| 1. |
- Altmann, Robert, et al.
(författare)
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Numerical homogenization beyond scale separation
- 2021
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Ingår i: Acta Numerica. - : Cambridge University Press (CUP). - 0962-4929 .- 1474-0508. ; 30, s. 1-86
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Tidskriftsartikel (refereegranskat)abstract
- Numerical homogenization is a methodology for the computational solution of multiscale partial differential equations. It aims at reducing complex large-scale problems to simplified numerical models valid on some target scale of interest, thereby accounting for the impact of features on smaller scales that are otherwise not resolved. While constructive approaches in the mathematical theory of homogenization are restricted to problems with a clear scale separation, modern numerical homogenization methods can accurately handle problems with a continuum of scales. This paper reviews such approaches embedded in a historical context and provides a unified variational framework for their design and numerical analysis. Apart from prototypical elliptic model problems, the class of partial differential equations covered here includes wave scattering in heterogeneous media and serves as a template for more general multi-physics problems.
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| 2. |
- Arridge, Simon, et al.
(författare)
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Solving inverse problems using data-driven models
- 2019
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Ingår i: Acta Numerica. - : Cambridge University Press. - 0962-4929 .- 1474-0508. ; 28, s. 1-174
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Tidskriftsartikel (refereegranskat)abstract
- Recent research in inverse problems seeks to develop a mathematically coherent foundation for combining data-driven models, and in particular those based on deep learning, with domain-specific knowledge contained in physical-analytical models. The focus is on solving ill-posed inverse problems that are at the core of many challenging applications in the natural sciences, medicine and life sciences, as well as in engineering and industrial applications. This survey paper aims to give an account of some of the main contributions in data-driven inverse problems.
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| 3. |
- Elden, Lars
(författare)
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Numerical linear algebra in data mining
- 2006
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Ingår i: Acta Numerica. - 0962-4929 .- 1474-0508. ; 15, s. 327-384
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Forskningsöversikt (refereegranskat)abstract
- Ideas and algorithms from numerical linear algebra are important in several areas of data mining. We give an overview of linear algebra methods in text mining (information retrieval), pattern recognition (classification of handwritten digits), and Page Rank computations for web search engines. The emphasis is on rank reduction as a method of extracting information from a data matrix, low-rank approximation of matrices using the singular value decomposition and clustering, and on eigenvalue methods for network analysis. © Cambridge University Press, 2006.
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| 4. |
- Engquist, Björn, et al.
(författare)
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Asymptotic and numerical homogenization
- 2008
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Ingår i: Acta Numerica. - 0962-4929 .- 1474-0508. ; 17, s. 147-190
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Tidskriftsartikel (refereegranskat)abstract
- Homogenization is an important mathematical framework for developing effective models of differential equations with oscillations. We include in the presentation techniques for deriving effective equations, a brief discussion on analysis of related limit processes and numerical methods that are based on homogenization principles. We concentrate on first- and second-order partial differential equations and present results concerning both periodic and random media for linear as well as nonlinear problems. In the numerical sections, we comment on computations of multi-scale problems in general and then focus on projection-based numerical homogenization and the heterogeneous multi-scale method.
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| 5. |
- Engquist, Björn, et al.
(författare)
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Computational high frequency wave propagation
- 2003
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Ingår i: Acta Numerica. - 0962-4929 .- 1474-0508. ; 12, s. 181-266
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Tidskriftsartikel (refereegranskat)abstract
- Numerical simulation of high frequency acoustic, elastic or electro-magnetic wave propagation is important in many applications. Recently the traditional techniques of ray tracing based on geometrical optics have been augmented by numerical procedures based on partial differential equations. Direct simulations of solutions to the eikonal equation have been used in seismology, and lately approximations of the Liouville or Vlasov equation formulations of geometrical optics have generated impressive results. There are basically two techniques that follow from this latter approach: one is wave front methods and the other moment methods. We shall develop these methods in some detail after a brief review of more traditional algorithms for simulating high frequency wave propagation.
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| 6. |
- Eriksson, Kenneth, et al.
(författare)
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Introduction to Adaptive Methods for Differential Equations
- 1995
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Ingår i: Acta Numerica. - : Cambridge University Press. - 0962-4929 .- 1474-0508. ; 4, s. 105-158
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Tidskriftsartikel (refereegranskat)abstract
- Knowing thus the Algorithm of this calculus, which I call Differential Calculus, all differential equations can be solved by a common method (Gottfried Wilhelm von Leibniz, 1646–1719). When, several years ago, I saw for the first time an instrument which, when carried, automatically records the number of steps taken by a pedestrian, it occurred to me at once that the entire arithmetic could be subjected to a similar kind of machinery so that not only addition and subtraction, but also multiplication and division, could be accomplished by a suitably arranged machine easily, promptly and with sure results…. For it is unworthy of excellent men to lose hours like slaves in the labour of calculations, which could safely be left to anyone else if the machine was used…. And now that we may give final praise to the machine, we may say that it will be desirable to all who are engaged in computations which, as is well known, are the managers of financial affairs, the administrators of others estates, merchants, surveyors, navigators, astronomers, and those connected with any of the crafts that use mathematics (Leibniz).
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| 7. |
- Eilertsen, G., et al.
(författare)
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Similarities and differences in the experience of fatigue among people living with fibromyalgia, multiple sclerosis, ankylosing spondylitis and stroke
- 2015
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Ingår i: Journal of Clinical Nursing. - : Wiley. - 0962-1067 .- 1365-2702. ; 24:13-14, s. 2023-2034
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Tidskriftsartikel (refereegranskat)abstract
- Aims and objectives: To elucidate the experience of fatigue across several long-term illnesses, focusing on the similarities and differences. Background: Fatigue is common to many long-term illnesses, but it has been studied mainly within the context of a single illness; qualitative studies comparing the experience and its impact on daily life across different long-term illnesses are lacking. Design: Qualitative design. Methods: A secondary analysis was conducted of five original interview studies involving 95 persons with ankylosing spondylitis, fibromyalgia, multiple sclerosis or stroke. Results: Similarities and differences concerning experiences of fatigue were found across the studied long-term illnesses. All patients expressed the perception of having an unfamiliar body. Fatigue was also commonly expressed as unpredictable, uncontrollable and invisible to others. Differences were related to a constant versus a varying condition, a sudden and an uncontrollable sleepiness, a mutual reinforcement with pain and increased stress sensitivity. A lack of energy and a need for sleep and rest were common experiences, as was the impact on social relationships. There were also similarities regarding how the patients managed their daily life. The search for practical solutions and attitude adjustment differed with the fatigue characteristics. All patients felt a lack of understanding and disbelief from others. Conclusion and relevance to clinical practice: Fatigue is commonly expressed by patients with long-term illnesses. Variations in experience are related to the type of diagnosis. The disparity between experiences influences how patients managed and adjusted to the conditions of everyday life. The illness-specific characteristics of fatigue warrant increased clinical awareness and may allow professionals to offer adequate information and establish effective methods of managing the condition. The feeling of invisibility and difficulty describing the experience of fatigue in particular highlights this need. © 2015 John Wiley & Sons Ltd.
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| 8. |
- Chaturvedi, Nish, et al.
(författare)
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Effect of candesartan on prevention (DIRECT-Prevent 1) and progression (DIRECT-Protect 1) of retinopathy in type 1 diabetes: randomised, placebo-controlled trials.
- 2008
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Ingår i: Lancet. - 1474-547X. ; 372:9647, s. 1394-402
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Tidskriftsartikel (refereegranskat)abstract
- BACKGROUND: Results of previous studies suggest that renin-angiotensin system blockers might reduce the burden of diabetic retinopathy. We therefore designed the DIabetic REtinopathy Candesartan Trials (DIRECT) Programme to assess whether candesartan could reduce the incidence and progression of retinopathy in type 1 diabetes. METHODS: Two randomised, double-blind, parallel-design, placebo-controlled trials were done in 309 centres worldwide. Participants with normotensive, normoalbuminuric type 1 diabetes without retinopathy were recruited to the DIRECT-Prevent 1 trial and those with existing retinopathy were recruited to DIRECT-Protect 1, and were assigned to candesartan 16 mg once a day or matching placebo. After 1 month, the dose was doubled to 32 mg. Investigators and participants were unaware of the treatment allocation status. The primary endpoints were incidence and progression of retinopathy and were defined as at least a two-step and at least a three-step increase on the Early Treatment Diabetic Retinopathy Study (ETDRS) scale, respectively. These trials are registered with ClinicalTrials.gov, numbers NCT00252733 for DIRECT-Prevent 1 and NCT00252720 for DIRECT-Protect 1. FINDINGS: 1421 participants (aged 18-50 years) were randomly assigned to candesartan (n=711) or to placebo (n=710) in DIRECT-Prevent 1, and 1905 (aged 18-55 years) to candesartan (n=951) or to placebo (n=954) in DIRECT-Protect 1. Incidence of retinopathy was seen in 178 (25%) participants in the candesartan group versus 217 (31%) in the placebo group. Progression of retinopathy occurred in 127 (13%) participants in the candesartan group versus 124 (13%) in the placebo group. Hazard ratio (HR for candesartan vs placebo) was 0.82 (95% CI 0.67-1.00, p=0.0508) for incidence of retinopathy and 1.02 (0.80-1.31, p=0.85) for progression of retinopathy. The post-hoc outcome of at least a three-step increase for incidence yielded an HR of 0.65 (0.48-0.87, p=0.0034), which was attenuated but still significant after adjustment for baseline characteristics (0.71, 0.53-0.95, p=0.046). Final ETDRS level was more likely to have improved with candesartan treatment in both DIRECT-Prevent 1 (odds 1.16, 95% CI 1.05-1.30, p=0.0048) and DIRECT-Protect 1 (1.12, 95% CI 1.01-1.25, p=0.0264). Adverse events did not differ between the treatment groups. INTERPRETATION: Although candesartan reduces the incidence of retinopathy, we did not see a beneficial effect on retinopathy progression.
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