims to investigate the influence of different dietary patterns on MetS and its components, examining both associations and predictive performance.<p> <p>Methods and results: The study sample included 10,750 participants from ... 
Probabilistic Load Forecasting With Reservoir Computing
(Journal article; Tidsskriftartikkel; Peer reviewed, 20231215)Some applications of deep learning require not only to provide accurate results but also to quantify the amount of confidence in their prediction. The management of an electric power grid is one of these cases: to avoid risky scenarios, decisionmakers need both precise and reliable forecasts of, for example, power loads. For this reason, point forecasts are not enough hence it is necessary to adopt ... 
Probabilistic load forecasting with Reservoir Computing
(Journal article; Tidsskriftartikkel; Peer reviewed, 20231215)Some applications of deep learning require not only to provide accurate results but also to quantify the amount of confidence in their prediction. The management of an electric power grid is one of these cases: to avoid risky scenarios, decisionmakers need both precise and reliable forecasts of, for example, power loads. For this reason, point forecasts are not enough hence it is necessary to adopt ... 
Numerical evaluation of line, surface and toroidal integrals on level sets of toroidally symmetric functions
(Journal article; Tidsskriftartikkel; Peer reviewed, 20230805)We investigate strategies to numerically integrate closed lines and surfaces that are implicitly defined by level sets (isocontours) of continuously differentiable toroidally symmetric functions. The “gridtransform” approach transforms quantities given in nonsurfacealigned coordinates onto a numerically constructed surfacealigned grid. Here, line and surface integrals, as well as socalled ... 
Interplay between advective, diffusive and active barriers in (rotating) RayleighBénard flow
(Journal article; Tidsskriftartikkel; Peer reviewed, 20230822)Our understanding of the material organization of complex fluid flows has benefited recently from mathematical developments in the theory of objective coherent structures. These methods have provided a wealth of approaches that identify transport barriers in threedimensional (3D) turbulent flows. Specifically, theoretical advances have been incorporated into numerical algorithms that extract ...