| 1. |
- Diehl, Stefan, et al.
(författare)
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Shock-wave behaviour of sedimentation in wastewater treatment: a rich problem
- 2012
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Ingår i: Springer Proceedings in Mathematics. - Berlin, Heidelberg : Springer Berlin Heidelberg. - 2190-5622 .- 2190-5614. - 9783642202353 - 9783642202360 ; 6, s. 175-214
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Konferensbidrag (refereegranskat)abstract
- A common industrial process for separating particles from a liquid is continuous sedimentation, which is used in the chemical, mining, pulp-and-paper and food industries. It can also be found in most wastewater treatment plants, where it is a crucial subprocess of a complex biological system. The process has provided, and will continue to provide, scientific problems that lead to fundamental research in different disciplines such as mathematics, wastewater, chemical, mineral, control and automation engineering. A selective survey of previous results within the field of pure and applied mathematics is presented with focus on a nonlinear convection-diffusion partial differential equation with discontinuous coefficients. In a model of a wastewater treatment plant, such an equation is coupled to a set of ordinary differential equations. Some new results on the steady-state solutions of such a coupled system are also presented.
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| 2. |
- Dutkay, Dorin Ervin, et al.
(författare)
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Wavelet Representations and Their Commutant
- 2012
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Ingår i: Analysis for Science, Engineering and Beyond. - Berlin, Heidelberg : Springer Berlin/Heidelberg. - 9783642202353 ; , s. 253-265
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Bokkapitel (refereegranskat)abstract
- We study the reducibility of the wavelet representation associated to various QMF filters, including those associated to Cantor sets. We show there are connections between this problem, the harmonic analysis of transfer operators and the ergodic properties of shifts on solenoids. We prove that if the QMF filter does not have constant absolute value, then the wavelet representations is reducible.
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| 3. |
- Eriksson, Anders P, et al.
(författare)
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On the bijectivity of thin-plate splines
- 2012
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Ingår i: Analysis for Science, Engineering and Beyond, The Tribute Workshop in Honour of Gunnar Sparr held in Lund, May 8-9, 2008. - Berlin, Heidelberg : Springer Berlin Heidelberg. - 9783642202360 - 9783642202353 ; 6, s. 93-141
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- The thin-plate spline (TPS) has been widely used in a number of areas such as image warping, shape analysis and scattered data interpolation. Introduced by Bookstein (IEEE Trans. Pattern Anal. Mach. Intell. 11(6):567–585 1989), it is a natural interpolating function in two dimensions, parameterized by a finite number of landmarks. However, even though the thin-plate spline has a very intuitive interpretation as well as an elegant mathematical formulation, it has no inherent restriction to prevent folding, i.e. a non-bijective interpolating function. In this chapter we discuss some of the properties of the set of parameterizations that form bijective thin-plate splines, such as convexity and boundness. Methods for finding sufficient as well as necessary conditions for bijectivity are also presented. The methods are used in two settings (a) to register two images using thin-plate spline deformations, while ensuring bijectivity and (b) group-wise registration of a set of images, while enforcing bijectivity constraints.
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| 4. |
- Fontes, Magnus, et al.
(författare)
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Statistical and Knowledge Supported Visualization of Multivariate data
- 2012
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Ingår i: Analysis for Science, Engineering and Beyond. - Berlin, Heidelberg : Springer Berlin Heidelberg. - 2190-5622 .- 2190-5614. - 9783642202353 - 9783642202360 ; Springer Proceedings in Mathematics Volume 6, s. 143-173
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Bokkapitel (refereegranskat)abstract
- In the present work we have selected a collection of statistical and mathematical tools useful for the exploration of multivariate data and we present them in a form that is meant to be particularly accessible to a classically trained mathematician. We give self contained and streamlined introductions to principal component analysis, multidimensional scaling and statistical hypothesis testing. Within the presented mathematical framework we then propose a general exploratory methodology for the investigation of real world high dimensional datasets that builds on statistical and knowledge supported visualizations. We exemplify the proposed methodology by applying it to several different genomewide DNA-microarray datasets. The exploratory methodology should be seen as an embryo that can be expanded and developed in many directions. As an example we point out some recent promising advances in the theory for random matrices that, if further developed, potentially could provide practically useful and theoretically well founded estimations of information content in dimension reducing visualizations. We hope that the present work can serve as an introduction to, and help to stimulate more research within, the interesting and rapidly expanding field of data exploration.
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| 5. |
- Johansson, Maria, et al.
(författare)
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Multidimensional inequalities of Hardy and (limit) Pólya-Knopp types
- 2012
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Ingår i: Analysis for science, engineering and beyond. - Heidelberg : Encyclopedia of Global Archaeology/Springer Verlag. - 9783642202353 - 9783642202360 ; , s. 267-304
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Bokkapitel (refereegranskat)abstract
- In this review paper we complement the classical two-dimensional Hardy-type inequality by E. Sawyer (see MR87f:42052) in various ways. In particular, ideas and results from three recent Ph.D. theses are unified and presented in this frame. Also some complementary new results are proved and some open questions are raised.
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| 6. |
- Karlsson, Johan, et al.
(författare)
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Shape Modeling by Optimising Description Length Using Gradients and Parameterisation Invariance
- 2012
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Ingår i: Analysis for Science, Engineering and Beyond, The Tribute Workshop in Honour of Gunnar Sparr held in Lund, May 8-9, 2008. - Berlin, Heidelberg : Springer Berlin Heidelberg. - 9783642202353 - 9783642202360 ; 6, s. 51-91
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- In Statistical Shape Modeling, a dense correspondence between the shapes in the training set must be established. Traditionally this has been done by hand, a process that commonly requires a lot of work and is difficult, especially in 3D. In recent years there has been a lot of work on automatic construction of Shape Models. In recent papers (Davies et al., Medical Image Computing and Computer-Assisted Intervention MICCAI’2001, pp. 57–65, 2001; Davies et al., IEEE Trans. Med. Imaging. 21(5):525–537 2002; Kotcheff and Taylor, Med. Image Anal. 2:303–314 1998) Minimum Description Length, (MDL), is used to locate a dense correspondence between shapes. In this paper the gradient of the description length is derived. Using the gradient, MDL is optimised using steepest descent. The optimisation is therefore faster and experiments show that the resulting models are better. To characterise shape properties that are invariant to similarity transformations, it is first necessary to normalise with respect to the similarity transformations. This is normally done using Procrustes analysis. In this paper we propose to align shapes using the MDL criterion. The MDL based algorithm is compared to Procrustes on a number of data sets. It is concluded that there is improvement in generalisation when using MDL to align the shapes. In this paper novel theory to prevent the commonly occurring problem of clustering under correspondence optimisation is also presented. The problem is solved by calculating the covariance matrix of the shapes using a scalar product that is invariant to mutual reparameterisations. An algorithm for implementing the ideas is proposed and compared to Thodberg’s state of the art algorithm for automatic shape modeling. The suggested algorithm is more stable and the resulting models are of higher quality according to the generalisation measure and according to visual inspection of the specificity.
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| 7. |
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| 8. |
- Persson, Lars-Erik
(författare)
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Gunnar Sparr : the remarkable mathematician, entrepreneur and ambassador for mathematics
- 2012
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Ingår i: Analysis for science, engineering and beyond. - Heidelberg : Encyclopedia of Global Archaeology/Springer Verlag. - 9783642202353 ; , s. 1-22
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Bokkapitel (refereegranskat)abstract
- The article describes the wide range of activities of Professor Gunnar Sparr, Lund University, in mathematics, engineering mathematics, and in the education of mathematics. Scientifically he has made lasting contributions particularly in interpolation theory and mathematical computer vision. In the latter field, his contributions are further strengthened by his being the founder of a large and internationally recognized research group. The article also describes the impact of Gunnar Sparr on industrial mathematics in the region and Sweden, manifested by numerous collaboration projects, and even the founding of a successful start-up company. It also describes his role in the Swedish educational system, by being the driving force in the forming of a successful MSc-program in Engineering Mathematics, with the mathematical sciences providing the main engineering tools.
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| 9. |
- Silvestrov, Sergei
(författare)
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Interpolation of Normed Abelian Groups and Non-Commutative Integration
- 2012
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Ingår i: Analysis for Science, Engineering and Beyond. - Berlin : Springer Berlin/Heidelberg. - 9783642202353 ; , s. 325-341
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Bokkapitel (refereegranskat)abstract
- This is a concise review concerned first of all with the two pioneering far reaching and in many ways yet to be fully explored important papers by Gunnar Sparr and Jaak Peetre on interpolation of normed abelian groups and on non-commutative integration. These papers introduced a general framework unifying many previously known interpolation results and methods in the ways applicable for non-commutative integration and non-commutative extensions of the function spaces, the directions of importance for example in non-commutative geometry and applications in quantum physics. Whence some notions and methods from these papers have been applied in various contexts, many other methods and ideas are yet to be discovered and developed further. In addition to the concise review of these important works by Jaak Peetre and Gunnar Sparr, a brief review is presented also of some related works on non-commutative spaces and non-commutative integration in the contexts of the theory of operator algebras and non-commutative geometry
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| 10. |
- Åström, Kalle, et al.
(författare)
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Preface
- 2012
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Ingår i: Analysis for Science, Engineering and Beyond : The Tribute Workshop in Honour of Gunnar Sparr held in Lund, May 8-9, 2008. - 2190-5614. - 9783642202353 - 9783642202360 ; 6
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Bokkapitel (övrigt vetenskapligt/konstnärligt)
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