Artikler, rapporter og annet (matematikk og statistikk)
https://hdl.handle.net/10037/950
2024-10-13T01:28:26ZEffects of plasma resistivity in FELTOR simulations of three-dimensional full-F gyro-fluid turbulence
https://hdl.handle.net/10037/35115
Wiesenberger, M.; Held, Markus<br />
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 a critical resistivity the mass and energy confinement reduces with
increasing resistivity. Further, for high plasma resistivity the direction of parallel acceleration is
swapped compared to low resistivity.
Three-dimensional visualisations using ray tracing techniques are displayed and discussed.
The field-alignment of turbulent fluctuations in density and parallel current becomes evident.
Relative density fluctuation amplitudes increase from below 1% in the core to 15% in the edge
and up to 40% in the scrape-off layer.
Finally, the integration of exact conservation laws over the closed field line region allows for
an identification of numerical errors within the simulations. The electron force balance and
energy conservation show relative errors on the order of 10<sup>−3</sup> while the particle conservation
and ion momentum balance show errors on the order of 10<sup>−2</sup>
.
All simulations are performed with a new version of the FELTOR code, which is fully
parallelized on GPUs. Each simulation covers a couple of milliseconds of turbulence.<br />
2024-04-18T00:00:00ZEffects of plasma resistivity in FELTOR simulations of three-dimensional full-F gyro-fluid turbulenceWiesenberger, M.Held, MarkusA 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 a critical resistivity the mass and energy confinement reduces with
increasing resistivity. Further, for high plasma resistivity the direction of parallel acceleration is
swapped compared to low resistivity.
Three-dimensional visualisations using ray tracing techniques are displayed and discussed.
The field-alignment of turbulent fluctuations in density and parallel current becomes evident.
Relative density fluctuation amplitudes increase from below 1% in the core to 15% in the edge
and up to 40% in the scrape-off layer.
Finally, the integration of exact conservation laws over the closed field line region allows for
an identification of numerical errors within the simulations. The electron force balance and
energy conservation show relative errors on the order of 10<sup>−3</sup> while the particle conservation
and ion momentum balance show errors on the order of 10<sup>−2</sup>
.
All simulations are performed with a new version of the FELTOR code, which is fully
parallelized on GPUs. Each simulation covers a couple of milliseconds of turbulence.IOP PublishingJournal articleTidsskriftartikkelPeer reviewedWiesenberger, Held. Effects of plasma resistivity in FELTOR simulations of three-dimensional full-F gyro-fluid turbulence. Plasma Physics and Controlled Fusion. 2024;66(6)Plasma Physics and Controlled Fusioninfo:eu-repo/grantAgreement/Funder/H2020/101052200/EU/Implementation of activities described in the Roadmap to Fusion during Horizon Europe through a joint programme of the members of the EUROfusion consortium/EUROfusion/Combinatorial mutations of Gelfand–Tsetlin polytopes, Feigin–Fourier–Littelmann–Vinberg polytopes, and block diagonal matching field polytopes
https://hdl.handle.net/10037/35111
Clarke, Oliver; Higashitani, Akihiro; Mohammadi, Fatemeh<br />
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
description as the Stanley’s order and chain polytopes of a certain poset, as
shown by Ardila, Bliem and Salazar. We prove that these polytopes occur among
matching field polytopes. Moreover, we show that they are related by a sequence
of combinatorial mutations that passes only through matching field polytopes. As
a result, we obtain a family of matching fields that give rise to toric degenerations
for the Grassmannians. Moreover, all polytopes in the family are Newton-Okounkov
bodies for the Grassmannians.<br />
2024-02-19T00:00:00ZCombinatorial mutations of Gelfand–Tsetlin polytopes, Feigin–Fourier–Littelmann–Vinberg polytopes, and block diagonal matching field polytopesClarke, OliverHigashitani, AkihiroMohammadi, FatemehThe 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
description as the Stanley’s order and chain polytopes of a certain poset, as
shown by Ardila, Bliem and Salazar. We prove that these polytopes occur among
matching field polytopes. Moreover, we show that they are related by a sequence
of combinatorial mutations that passes only through matching field polytopes. As
a result, we obtain a family of matching fields that give rise to toric degenerations
for the Grassmannians. Moreover, all polytopes in the family are Newton-Okounkov
bodies for the Grassmannians.ElsevierJournal articleTidsskriftartikkelPeer reviewedClarke, Higashitani, Mohammadi. Combinatorial mutations of Gelfand–Tsetlin polytopes, Feigin–Fourier–Littelmann–Vinberg polytopes, and block diagonal matching field polytopes. Journal of Pure and Applied Algebra. 2024;228(7)Journal of Pure and Applied AlgebraOn the degree of varieties of sum of squares
https://hdl.handle.net/10037/34924
Ferguson, Andrew; Ottaviani, Giorgio; Safey el Din, Mohab; Teixeira Turatti, Ettore<br />
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 is bounded from below by the degree of O (<i>k</i>). In particular, for <i>k</i> = 2 we show that SOS<sub>2</sub>(<i>f</i>) is isomorphic to O(2)
and hence the degree bound becomes an equality. Moreover, we compute the dimension of the space of polynomials of SOS-rank <i>k</i> and obtain the degree in the special case <i>k</i> = 2.<br />
2024-02-10T00:00:00ZOn the degree of varieties of sum of squaresFerguson, AndrewOttaviani, GiorgioSafey el Din, MohabTeixeira Turatti, EttoreWe 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 is bounded from below by the degree of O (<i>k</i>). In particular, for <i>k</i> = 2 we show that SOS<sub>2</sub>(<i>f</i>) is isomorphic to O(2)
and hence the degree bound becomes an equality. Moreover, we compute the dimension of the space of polynomials of SOS-rank <i>k</i> and obtain the degree in the special case <i>k</i> = 2.ElsevierJournal articleTidsskriftartikkelPeer reviewedFerguson, Ottaviani, Safey el Din, Teixeira Turatti. On the degree of varieties of sum of squares. Journal of Pure and Applied Algebra. 2024;228(7)Journal of Pure and Applied AlgebraThe span of singular tuples of a tensor beyond the boundary format
https://hdl.handle.net/10037/34918
Sodomaco, Luca; Teixeira Turatti, Ettore<br />
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 on the tensor format. Furthermore, if we fix the first <i>k</i> - 1 dimensions <i>n</i><sub>i</sub></i>, then the number of singular <i>k</i>-tuples of a generic tensor becomes a monotone non-decreasing function in one integer variable <i>n>sub>k</sub></i>, that stabilizes when (<i>n<sub>1</sub>, ..., n<sub>k</sub></i>) reaches a boundary format.<p> <p>In this paper, we study the linear span of singular k-tuples of a generic tensor. Its dimension also depends only on the tensor format. In particular, we concentrate on special order three tensors and order-<i>k</i> tensors of format (2, ..., 2, <i>n</i>). . As a consequence, if again we fix the first <i>k</i> - 1 dimensions <i>n</i> > 3 and let <i>n<sub>k</sub></i> increase, we show that in these special formats, the dimension of the linear span stabilizes as well, but at some concise non-sub-boundary format. We conjecture that this phenomenon holds for an arbitrary format with <i>k</i>>3. . Finally, we provide equations for the linear span of singular triples of a generic order three tensor <i>T</i> of some special non-sub-boundary format. From these equations, we conclude that <i>T</i> belongs to the linear span of its singular triples, and we conjecture that this is the case for every tensor format.<br />
2023-05-10T00:00:00ZThe span of singular tuples of a tensor beyond the boundary formatSodomaco, LucaTeixeira Turatti, EttoreA 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 on the tensor format. Furthermore, if we fix the first <i>k</i> - 1 dimensions <i>n</i><sub>i</sub></i>, then the number of singular <i>k</i>-tuples of a generic tensor becomes a monotone non-decreasing function in one integer variable <i>n>sub>k</sub></i>, that stabilizes when (<i>n<sub>1</sub>, ..., n<sub>k</sub></i>) reaches a boundary format.<p> <p>In this paper, we study the linear span of singular k-tuples of a generic tensor. Its dimension also depends only on the tensor format. In particular, we concentrate on special order three tensors and order-<i>k</i> tensors of format (2, ..., 2, <i>n</i>). . As a consequence, if again we fix the first <i>k</i> - 1 dimensions <i>n</i> > 3 and let <i>n<sub>k</sub></i> increase, we show that in these special formats, the dimension of the linear span stabilizes as well, but at some concise non-sub-boundary format. We conjecture that this phenomenon holds for an arbitrary format with <i>k</i>>3. . Finally, we provide equations for the linear span of singular triples of a generic order three tensor <i>T</i> of some special non-sub-boundary format. From these equations, we conclude that <i>T</i> belongs to the linear span of its singular triples, and we conjecture that this is the case for every tensor format.ElsevierJournal articleTidsskriftartikkelPeer reviewedSodomaco, Teixeira Turatti. The span of singular tuples of a tensor beyond the boundary format. Journal of symbolic computation. 2024;120Journal of symbolic computationGeneralized identifiability of sums of squares
https://hdl.handle.net/10037/34886
Ottaviani, Giorgio; Teixeira Turatti, Ettore<br />
2025-01-01T00:00:00ZGeneralized identifiability of sums of squaresOttaviani, GiorgioTeixeira Turatti, EttoreElsevierJournal articleTidsskriftartikkelPeer reviewedOttaviani, Teixeira Turatti. Generalized identifiability of sums of squares. Journal of Algebra. 2025;661:641-656Journal of AlgebraBinary forms of suprageneric rank and the multiple root loci
https://hdl.handle.net/10037/34885
González Nevado, Alejandro; Teixeira Turatti, Ettore<br />
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.<br />
2023-08-11T00:00:00ZBinary forms of suprageneric rank and the multiple root lociGonzález Nevado, AlejandroTeixeira Turatti, EttoreWe 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.Taylor & FrancisJournal articleTidsskriftartikkelPeer reviewedGonzález Nevado, Teixeira Turatti. Binary forms of suprageneric rank and the multiple root loci. Communications in Algebra. 2023;52(2):466-472Communications in Algebrainfo:eu-repo/grantAgreement/EC/H2020/813211/Norway/Polynomial Optimization, Efficiency through Moments and Algebra/POEMA/The 3-billion fossil question: How to automate classification of microfossils
https://hdl.handle.net/10037/34829
Martinsen, Iver; Wade, David; Godtliebsen, Fred; Ricaud, Benjamin<br />
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 this process face two key challenges: (1) the input data are very large - our dataset is projected to grow to 3 billion microfossils, and (2) there are not enough labeled data to use the standard procedure of training a deep learning classifier. We propose an efficient pipeline for processing and grouping fossils by genus, or even species, from microscope slides using self-supervised learning. First we show how to efficiently extract crops from whole slide images by adapting previously trained object detection algorithms. Second, we provide a comparison of a range of self-supervised learning methods to classify and identify microfossils from very few labels. We obtain excellent results with both convolutional neural networks and vision transformers fine-tuned by self-supervision. Our approach is fast and computationally light, providing a handy tool for geologists working with microfossils.<br />
2024-06-08T00:00:00ZThe 3-billion fossil question: How to automate classification of microfossilsMartinsen, IverWade, DavidGodtliebsen, FredRicaud, BenjaminMicrofossil 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 this process face two key challenges: (1) the input data are very large - our dataset is projected to grow to 3 billion microfossils, and (2) there are not enough labeled data to use the standard procedure of training a deep learning classifier. We propose an efficient pipeline for processing and grouping fossils by genus, or even species, from microscope slides using self-supervised learning. First we show how to efficiently extract crops from whole slide images by adapting previously trained object detection algorithms. Second, we provide a comparison of a range of self-supervised learning methods to classify and identify microfossils from very few labels. We obtain excellent results with both convolutional neural networks and vision transformers fine-tuned by self-supervision. Our approach is fast and computationally light, providing a handy tool for geologists working with microfossils.ElsevierJournal articleTidsskriftartikkelPeer reviewedMartinsen, Wade, Godtliebsen, Ricaud. The 3-billion fossil question: How to automate classification of microfossils. Artificial Intelligence in Geosciences. 2024;5Artificial Intelligence in GeosciencesDisease activity trajectories from childhood to adulthood in the population-based Nordic juvenile idiopathic arthritis cohort
https://hdl.handle.net/10037/34826
Rypdal, Veronika Gjertsen; Glerup, Mia; Rypdal, Martin Wibe; Arnstad, Ellen Dalen; Aalto, Kristiina; Berntson, Lillemor; Fasth, Anders; Herlin, Troels; Myrup, Charlotte; Peltoniemi, Suvi; Rygg, Marite; Nordal, Ellen Berit<br />
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 JIA in 1997–2000 were
followed for 18 years in the population-based Nordic JIA
cohort. We used a discrete mixture model for longitudinal
clustering of the cJADAS10 and its components. We
assessed factors potentially associated with higher scores
on the patient’s global assessment of well-being (PaGA) by
hierarchical clustering and correlation analysis.
<p>Results Four disease activity trajectories were identified
based on the cJADAS10 components among 427 patients.
In trajectory-group 2, the PaGA and the physician’s
global assessment of disease activity (PhGA) increased
significantly during the course, but not the active joint
count. The increase in the PaGA was significantly higher
than the increases in the PhGA and the active joint count
(p<0.0001). A similar pattern was found among all the
patients with active disease in the total cohort. Patients
with higher PaGA scores had unfavourable scores on
several other patient-reported outcomes.
<p>Conclusions We have identified groups of patients based
on long-term disease activity trajectories. In our study the
PaGA was the most important driver of disease activity
into adulthood assessed by cJADAS10. We need to better
understand how our patients interpret global well-being
and implement strategies to achieve inactive disease
perceived both by the patient and the physician.<br />
2024-03-08T00:00:00ZDisease activity trajectories from childhood to adulthood in the population-based Nordic juvenile idiopathic arthritis cohortRypdal, Veronika GjertsenGlerup, MiaRypdal, Martin WibeArnstad, Ellen DalenAalto, KristiinaBerntson, LillemorFasth, AndersHerlin, TroelsMyrup, CharlottePeltoniemi, SuviRygg, MariteNordal, Ellen BeritObjectives 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 JIA in 1997–2000 were
followed for 18 years in the population-based Nordic JIA
cohort. We used a discrete mixture model for longitudinal
clustering of the cJADAS10 and its components. We
assessed factors potentially associated with higher scores
on the patient’s global assessment of well-being (PaGA) by
hierarchical clustering and correlation analysis.
<p>Results Four disease activity trajectories were identified
based on the cJADAS10 components among 427 patients.
In trajectory-group 2, the PaGA and the physician’s
global assessment of disease activity (PhGA) increased
significantly during the course, but not the active joint
count. The increase in the PaGA was significantly higher
than the increases in the PhGA and the active joint count
(p<0.0001). A similar pattern was found among all the
patients with active disease in the total cohort. Patients
with higher PaGA scores had unfavourable scores on
several other patient-reported outcomes.
<p>Conclusions We have identified groups of patients based
on long-term disease activity trajectories. In our study the
PaGA was the most important driver of disease activity
into adulthood assessed by cJADAS10. We need to better
understand how our patients interpret global well-being
and implement strategies to achieve inactive disease
perceived both by the patient and the physician.BMJJournal articleTidsskriftartikkelPeer reviewedRypdal, Glerup, Rypdal, Arnstad, Aalto, Berntson, Fasth, Herlin, Myrup, Peltoniemi, Rygg, Nordal. Disease activity trajectories from childhood to adulthood in the population-based Nordic juvenile idiopathic arthritis cohort. RMD Open. 2024;10(1)RMD OpenOrbit Spaces of Weyl Groups Acting on Compact Tori: A Unified and Explicit Polynomial Description
https://hdl.handle.net/10037/34443
Hubert, Evelyne; Metzlaff, Tobias; Riener, Cordian Benedikt<br />
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 quadratic forms and a closed form formula for the matrix entries. The orbit space of the multiplicative Weyl group action is the orthogonality region of generalized Chebyshev polynomials. In this polynomial basis, we show that the matrices obtained for the five types follow the same, surprisingly simple pattern. This is applied to the optimization of trigonometric polynomials with crystallographic symmetries.<br />
2024-01-01T00:00:00ZOrbit Spaces of Weyl Groups Acting on Compact Tori: A Unified and Explicit Polynomial DescriptionHubert, EvelyneMetzlaff, TobiasRiener, Cordian BenediktThe 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 quadratic forms and a closed form formula for the matrix entries. The orbit space of the multiplicative Weyl group action is the orthogonality region of generalized Chebyshev polynomials. In this polynomial basis, we show that the matrices obtained for the five types follow the same, surprisingly simple pattern. This is applied to the optimization of trigonometric polynomials with crystallographic symmetries.Society for Industrial and Applied MathematicsJournal articleTidsskriftartikkelPeer reviewedHubert, Metzlaff, Riener. Orbit Spaces of Weyl Groups Acting on Compact Tori: A Unified and Explicit Polynomial Description. SIAM Journal on applied algebra and geometry. 2024SIAM Journal on applied algebra and geometrySymmetries in Polynomial Optimization
https://hdl.handle.net/10037/34442
Moustrou, Philippe; Riener, Cordian Benedikt; Verdure, Hugues<br />
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.<br />
2023-12-28T00:00:00ZSymmetries in Polynomial OptimizationMoustrou, PhilippeRiener, Cordian BenediktVerdure, HuguesThis 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.Springer NatureChapterBokkapittelMoustrou, Riener, Verdure: Symmetries in Polynomial Optimization. In: Kočvara, Mourrain, Riener. Polynomial Optimization, Moments, and Applications, 2023. SpringerEU – Horisont Europa (EC/HEU): POEMATromsø forskningsstiftelse: 17MatteCRinfo:eu-repo/grantAgreement/EC/H2020/813211/Norway/Polynomial Optimization, Efficiency through Moments and Algebra/POEMA/