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Optimization of trigonometric polynomials with crystallographic symmetry and spectral bounds for set avoiding graphs
(Journal article; Tidsskriftartikkel; Peer reviewed, 2024-11-05)We provide a new approach to the optimization of trigonometric polynomials with crystallographic symmetry. This approach widens the bridge between trigonometric and polynomial optimization. The trigonometric polynomials considered are supported on weight lattices associated to crystallographic root systems and are assumed invariant under the associated reflection group. On one hand the invariance ... -
The consequences of tritium mix for simulated ion cyclotron emission spectra from deuterium-tritium plasmas
(Journal article; Tidsskriftartikkel; Peer reviewed, 2024-10-16)Measurements of ion cyclotron emission (ICE) are obtained from most large magnetically confined fusion plasma experiments, and may be used in future to quantify properties of the fusion-born alpha-particle population in deuterium-tritium (DT) plasmas in ITER. ICE is driven by spatially localised, strongly non-Maxwellian, minority energetic ion populations which relax collectively under the ... -
Liftable Point-Line Configurations: Defining Equations and Irreducibility of Associated Matroid and Circuit Varieties
(Journal article; Tidsskriftartikkel; Peer reviewed, 2024-09-28)We study point-line configurations through the lens of projective geometry and matroid theory. Our focus is on their realization spaces, where we introduce the concepts of liftable and quasi-liftable configurations, exploring cases in which an n-tuple of collinear points can be lifted to a nondegenerate realization of a point-line configuration. We show that forest configurations are liftable ... -
Comments on: Data integration via analysis of subspaces (DIVAS)
(Journal article; Tidsskriftartikkel; Peer reviewed, 2024-06-06)We would like to start by saying that this is a very interesting paper that outlines a powerful tool that can be applied in a wide range of areas. In our discussion, we focus on how the novel approach potentially can improve classification results in hard tasks within e.g., medicine and geoscience. In such situations, where it is hard to make precise predictions, it is natural to acquire information ... -
Understanding Coherent Turbulence and the Roll-Cell Transition With Lagrangian Coherent Structures and Frame-Indifferent Fluxes
(Journal article; Tidsskriftartikkel; Peer reviewed, 2024-09-18)We present the first analysis of frame-indifferent (objective) fluxes and material vortices in Large Eddy Simulations of atmospheric boundary layer turbulence. We extract rotating fluid features that maintain structural coherence over time for near-neutral, transitional, and convective boundary layers. In contrast to traditional analysis of coherent structures in turbulent boundary layers, we provide ... -
Lie Admissible Triple Algebras: The Connection Algebra of Symmetric Spaces
(Journal article; Tidsskriftartikkel; Peer reviewed, 2024-07-25)Associated to a symmetric space there is a canonical connection with zero torsion and parallel curvature. This connection acts as a binary operator on the vector space of smooth sections of the tangent bundle, and it is linear with respect to the real numbers. Thus the smooth section of the tangent bundle together with the connection form an algebra we call the connection algebra. The constraints ... -
On nonnegative invariant quartics in type A
(Journal article; Tidsskriftartikkel; Peer reviewed, 2024-10-09)The equivariant nonnegativity versus sums of squares question has been solved for any infinite series of essential reflection groups but type <i>A</i>. As a first step to a classification, we analyse <i>A<sub>n</sub></i> -invariant quartics. We prove that the cones of invariant sums of squares and nonnegative forms are equal if and only if the number of variables is at most 3 or odd. -
The Universal Equivariance Properties of Exotic Aromatic B-Series
(Journal article; Tidsskriftartikkel; Peer reviewed, 2024-08-16)The exotic aromatic Butcher series were originally introduced for the calculation of order conditions for the high order numerical integration of ergodic stochastic differential equations in Rd and on manifolds. We prove in this paper that exotic aromatic B-series satisfy a universal geometric property, namely that they are characterised by locality and equivariance with respect to orthogonal ... -
Exploring Pain Reduction through Physical Activity: A Case Study of Seven Fibromyalgia Patients
(Journal article; Tidsskriftartikkel; Peer reviewed, 2024-07-29)Fibromyalgia is a chronic disease that affects a considerable fraction of the global population, primarily women. Physical activity is often recommended as a tool to manage the symptoms. In this study, we tried to replicate a positive result of pain reduction through physical activity. After collecting pain and physical activity data from seven women with fibromyalgia, one patient experienced ... -
Convergence rates for sums-of-squares hierarchies with correlative sparsity
(Journal article; Tidsskriftartikkel; Peer reviewed, 2024-03-25)This work derives upper bounds on the convergence rate of the moment-sum-of-squares hierarchy with correlative sparsity for global minimization of polynomials on compact basic semialgebraic sets. The main conclusion is that both sparse hierarchies based on the Schmüdgen and Putinar Positivstellensätze enjoy a polynomial rate of convergence that depends on the size of the largest clique in the sparsity ... -
Effects of plasma resistivity in FELTOR simulations of three-dimensional full-F gyro-fluid turbulence
(Journal article; Tidsskriftartikkel; Peer reviewed, 2024-04-18)A full-F, isothermal, electromagnetic, gyro-fluid model is used to simulate plasma turbulence in a COMPASS-sized, diverted tokamak. A parameter scan covering three orders of magnitude of plasma resistivity and two values for the ion to electron temperature ratio with otherwise fixed parameters is setup and analysed. Two transport regimes for high and low plasma resistivities are revealed. Beyond ... -
Combinatorial mutations of Gelfand–Tsetlin polytopes, Feigin–Fourier–Littelmann–Vinberg polytopes, and block diagonal matching field polytopes
(Journal article; Tidsskriftartikkel; Peer reviewed, 2024-02-19)The Gelfand-Tsetlin and the Feigin–Fourier–Littelmann–Vinberg polytopes for the Grassmannians are defined, from the perspective of representation theory, to parametrize certain bases for highest weight irreducible modules. These polytopes are Newton-Okounkov bodies for the Grassmannian and, in particular, the GT polytope is an example of a string polytope. The polytopes admit a combinatorial ... -
On the degree of varieties of sum of squares
(Journal article; Tidsskriftartikkel; Peer reviewed, 2024-02-10)We study the problem of how many different sum of squares decompositions a general polynomial <i>f</i> with SOS-rank <i>k</i> admits. We show that there is a link between the variety SOS<sub><i>k</sub></i>(<i>f</i>) of all SOS-decompositions of <i>f</i> and the orthogonal group O(<i>k</i>). We exploit this connection to obtain the dimension of SOS<sub><i>k</sub></i>(<i>f</i>) and show that its degree ... -
The span of singular tuples of a tensor beyond the boundary format
(Journal article; Tidsskriftartikkel; Peer reviewed, 2023-05-10)A singular <i>k</i>-tuple of a tensor T of format (<i>n<sub>1</sub></i>, ..., <i>n</i><sub><i><k></i></sub>) is essentially a complex critical point of the distance function from <i>T</i> constrained to the cone of tensors of format (<i>n</i><sub>1</sub>, ..., <i>n<sub>k</sub></i>) of rank at most one. A generic tensor has finitely many complex singular <i>k</i>-tuples, and their number depends only ... -
Generalized identifiability of sums of squares
(Journal article; Tidsskriftartikkel; Peer reviewed, 2025) -
Binary forms of suprageneric rank and the multiple root loci
(Journal article; Tidsskriftartikkel; Peer reviewed, 2023-08-11)We state the relation between the variety of binary forms of given rank and the dual of the multiple root loci. This is a new result for the suprageneric rank that appears as a continuation of the cited work by Buczyński, Han, Mella and Teitler. We describe the strata of these varieties and explore their singular loci. -
The 3-billion fossil question: How to automate classification of microfossils
(Journal article; Tidsskriftartikkel; Peer reviewed, 2024-06-08)Microfossil classification is an important discipline in subsurface exploration, for both oil & gas and Carbon Capture and Storage (CCS). The abundance and distribution of species found in sedimentary rocks provide valuable information about the age and depositional environment. However, the analysis is difficult and time-consuming, as it is based on manual work by human experts. Attempts to automate ... -
Disease activity trajectories from childhood to adulthood in the population-based Nordic juvenile idiopathic arthritis cohort
(Journal article; Tidsskriftartikkel; Peer reviewed, 2024-03-08)Objectives To identify long-term disease activity trajectories from childhood to adulthood by using the clinical Juvenile Arthritis Disease Activity Score (cJADAS10) in juvenile idiopathic arthritis (JIA). Second, to evaluate the contribution of the cJADAS10 components and explore characteristics associated with active disease at the 18- year follow-up.<p> <p>Methods Patients with onset of ... -
Orbit Spaces of Weyl Groups Acting on Compact Tori: A Unified and Explicit Polynomial Description
(Journal article; Tidsskriftartikkel; Peer reviewed, 2024)The Weyl group of a crystallographic root system has a multiplicative action on the compact torus. The orbit space of this action is a compact basic semi-algebraic set. We present a polynomial description of this set for the Weyl groups associated to root systems of types A, B, C, D and G. Our description is given through a polynomial matrix inequality. The novelty lies in an approach via Hermite ... -
Symmetries in Polynomial Optimization
(Chapter; Bokkapittel, 2023-12-28)This chapter investigates how symmetries can be used to reduce the computational complexity in polynomial optimization problems. A focus will be specifically given on the Moment-SOS hierarchy in polynomial optimization, where results from representation theory and invariant theory of groups can be used. In addition, symmetry reduction techniques which are more generally applicable are also presented.
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