| 1. |
- Strömberg, Ann-Brith, 1961, et al.
(author)
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Mixed-Integer Linear Optimization: Primal–Dual Relations and Dual Subgradient and Cutting-Plane Methods
- 2020
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In: Numerical Nonsmooth Optimization: State of the Art Algorithms. - Cham : Springer International Publishing. ; , s. 499-547, s. 499-547
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Book chapter (other academic/artistic)abstract
- This chapter presents several solution methodologies for mixed-integer linear optimization, stated as mixed-binary optimization problems, by means of Lagrangian duals, subgradient optimization, cutting-planes, and recovery of primal solutions. It covers Lagrangian duality theory for mixed-binary linear optimization, a problem framework for which ultimate success—in most cases—is hard to accomplish, since strong duality cannot be inferred. First, a simple conditional subgradient optimization method for solving the dual problem is presented. Then, we show how ergodic sequences of Lagrangian subproblem solutions can be computed and used to recover mixed-binary primal solutions. We establish that the ergodic sequences accumulate at solutions to a convexified version of the original mixed-binary optimization problem. We also present a cutting-plane approach to the Lagrangian dual, which amounts to solving the convexified problem by Dantzig–Wolfe decomposition, as well as a two-phase method that benefits from the advantages of both subgradient optimization and Dantzig–Wolfe decomposition. Finally, we describe how the Lagrangian dual approach can be used to find near optimal solutions to mixed-binary optimization problems by utilizing the ergodic sequences in a Lagrangian heuristic, to construct a core problem, as well as to guide the branching in a branch-and-bound method. The chapter is concluded with a section comprising notes, references, historical downturns, and reading tips.
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| 2. |
- Dupuch, Marie, et al.
(author)
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Comparison of Clustering Approaches through Their Application to Pharmacovigilance Terms
- 2013
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In: Artificial Intelligence in Medicine. Lecture Notes in Computer Science, vol. 7885. - Berlin Heidelberg : Springer. - 9783642383250 - 9783642383267 ; , s. 58-67
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Book chapter (peer-reviewed)abstract
- In different applications (i.e., information retrieval, filteringor analysis), it is useful to detect similar terms and to provide the possibilityto use them jointly. Clustering of terms is one of the methods whichcan be exploited for this. In our study, we propose to test three methodsdedicated to the clustering of terms (hierarchical ascendant classification,Radius and maximum), to combine them with the semantic distance algorithmsand to compare them through the results they provide whenapplied to terms from the pharmacovigilance area. The comparison indicatesthat the non disjoint clustering (Radius and maximum) outperformthe disjoint clusters by 10 to up to 20 points in all the experiments.
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| 3. |
- Engström, Christopher, 1987-, et al.
(author)
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PageRank, a Look at Small Changes in a Line of Nodes and the Complete Graph
- 2016
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In: Engineering Mathematics II. - Cham : Springer. - 9783319421049 - 9783319421056 ; , s. 223-247
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Book chapter (peer-reviewed)abstract
- In this article we will look at the PageRank algorithm used as part of the ranking process of different Internet pages in search engines by for example Google. This article has its main focus in the understanding of the behavior of PageRank as the system dynamically changes either by contracting or expanding such as when adding or subtracting nodes or links or groups of nodes or links. In particular we will take a look at link structures consisting of a line of nodes or a complete graph where every node links to all others. We will look at PageRank as the solution of a linear system of equations and do our examination in both the ordinary normalized version of PageRank as well as the non-normalized version found by solving corresponding linear system. We will show that using two different methods we can find explicit formulas for the PageRank of some simple link structures.
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| 4. |
- Engström, Christopher, 1987-, et al.
(author)
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PageRank, Connecting a Line of Nodes with a Complete Graph
- 2016
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In: Engineering Mathematics II. - Cham : Springer. - 9783319421049 - 9783319421056
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Book chapter (peer-reviewed)abstract
- The focus of this article is the PageRank algorithm originally defined by S. Brin and L. Page as the stationary distribution of a certain random walk on a graph used to rank homepages on the Internet. We will attempt to get a better understanding of how PageRank changes after you make some changes to the graph such as adding or removing edge between otherwise disjoint subgraphs. In particular we will take a look at link structures consisting of a line of nodes or a complete graph where every node links to all others and different ways to combine the two. Both the ordinary normalized version of PageRank as well as a non-normalized version of PageRank found by solving corresponding linear system will be considered. We will see that it is possible to find explicit formulas for the PageRank in some simple link structures and using these formulas take a more in-depth look at the behavior of the ranking as the system changes.
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| 5. |
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| 6. |
- Andersson, Anders, 1957-
(author)
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Numerical Conformal Mappings for Waveguides
- 2010
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In: Computational Mathematics. - Hauppauge, NY, USA : Nova Science Publishers, Inc.. - 9781608762712
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Book chapter (other academic/artistic)abstract
- A number of newly developed numerical conformal mapping techniques are described. Their purpose is to achieve conformal mappings with good accuracy for regions bounded by smooth or piecewise smooth curves in which the boudary curve direction can be controllod, especially towards infinity in unbounded regions as for example waveguides.Most of the mappings are variants of the Schwarz-Christoffel mappings.
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| 7. |
- Larson, Mats G., et al.
(author)
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Adaptive submodeling for linear elasticity problems with multiscale geometric features
- 2005
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In: Multiscale Methods in Science and Engineering. - Berlin Heidelberg : Springer Verlag. - 9783540253358 - 9783540264446 ; , s. 169-180
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Book chapter (other academic/artistic)abstract
- Submodeling is a procedure for local enhancement of the resolution of a coarse global finite element solution by solving a local problem on a subdomain containing an area of particular interest. We focus on linear elasticity and computation of local stress levels determined by the local geometry of the domain. We derive a posteriori error estimates for the submodeling procedure using duality techniques. Based on these estimates we propose an adaptive procedure for automatic choice of the resolution and size of the submodel. The procedure is illustrated for problems of industrial interest.
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| 8. |
- Pettersson, Astrid, 1947-, et al.
(author)
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Matematiken i PISA
- 2010
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In: Rustad att möta framtiden? PISA 2009 om 15-åringars läsförståelse och kunskaper i matematik och naturvetenskap. - Stockholm : Skolverket. ; , s. 97-112
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Book chapter (other academic/artistic)
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| 9. |
- Ostoja-Starzewski, Martin, et al.
(author)
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Scaling to RVE in Random Media
- 2016
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In: Advances in Applied Mechanics. - : Academic Press. - 9780128047798 ; , s. 111-211
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Book chapter (peer-reviewed)abstract
- The problem of effective properties of material microstructures has received considerableattention over the past half a century. By effective (or overall, macroscopic, global) ismeant the response assuming the existence of a representative volume element (RVE)on which a homogeneous continuum is being set up. Since the efforts over the pastquarter century have been shifting to the problem of the size of RVE, this chapterreviews the results and challenges in this broad field for a wide range of materials.For the most part, the approach employed to assess the scaling to the RVE is basedon the Hill–Mandel macrohomogeneity condition. This leads to bounds that explicitlyinvolve the size of a mesoscale domain—this domain also being called a statisticalvolume element (SVE)—relative to the microscale and the type of boundary conditionsapplied to this domain. In general, the trend to pass from the SVE to RVE depends onrandom geometry and mechanical properties of the microstructure, and displayscertain, possibly universal tendencies. This chapter discusses that issue first for linearelastic materials, where a scaling function plays a key role to concisely grasp theSVE-to-RVE scaling. This sets the stage for treatment of nonlinear and or/inelastic randommaterials, including elasto-plastic, viscoelastic, permeable, and thermoelasticclasses. This methodology can be extended to homogenization of random media bymicropolar (Cosserat) rather than by classical (Cauchy) continua as well as to homogenizationunder stationary (standing wave) or transient (wavefront) loading conditions.The final topic treated in this chapter is the formulation of continuum mechanicsaccounting for the violations of second law of thermodynamics, which have been studied on a molecular level in statistical physics over the past two decades. We end with anoverview of open directions and challenges of this research field.
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| 10. |
- Guariglia, Emanuel, et al.
(author)
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Fractional-Wavelet Analysis of Positive definite Distributions and Wavelets on D’(C)
- 2016
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In: Engineering Mathematics II. - Cham : Springer. - 9783319421049 - 9783319421056 ; , s. 337-353
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Book chapter (peer-reviewed)abstract
- In the following chapter we describe a wavelet expansion theory for positivedefinite distributions over the real line and define a fractional derivative operator for complex functions in the distribution sense. In order to obtain a characterisation of the complex fractional derivative through the distribution theory, the Ortigueira-Caputo fractional derivative operator is rewritten as a convolution product according to the fractional calculus of real distributions. In particular, the fractional derivative of the Gabor-Morlet wavelet is computed together with its plots and main properties.
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