| 1. |
|
|
| 2. |
- Gerken, Jan, 1991, et al.
(författare)
-
Equivariance versus augmentation for spherical images
- 2022
-
Ingår i: Proceedings of Machine Learning Resaerch. ; , s. 7404-7421
-
Konferensbidrag (refereegranskat)abstract
- We analyze the role of rotational equivariance in convolutional neural networks (CNNs) applied to spherical images. We compare the performance of the group equivariant networks known as S2CNNs and standard non-equivariant CNNs trained with an increasing amount of data augmentation. The chosen architectures can be considered baseline references for the respective design paradigms. Our models are trained and evaluated on single or multiple items from the MNIST- or FashionMNIST dataset projected onto the sphere. For the task of image classification, which is inherently rotationally invariant, we find that by considerably increasing the amount of data augmentation and the size of the networks, it is possible for the standard CNNs to reach at least the same performance as the equivariant network. In contrast, for the inherently equivariant task of semantic segmentation, the non-equivariant networks are consistently outperformed by the equivariant networks with significantly fewer parameters. We also analyze and compare the inference latency and training times of the different networks, enabling detailed tradeoff considerations between equivariant architectures and data augmentation for practical problems.
|
|
| 3. |
- Ivanenko, Yevhen, et al.
(författare)
-
Quasi-Herglotz functions and convex optimization
- 2020
-
Ingår i: Royal Society Open Science. - : The Royal Society Publishing. - 2054-5703. ; 7:1, s. 1-15
-
Tidskriftsartikel (refereegranskat)abstract
- We introduce the set of quasi-Herglotz functions and demonstrate that it has properties useful in the modelling of non-passive systems. The linear space of quasi-Herglotz functions constitutes a natural extension of the convex cone of Herglotz functions. It consists of differences of Herglotz functions and we show that several of the important properties and modelling perspectives are inherited by the new set of quasi-Herglotz functions. In particular, this applies to their integral representations, the associated integral identities or sum rules (with adequate additional assumptions), their boundary values on the real axis and the associated approximation theory. Numerical examples are included to demonstrate the modelling of a non-passive gain medium formulated as a convex optimization problem, where the generating measure is modelled by using a finite expansion of B-splines and point masses.
|
|
| 4. |
- Gourevitch, D., et al.
(författare)
-
EULERIANITY OF FOURIER COEFFICIENTS OF AUTOMORPHIC FORMS
- 2021
-
Ingår i: Representation Theory. - : American Mathematical Society (AMS). - 1088-4165. ; 25, s. 481-507
-
Tidskriftsartikel (refereegranskat)abstract
- We study the question of Eulerianity (factorizability) for Fourier coefficients of automorphic forms, and we prove a general transfer theorem that allows one to deduce the Eulerianity of certain coefficients from that of another coefficient. We also establish a `hidden' invariance property of Fourier coefficients. We apply these results to minimal and next-to-minimal automorphic representations, and deduce Eulerianity for a large class of Fourier and Fourier-Jacobi coefficients. In particular, we prove Eulerianity for parabolic Fourier coefficients with characters of maximal rank for a class of Eisenstein series in minimal and next-to-minimal representations of groups of ADE-type that are of interest in string theory.
|
|
| 5. |
- Grip, Niklas, 1970-, et al.
(författare)
-
Vibrationsanalys för tillståndsbedömning av byggkonstruktioner : Tillämpningsexempel : (Main results and summary in Swedish. Detailed results in English Appendices.)
- 2017
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- I projektet beskrivs och tillämpasnågra metoder för tillståndsbedömningav olika typer av konstruktioner med och utan skador.Tillståndsbedömningen skermed hjälp av vibrationsanalys.Detektering av skador av olika typ och storlekdiskuteras. Randvillkorens betydelse undersöks för att få överensstämmelse mellan förutspådda och uppmätta egenmoder och egenfrekvenser.Med den programvara som utvecklats är det möjligt att detektera sprickor i enkla betongplattor med hjälp av vibrationsmätningar. För mer avancerade konstruktioner finns en potential att vidareutveckla programvaran.Mätningar och analyser presenterasför femkonstruktioner: (1) En betongplatta –Sprickor har kunnat identifieras utifrån vibrationsmätningar och en successivt uppdaterad finit element modell (FEM).(2) En bågbro av betong över Långforsen i Kalix älv–Okända randvillkor har kunnat bestämmasför t ex undergrundens styvhetmedhjälp avuppmätta vibrationer. Detekteringav specifika skadorhar ännu inte kunnat genomföras.(3) En fackverksbro av stålöver Åby älv–Enviss skadedetektering har kunnat genomföras med vibrationsmätningar. Brons sårbarhet för korrosion och lokala mekaniska skador har studerats.(4) En förspänd betongbrotill gruvan i Kiruna–Modeller av bron har arbetats framför obelastatoch brottbelastat tillståndoch jämförts med uppmätta vibrationer med gott resultat.(5) Ett betonghus med nio våningar i Luleå –En FEM-modell av huseti bruksstadiethar tagits fram och resultat från den har jämförts med uppmätta vibrationer med gott resultat.Metoder och resultatpresenteras översiktligti rapportens huvudtext. Detaljerade beskrivningar gesi appendix.I appendix presenterasäven en programvaramed färdiga moduler för de undersökta konstruktionerna. Programmet kan laddas ner och användasfritt
|
|
| 6. |
- Almqvist, Andreas, et al.
(författare)
-
Homogenization of the unstationary incompressible Reynolds equation
- 2007
-
Ingår i: Tribology International. - : Elsevier BV. - 0301-679X .- 1879-2464. ; 40:9, s. 1344-1350
-
Tidskriftsartikel (refereegranskat)abstract
- This paper is devoted to the effects of surface roughness during hydrodynamic lubrication. In the numerical analysis a very fine mesh is needed to resolve the surface roughness, suggesting some type of averaging. A rigorous way to do this is to use the general theory of homogenization. In most works about the influence of surface roughness, it is assumed that only the stationary surface is rough. This means that the governing Reynolds type equation does not involve time. However, recently, homogenization was successfully applied to analyze a situation where both surfaces are rough and the lubricant is assumed to have constant bulk modulus. In this paper we will consider a case where both surfaces are assumed to be rough, but the lubricant is incompressible. It is also clearly demonstrated, in this case that homogenization is an efficient approach. Moreover, several numerical results are presented and compared with those corresponding to where a constant bulk modulus is assumed to govern the lubricant compressibility. In particular, the result shows a significant difference in the asymptotic behavior between the incompressible case and that with constant bulk modulus.
|
|
| 7. |
- Kruglyak, Natan, et al.
(författare)
-
The limiting case of the Marcinkiewicz integral : growth for convex sets
- 2007
-
Ingår i: Proceedings of the American Mathematical Society. - : American Mathematical Society (AMS). - 0002-9939 .- 1088-6826. ; 135:10, s. 3283-3293
-
Tidskriftsartikel (refereegranskat)abstract
- The Marcinkiewicz integral Iλ (x)= ∫ (dist (y, ℝn\Ω))λ/Ω| x - y | n+λ dy, where λ > 0, plays a well-known and prominent role in harmonic analysis. In this paper, we estimate the growth of it in the limiting case λ → 0. Throughout, we assume that Ω is convex; it is interesting that this condition cannot be dropped
|
|
| 8. |
|
|
| 9. |
- Bourne, D., et al.
(författare)
-
Is adding charcoal to soil a good method for CO2 sequestration? - : Modeling a spatially homogeneous soil
- 2014
-
Ingår i: Applied Mathematical Modelling. - : Elsevier. - 0307-904X .- 1872-8480. ; 38:9-10, s. 2463-2475
-
Tidskriftsartikel (refereegranskat)abstract
- Carbon sequestration is the process of capture and long-term storage of atmospheric carbon dioxide (CO2) with the aim to avoid dangerous climate change. In this paper, we propose a simple mathematical model (a coupled system of nonlinear ODEs) to capture some of the dynamical effects produced by adding charcoal to fertile soils. The main goal is to understand to which extent charcoal is able to lock up carbon in soils. Our results are preliminary in the sense that we do not solve the CO2 sequestration problem. Instead, we do set up a flexible modeling framework in which the interaction between charcoal and soil can be tackled by means of mathematical tools.We show that our model is well-posed and has interesting large-time behaviour. Depending on the reference parameter range (e.g., type of soil) and chosen time scale, numerical simulations suggest that adding charcoal typically postpones the release of CO2. © 2013 Elsevier Inc.
|
|
| 10. |
- Gerlee, Philip, 1980, et al.
(författare)
-
Scientific Models : Red Atoms, White Lies and Black Boxes in a Yellow Book
- 2016
-
Bok (övrigt vetenskapligt/konstnärligt)abstract
- A zebrafish, the hull of a miniature ship, a mathematical equation and a food chain - what do these things have in common? They are examples of models used by scientists to isolate and study particular aspects of the world around us. This book begins by introducing the concept of a scientific model from an intuitive perspective, drawing parallels to mental models and artistic representations. It then recounts the history of modelling from the 16th century up until the present day. The iterative process of model building is described and discussed in the context of complex models with high predictive accuracy versus simpler models that provide more of a conceptual understanding. To illustrate the diversity of opinions within the scientific community, we also present the results of an interview study, in which ten scientists from different disciplines describe their views on modelling and how models feature in their work. Lastly, it includes a number of worked examples that span different modelling approaches and techniques. It provides a comprehensive introduction to scientific models and shows how models are constructed and used in modern science. It also addresses the approach to, and the culture surrounding modelling in different scientific disciplines. It serves as an inspiration for model building and also facilitates interdisciplinary collaborations by showing how models are used in different scientific fields. The book is aimed primarily at students in the sciences and engineering, as well as students at teacher training colleges but will also appeal to interested readers wanting to get an overview of scientific modelling in general and different modelling approaches in particular.
|
|
