Model Reduction using a Frequency-Limited H2-Cost

We propose a method for model reduction on a given frequency range, without the use of input and output filter weights. The method uses a nonlinear optimization approach to minimize a frequency limited H2 like cost function. An important contribution in the paper is the derivation of the gradient of the proposed cost function. The fact that we have a closed form expression for the gradient and that considerations have been taken to make the gradient computationally efficient to compute enables us to efficiently use off-the-shelf optimization software to solve the optimization problem.Comment: Submitted to Systems and Control Letter

A Stable Finite Difference Method for the Elastic Wave Equation on Complex Geometries with Free Surfaces

A stable and explicit second order accurate finite difference method for the elastic wave equation in curvilinear coordinates is presented. The discretization of the spatial operators in the method is shown to be self-adjoint for free-surface, Dirichlet and periodic boundary conditions. The fully discrete version of the method conserves a discrete energy to machine precision

Three dimensional finite temperature SU(3) gauge theory in the confined region and the string picture

We determine the correlation between Polyakov loops in three dimensional SU(3) gauge theory in the confined region at finite temperature. For this purpose we perform lattice calculations for the number of steps in the temperature direction equal to six. This is expected to be in the scaling region of the lattice theory. We compare the results to the bosonic string model. The agreement is very good for temperatures T<0.7T_c, where T_c is the critical temperature. In the region 0.7T_c<T<T_c we enter the critical region, where the critical properties of the correlations are fixed by universality to be those of the two dimensional three state Potts model. Nevertheless, by calculating the critical lattice coupling, we show that the ratio of the critical temperature to the square root of the zero temperature string tension, where the latter is taken from the literature, remains very near to the string model prediction.Comment: 11 pages, 1 figure, 1 tabl

Utomståenderegeln i 57:5 IL – Är den ändamålsenlig?

I uppsatsen har gällande rätt avseende utomståenderegeln i 57 kap. 5 § IL fram-ställts och analyserats. Utomståenderegeln är en undantagsregel från de särskilda beskattningsreglerna i 3:12-regelverket. Bestämmelsen blir tillämplig om aktie-ägaren visar att utomstående i betydande omfattning äger del i företaget. Syftet med uppsatsen har varit att undersöka om tillämpningen av bestämmelsen är ändamålsenlig i bemärkelsen att regeln tillgodoser lagstiftarens syfte. I uppsat-sen har samspelet mellan ändamål, den tekniska utformningen av bestämmelsen och rättstillämpningen granskats, i syfte att utreda om dagens reglering och rättstillämpning är lämplig med hänsyn till ändamålen. Utifrån redogörelsen går det att konstatera att rättstillämpningen av bestämmelsen i flera avseenden inte överensstämmer med ändamålen. HFD accepterar idag ett utomstående ägande på 30 procent för att regeln ska bli tillämplig trots att gränsen kanske borde ligga närmre 45 procent med hänsyn till ändamålen. Enligt min upp-fattning går HFD även längre än vad som är motiverat sett till bestämmelsens ut-formning och vad som uttrycktes i förarbetena avseende karenstiden. Med tanke på hur praxis utvecklats kan det vara aktuellt att se över regleringen för att bättre överensstämma med ändamålen.This bachelor thesis deals with the outsider rule in 57:5 Swedish income tax law (IL). The outsider rule is an exemption clause, and if found applicable the general taxation rules will be applied instead of the special close company rules. The out-sider rule will be applicable if the shareholder shows that outsiders own a signifi-cant amount of the company's shares. The purpose of this thesis has been to investigate if the application of the law is appropriate with respect to the purposes. In the thesis the interaction between pur-pose, the regulation and the application of the law has been studied to determine if todays regulation and application of the law is appropriate with respect to the pur-poses. Based on the findings, it's possible to conclude that the application of the law in several aspects isn't consistent with the purposes of the regulation. Today the out-sider rule can be applied when outsiders own at least 30 percent of the company, while it should be closer to 45 percent with respect to the purpose. Also, in my view the court's view on the qualifying period cannot be justified with respect to the regulation and its purpose. Given how the application of the law has evolved, it may be necessary to revise the regulation in order to better comply with the purposes

Hip and fragility fracture prediction by 4-item clinical risk score and mobile heel BMD: a women cohort study

<p>Abstract</p> <p>Background</p> <p>One in four Swedish women suffers a hip fracture yielding high morbidity and mortality. We wanted to revalidate a 4-item clinical risk score and evaluate a portable heel bone mineral density (BMD) technique regarding hip and fragility fracture risk among elderly women.</p> <p>Methods</p> <p>In a population-based prospective cohort study we used clinical risk factors from a baseline questionnaire and heel BMD to predict a two-year hip and fragility fracture outcome for women, in a fracture preventive program. Calcaneal heel BMD was measured by portable dual X-ray laser absorptiometry (DXL) and compared to hip BMD, measured with stationary dual X-ray absorptiometry (DXA) technique.</p> <p>Results</p> <p>Seven women suffered hip fracture and 14 women fragility fracture/s (at hip, radius, humerus and pelvis) among 285 women; 60% having heel BMD ≤ -2.5 SD. The 4-item FRAMO (Fracture and Mortality) Index combined the clinical risk factors age ≥80 years, weight <60 kg, prior fragility fracture, and impaired rise-up ability. Women having 2-4 risk factors showed odds ratio (OR) for hip fracture of 5.9 and fragility fracture of 4.4. High risk group hip fracture risk was 2.8% annually compared to 0.5% for the low risk majority (69%). Heel BMD showed hip fracture OR of 3.1 and fragility fracture OR of 2.6 per SD decrease. For 30 DXA assessed participants mean hip BMD at -2.5 SD level corresponded to a lower BMD at the heel. Five of seven hip fractures occurred within a small risk group of 32 women, identified by high FRAMO Index + prior fragility fracture + heel T-score ≤-3.5 SD.</p> <p>Conclusions</p> <p>In a follow-up study we identified high risk groups for hip and fragility fracture with our plain 4-item risk model. Increased fracture risk was also related to decreasing heel BMD in calcaneal bone, measured with a mobile DXL technique. A combination of high FRAMO Index, prior fragility fracture, and very low BMD restricted the high risk group to 11%, among whom most hip fractures occurred (71%). These practical screening methods could eventually reduce hip fracture incidence by concentrating preventive resources to high fracture risk women.</p

The Business Rules Approach - Application in practice

Business agility is emerging as an essential organizational characteristic due to the changing macro environment. The accelerated change has resulted in a substantial deployment of IT. However, the preconceived idea of ISD may be flawed. The final product of ISD is rarely aligned with the business needs. The historical review emphasizes a prominent attempt of increasing the level of business user inclusion through agile project management. However, there is a continued disconnect between business users and IS developers. A recent approach proposed to close the chasm through business user empowerment is the Business Rules Approach, BRA. At the core of the approach exists the business rules manifesto containing ten articles, the key notions of the BRA. The purpose of this study was to explore which key no-tions were applied in practice with emphasis on business user empowerment and business agility. Six semi-structured interviews were conducted at a single organization. The application of the key notions was found to be limited. However, the manifesto is dependent on the use of a BRMS which the organization had removed. Business agility was found to be the primary objective of adopting the BRA while business user inclusion was accentuated rather than business user empowerment

The Power of District Judges and the Responsibility of Courts of Appeals

In this paper we have formulated the problem offinding an LPV-approximation to a system as an optimization problem. For this optimization problem we have presented two possible ways to solve this. The problem is posed as a model reduction problem and formulated such that it should try to preserve the input-output behavior of the system. In the two examples in the paper the potential of the new methods are shown. We have also shown the benefits of using model reduction techniques to capture the input-output behavior to obtain accurate low order LPV-approximations. One method uses SDP-optimization to solve the problem. SDP optimization has been a hot topic during the last years, but the problem with the SDP method is that it scales badly with the dimension of the problem. Also here it has bilinear constraint swhich makes the problem really difficult. With the other method we try to use a more general nonlinear approach which seem to be more suitable for this problem. For this method we have also calculated a gradient that can be used to apply a descentor Newton-like method to solve the problem

Geometric deep learning and equivariant neural networks

We survey the mathematical foundations of geometric deep learning, focusing on group equivariant and gauge equivariant neural networks. We develop gauge equivariant convolutional neural networks on arbitrary manifolds M using principal bundles with structure group K and equivariant maps between sections of associated vector bundles. We also discuss group equivariant neural networks for homogeneous spaces M= G/ K , which are instead equivariant with respect to the global symmetry G on M . Group equivariant layers can be interpreted as intertwiners between induced representations of G, and we show their relation to gauge equivariant convolutional layers. We analyze several applications of this formalism, including semantic segmentation and object detection networks. We also discuss the case of spherical networks in great detail, corresponding to the case M= S2= SO (3) / SO (2) . Here we emphasize the use of Fourier analysis involving Wigner matrices, spherical harmonics and Clebsch–Gordan coefficients for G= SO (3) , illustrating the power of representation theory for deep learning

HEAL-SWIN: A Vision Transformer On The Sphere

High-resolution wide-angle fisheye images are becoming more and more important for robotics applications such as autonomous driving. However, using ordinary convolutional neural networks or vision transformers on this data is problematic due to projection and distortion losses introduced when projecting to a rectangular grid on the plane. We introduce the HEAL-SWIN transformer, which combines the highly uniform Hierarchical Equal Area iso-Latitude Pixelation (HEALPix) grid used in astrophysics and cosmology with the Hierarchical Shifted-Window (SWIN) transformer to yield an efficient and flexible model capable of training on high-resolution, distortion-free spherical data. In HEAL-SWIN, the nested structure of the HEALPix grid is used to perform the patching and windowing operations of the SWIN transformer, resulting in a one-dimensional representation of the spherical data with minimal computational overhead. We demonstrate the superior performance of our model for semantic segmentation and depth regression tasks on both synthetic and real automotive datasets. Our code is available at https://github.com/JanEGerken/HEAL-SWIN.Comment: Main body: 10 pages, 7 figures. Appendices: 4 pages, 2 figure