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  • 1. Aalto, Daniel
    et al.
    Berkovits, Lauri
    Kansanen, Outi Elina
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Yue, Hong
    John-Nirenberg lemmas for a doubling measure2011In: Studia Mathematica, ISSN 0039-3223, Vol. 204, no 1, 21-37 p.Article in journal (Refereed)
    Abstract [en]

    We study, in the context of doubling metric measure spaces, a class of BMO type functions defined by John and Nirenberg. In particular, we present a new version of the Calderon-Zygmund decomposition in metric spaces and use it to prove the corresponding John Nirenberg inequality.

  • 2.
    Aas, Erik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    A Markov Process on Cyclic Words2014Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    The TASEP (totally asymmetric simple exclusion process) studied here is a Markov chain on cyclic words over the alphabet{1,2,...,n} given by at each time step sorting an adjacent pair of letters chosen uniformly at random. For example, from the word 3124 one may go to 1324, 3124, 3124, 4123 by sorting the pair 31, 12, 24, or 43.

    Two words have the sametype if they are permutations of each other. If we restrict TASEP to words of some particular type m we get an ergodic Markov chain whose stationary distribution we denote by ζm. Soζm (u) is the asymptotic proportion of time spent in the state u if the chain started in some word of type m. The distribution ζ is the main object of study in this thesis. This distribution turns out to have several remarkable properties, and alternative characterizations. It has previously been studied both from physical, combinatorial, and probabilitistic viewpoints.

    In the first chapter we give an extended summary of known results and results in this thesis concerning ζ. The new results are described (and proved) in detail in Papers I - IV.

    The new results in Papers I and II include an explicit formula for the value ofζat sorted words and a product formula for decomposable words. We also compute some correlation functions for ζ. In Paper III we study of a generalization of TASEP to Weyl groups. In Paper IV we study a certain scaling limit of ζ, finding several interesting patterns of which we prove some. We also study an inhomogenous version of TASEP, in which different particles get sorted at different rates, which generalizes the homogenous version in several aspects. In the first chapter we compute some correlation functions for ζ

  • 3.
    Aas, Erik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Limit points of the iterative scaling procedure2014In: Annals of Operations Research, ISSN 0254-5330, E-ISSN 1572-9338, Vol. 215, no 1, 15-23 p.Article in journal (Refereed)
    Abstract [en]

    The iterative scaling procedure (ISP) is an algorithm which computes a sequence of matrices, starting from some given matrix. The objective is to find a matrix 'proportional' to the given matrix, having given row and column sums. In many cases, for example if the initial matrix is strictly positive, the sequence is convergent. It is known that the sequence has at most two limit points. When these are distinct, convergence to these two points can be slow. We give an efficient algorithm which finds the limit points, invoking the ISP only on subproblems for which the procedure is convergent.

  • 4.
    Aas, Erik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Stationary probability of the identity for the TASEP on a Ring2012Other (Other academic)
    Abstract [en]

    Consider the following Markov chain on permutations of length n. At each time step we choose a random position. If the letter at that position is smaller than the letter immediately to the left (cyclically) then these letters swap positions. Otherwise nothing happens, corresponding to a loop in the Markov chain. This is the circular TASEP. We compute the average proportion of time the chain spends at the identity permutation (and, in greater generality, at sorted words). This answers a conjecture by Thomas Lam.

  • 5.
    Aas, Erik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    TASEP in any Weyl groupManuscript (preprint) (Other academic)
    Abstract [en]

    We investigate a Markov chain dened by Thomas Lam [6], whichgeneralizes the multi-type TASEP on a ring to any Weyl group. For groups of typeC we dene an analogue of the multiline queues of Ferrari and Martin (which com-pute the stationary distribution for the classical TASEP). While our constructiondoes not suce for nding the stationary distribution, the construction gives thestationary distribution of a certain projection of Lam's chain. Also, our approach isincremental, in the sense that the construction appears to t into a pattern of 'con-jugation matrices', which remains to be fully worked out. We conjecture an explicitformula for the partition function of the model. Finally, we prove a theorem for theclassical TASEP which ts into the picture of viewing TASEP in a permutation-freeway.

  • 6.
    Aas, Erik
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Linusson, Svante
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Continuous multiline queues and TASEPManuscript (preprint) (Other academic)
  • 7.
    Aas, Erik
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Sjöstrand, Jonas
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    A product formula for the TASEP on a ring2016In: Random structures & algorithms (Print), ISSN 1042-9832, E-ISSN 1098-2418, Vol. 48, no 2, 247-259 p.Article in journal (Refereed)
    Abstract [en]

    For a random permutation sampled from the stationary distributionof the TASEP on a ring, we show that, conditioned on the event that the rstentries are strictly larger than the last entries, the order of the rst entries isindependent of the order of the last entries. The proof uses multi-line queues asdened by Ferrari and Martin, and the theorem has an enumerative combinatorialinterpretation in that setting.As an application we prove a conjecture of Lam and Williams concerningSchubert factors of the stationary probability of certain states.Finally, we present a conjecture for the case where the small and large entriesare not separated.

  • 8.
    Abbaszadeh Shahri, Abbas
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering.
    Larsson, Stefan
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Soil and Rock Mechanics.
    Johansson, Fredrik
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Soil and Rock Mechanics.
    Updated relations for the uniaxial compressive strength of marlstones based on P-wave velocity and point load index test2016In: INNOVATIVE INFRASTRUCTURE SOLUTIONS, ISSN 2364-4176, Vol. 1, no 1, UNSP 17Article in journal (Refereed)
    Abstract [en]

    Although there are many proposed relations for different rock types to predict the uniaxial compressive strength (UCS) as a function of P-wave velocity (V-P) and point load index (Is), only a few of them are focused on marlstones. However, these studies have limitations in applicability since they are mainly based on local studies. In this paper, an attempt is therefore made to present updated relations for two previous proposed correlations for marlstones in Iran. The modification process is executed through multivariate regression analysis techniques using a provided comprehensive database for marlstones in Iran, including UCS, V-P and Is from publications and validated relevant sources comprising 119 datasets. The accuracy, appropriateness and applicability of the obtained modifications were tested by means of different statistical criteria and graph analyses. The conducted comparison between updated and previous proposed relations highlighted better applicability in the prediction of UCS using the updated correlations introduced in this study. However, the derived updated predictive models are dependent on rock types and test conditions, as they are in this study.

  • 9.
    Abdullah Al Ahad, Muhammed
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Non-linearstates in parallel Blasius boundary layer2014Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    There is large theoretical, experimental and numerical interest in studying boundary layers, which develop around any body moving through a fluid. The simplest of these boundary layers lead to the theoretical abstraction of a so-called Blasius boundary layer, which can be derived under the assumption of a flat plate and zero external pressure gradient. The Blasius solution is characterised by a slow growth of the boundary layer in the streamwise direction. For practical purposes, in particular related to studying transition scenarios, non-linear finite-amplitude states (exact coherent states, edge states), but also for turbulence, a major simplification of the problem could be attained by removing this slow streamwise growth, and instead consider a parallel boundary layer. Parallel boundary layers are found in reality, e.g. when applying suction (asymptotic suction boundary layer) or rotation (Ekman boundary layer), but not in the Blasius case. As this is only a model which is not an exact solution to the Navier-Stokes (or boundary-layer) equations, some modifications have to be introduced into the governing equations in order for such an approach to be feasible. Spalart and Yang introduced a modification term to the governing Navier-Stokes equations in 1987. In this thesis work, we adapted the amplitude of the modification term introduced by Spalart and Yang to identify the nonlinear states in the parallel Blasius boundary layer. A final application of this modification was in determining the so-called edge states for boundary layers, previously found in the asymptotic suction boundary layer

  • 10. Abdulle, Assyr
    et al.
    Henning, Patrick
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Localized orthogonal decomposition method for the wave equation with a continuum of scales2017In: Mathematics of Computation, ISSN 0025-5718, E-ISSN 1088-6842, Vol. 86, no 304, 549-587 p.Article in journal (Refereed)
    Abstract [en]

    This paper is devoted to numerical approximations for the wave equation with a multiscale character. Our approach is formulated in the framework of the Localized Orthogonal Decomposition (LOD) interpreted as a numerical homogenization with an L2-projection. We derive explicit convergence rates of the method in the L∞(L2)-, W1,∞(L2)-and L∞(H1)-norms without any assumptions on higher order space regularity or scale-separation. The order of the convergence rates depends on further graded assumptions on the initial data. We also prove the convergence of the method in the framework of G-convergence without any structural assumptions on the initial data, i.e. without assuming that it is well-prepared. This rigorously justifies the method. Finally, the performance of the method is demonstrated in numerical experiments.

  • 11.
    Abramson, Nils
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Production Engineering.
    Boman, J.
    Bonnevier, Björn
    KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
    Plane intersections of rotational ellipsoids2006In: The American mathematical monthly, ISSN 0002-9890, Vol. 113, no 4, 336-339 p.Article in journal (Refereed)
  • 12. Acker, A.
    et al.
    Henrot, A.
    Poghosyan, M.
    Shahgholian, Henrik
    KTH, Superseded Departments, Mathematics.
    The multi-layer free boundary problem for the p-Laplacian in convex domains2004In: Interfaces and free boundaries (Print), ISSN 1463-9963, Vol. 6, no 1, 81-103 p.Article in journal (Refereed)
    Abstract [en]

    The main result of this paper concerns existence of classical solutions to the multi-layer Bernoulli free boundary problem with nonlinear joining conditions and the p-Laplacian as governing operator. The present treatment of the two-layer case involves technical refinements of the one-layer case, studied earlier by two of the authors. The existence treatment of the multi-layer case is largely based on a reduction to the two-layer case, in which uniform separation of the free boundaries plays a key role.

  • 13. Adamaszek, Michal
    et al.
    Barmak, Jonathan Ariel
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    On a lower bound for the connectivity of the independence complex of a graph2011In: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 311, no 21, 2566-2569 p.Article in journal (Refereed)
    Abstract [en]

    Aharoni, Berger and Ziv proposed a function which is a lower bound for the connectivity of the independence complex of a graph. They conjectured that this bound is optimal for every graph. We give two different arguments which show that the conjecture is false.

  • 14. Adams, Henry
    et al.
    Tausz, Andrew
    Vejdemo-Johansson, Mikael
    KTH, School of Computer Science and Communication (CSC), Computer Vision and Active Perception, CVAP. Institut Jozef Stefan, Slovenia .
    javaPlex: A Research Software Package for Persistent (Co) Homology2014Conference paper (Refereed)
    Abstract [en]

    The computation of persistent homology has proven a fundamental component of the nascent field of topological data analysis and computational topology. We describe a new software package for topological computation, with design focus on needs of the research community. This tool, replacing previous jPlex and Plex, enables researchers to access state of the art algorithms for persistent homology, cohomology, hom complexes, filtered simplicial complexes, filtered cell complexes, witness complex constructions, and many more essential components of computational topology. We describe, herewithin, the design goals we have chosen, as well as the resulting software package, and some of its more novel capabilities.

  • 15.
    Adelstrand, Carl
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Gavefalk, Sofia
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    In times of regional geopolitical turmoil – Why do some equity funds performbetter than others?2014Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    In times of regional geopolitical turmoil – why do some investment portfolios, equity funds, perform better than others? Is it simply luck, the effects of systematic risk or do factors such as investment styles and managerial skills play a significant part in the performance of a fund?

    As financial markets often reflect the macro environment, much of the previous year’s fluctuations of Eastern European stocks can be seen to derive from a number of geopolitical events; from the 2013 summer clashes between the Turkish police and opposing parties to the current issue concerning Russia and Ukraine. Needless to say, these events have affected return on equity in their regions and created a distressed environment for investors and equity fund managers investing in Eastern Europe.

    This thesis aims to explore how the aforementioned macroeconomic events impact the market and thus the portfolios of asset managers. The thesis also intends to provide aspects of eventual investment strategies that are more preferable than others under such circumstances, in order to mitigate the subsequent risks.

  • 16. Adiprasito, Karim
    et al.
    Björner, Anders
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Goodarzi, Afshin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Face numbers of sequentially Cohen-Macaulay complexes and Betti numbers of componentwise linear idealsArticle in journal (Other academic)
    Abstract [en]

    A numerical characterization is given of the so-called h-triangles of sequentially Cohen-Macaulay simplicial complexes. This result characterizes the number of faces of various dimensions and codimensions in such a complex, generalizing the classical Macaulay-Stanley theorem to the nonpure case. Moreover, we characterize the possible Betti tables of componentwise linear ideals. A key tool in our investigation is a bijection between shifted multicomplexes of degree at most d and shifted pure (d-1)-dimensional simplicial complexes.

  • 17. Adiprasito, Karim
    et al.
    Goodarzi, Afshin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Varbaro, Matteo
    Connectivity of pseudomanifold graphs from an algebraic point of view2015In: Comptes Rendus Mathematiques de l'Academie des Sciences = Mathematical reports of the academy of science, ISSN 0706-1994, Vol. 353, no 12, 1061-1065 p.Article in journal (Refereed)
    Abstract [en]

    The connectivity of graphs of simplicial and polytopal complexes is a classical subject going back at least to Steinitz, and the topic has since been studied by many authors, including Balinski, Barnette, Athanasiadis, and Bjorner. In this note, we provide a unifying approach that allows us to obtain more general results. Moreover, we provide a relation to commutative algebra by relating connectivity problems to graded Betti numbers of the associated Stanley-Reisner rings.

  • 18.
    Adler, Jonas
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    GPU Monte Carlo scatter calculations for Cone Beam Computed Tomography2014Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    A GPU Monte Carlo code for x-ray photon transport has been implemented and extensively tested. The code is intended for scatter compensation of cone beam computed tomography images.

    The code was tested to agree with other well known codes within 5% for a set of simple scenarios. The scatter compensation was also tested using an artificial head phantom. The errors in the reconstructed Hounsfield values were reduced by approximately 70%.

    Several variance reduction methods have been tested, although most were found infeasible on GPUs. The code is nonetheless fast, and can simulate approximately 3 ·109 photons per minute on a NVIDIA Quadro 4000 graphics card. With the use of appropriate filtering methods, the code can be used to calculate patient specific scatter distributions for a full CBCT scan in approximately one minute, allowing scatter reduction in clinical applications.

  • 19. Adler, M.
    et al.
    Chhita, S.
    Johansson, Kurt
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    van Moerbeke, P.
    Tacnode GUE-minor processes and double Aztec diamonds2015In: Probability theory and related fields, ISSN 0178-8051, E-ISSN 1432-2064, Vol. 162, no 1-2, 275-325 p.Article in journal (Refereed)
    Abstract [en]

    We study determinantal point processes arising in random domino tilings of a double Aztec diamond, a region consisting of two overlapping Aztec diamonds. At a turning point in a single Aztec diamond where the disordered region touches the boundary, the natural limiting process is the GUE-minor process. Increasing the size of a double Aztec diamond while keeping the overlap between the two Aztec diamonds finite, we obtain a new determinantal point process which we call the tacnode GUE-minor process. This process can be thought of as two colliding GUE-minor processes. As part of the derivation of the particle kernel whose scaling limit naturally gives the tacnode GUE-minor process, we find the inverse Kasteleyn matrix for the dimer model version of the Double Aztec diamond.

  • 20. Adler, Mark
    et al.
    Johansson, Kurt
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    van Moerbeke, Pierre
    Double Aztec diamonds and the tacnode process2014In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 252, 518-571 p.Article in journal (Refereed)
    Abstract [en]

    Discrete and continuous non-intersecting random processes have given rise to critical "infinite-dimensional diffusions", like the Airy process, the Pearcey process and variations thereof. It has been known that domino tilings of very large Aztec diamonds lead macroscopically to a disordered region within an inscribed ellipse (arctic circle in the homogeneous case), and a regular brick-like region outside the ellipse. The fluctuations near the ellipse, appropriately magnified and away from the boundary of the Aztec diamond, form an Airy process, run with time tangential to the boundary. This paper investigates the domino tiling of two overlapping Aztec diamonds; this situation also leads to non-intersecting random walks and an induced point process; this process is shown to be determinantal. In the large size limit, when the overlap is such that the two arctic ellipses for the single Aztec diamonds merely touch, a new critical process will appear near the point of osculation (tacnode), which is run with a time in the direction of the common tangent to the ellipses: this is the tacnode process. It is also-shown here that this tacnode process is universal: it coincides with the one found in the context of two groups of non-intersecting random walks or also Brownian motions, meeting momentarily.

  • 21.
    af Klinteberg, Ludvig
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Computational methods for microfluidics2013Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis is concerned with computational methods for fluid flows on the microscale, also known as microfluidics. This is motivated by current research in biological physics and miniaturization technology, where there is a need to understand complex flows involving microscale structures. Numerical simulations are an important tool for doing this.

    The first paper of the thesis presents a numerical method for simulating multiphase flows involving insoluble surfactants and moving contact lines. The method is based on an explicit interface tracking method, wherein the interface between two fluids is decomposed into segments, which are represented locally on an Eulerian grid. The framework of this method provides a natural setting for solving the advection-diffusion equation governing the surfactant concentration on the interface. Open interfaces and moving contact lines are also incorporated into the method in a natural way, though we show that care must be taken when regularizing interface forces to the grid near the boundary of the computational domain.

    In the second paper we present a boundary integral formulation for sedimenting particles in periodic Stokes flow, using the completed double layer boundary integral formulation. The long-range nature of the particle-particle interactions lead to the formulation containing sums which are not absolutely convergent if computed directly. This is solved by applying the method of Ewald summation, which in turn is computed in a fast manner by using the FFT-based spectral Ewald method. The complexity of the resulting method is O(N log N), as the system size is scaled up with the number of discretization points N. We apply the method to systems of sedimenting spheroids, which are discretized using the Nyström method and a basic quadrature rule.

    The Ewald summation method used in the boundary integral method of the second paper requires a decomposition of the potential being summed. In the introductory chapters of the thesis we present an overview of the available methods for creating Ewald decompositions, and show how the methods and decompositions can be related to each other.

  • 22.
    af Klinteberg, Ludvig
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Ewald summation for the rotlet singularity of Stokes flow2016Report (Other academic)
    Abstract [en]

    Ewald summation is an efficient method for computing the periodic sums that appear when considering the Green's functions of Stokes flow together with periodic boundary conditions. We show how Ewald summation, and accompanying truncation error estimates, can be easily derived for the rotlet, by considering it as a superposition of electrostatic force calculations.

  • 23.
    af Klinteberg, Ludvig
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Fast and accurate integral equation methods with applications in microfluidics2016Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis is concerned with computational methods for fluid flows on the microscale, also known as microfluidics. This is motivated by current research in biological physics and miniaturization technology, where there is a need to understand complex flows involving microscale structures. Numerical simulations are an important tool for doing this.

    The first, and smaller, part of the thesis presents a numerical method for simulating multiphase flows involving insoluble surfactants and moving contact lines. The method is based on an interface decomposition resulting in local, Eulerian grid representations. This provides a natural setting for solving the PDE governing the surfactant concentration on the interface.

    The second, and larger, part of the thesis is concerned with a framework for simulating large systems of rigid particles in three-dimensional, periodic viscous flow using a boundary integral formulation. This framework can solve the underlying flow equations to high accuracy, due to the accurate nature of surface quadrature. It is also fast, due to the natural coupling between boundary integral methods and fast summation methods.

    The development of the boundary integral framework spans several different fields of numerical analysis. For fast computations of large systems, a fast Ewald summation method known as Spectral Ewald is adapted to work with the Stokes double layer potential. For accurate numerical integration, a method known as Quadrature by Expansion is developed for this same potential, and also accelerated through a scheme based on geometrical symmetries. To better understand the errors accompanying this quadrature method, an error analysis based on contour integration and calculus of residues is carried out, resulting in highly accurate error estimates.

  • 24.
    af Klinteberg, Ludvig
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Saffar Shamshirgar, Davoud
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Tornberg, Anna-Karin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Fast Ewald summation for free-space Stokes potentials2017In: Research in the Mathematical Sciences, ISSN 2197-9847, Vol. 4, no 1Article in journal (Refereed)
    Abstract [en]

    We present a spectrally accurate method for the rapid evaluation of free-space Stokes potentials, i.e., sums involving a large number of free space Green’s functions. We consider sums involving stokeslets, stresslets and rotlets that appear in boundary integral methods and potential methods for solving Stokes equations. The method combines the framework of the Spectral Ewald method for periodic problems (Lindbo and Tornberg in J Comput Phys 229(23):8994–9010, 2010. doi: 10.1016/j.jcp.2010.08.026 ), with a very recent approach to solving the free-space harmonic and biharmonic equations using fast Fourier transforms (FFTs) on a uniform grid (Vico et al. in J Comput Phys 323:191–203, 2016. doi: 10.1016/j.jcp.2016.07.028 ). Convolution with a truncated Gaussian function is used to place point sources on a grid. With precomputation of a scalar grid quantity that does not depend on these sources, the amount of oversampling of the grids with Gaussians can be kept at a factor of two, the minimum for aperiodic convolutions by FFTs. The resulting algorithm has a computational complexity of $$O(N \log N)$$ O ( N log N ) for problems with N sources and targets. Comparison is made with a fast multipole method to show that the performance of the new method is competitive.

  • 25.
    af Klinteberg, Ludvig
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Tornberg, Anna-Karin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    A fast integral equation method for solid particles in viscous flow using quadrature by expansionManuscript (preprint) (Other academic)
    Abstract [en]

    Boundary integral methods are advantageous when simulating viscous flow around rigid particles, due to the reduction in number of unknowns and straightforward handling of the geometry. In this work we present a fast and accurate framework for simulating spheroids in periodic Stokes flow, which is based on the completed double layer boundary integral formulation. The framework implements a new method known as quadrature by expansion (QBX), which uses surrogate local expansions of the layer potential to evaluate it to very high accuracy both on and off the particle surfaces. This quadrature method is accelerated through a newly developed precomputation scheme. The long range interactions are computed using the spectral Ewald (SE) fast summation method, which after integration with QBX allows the resulting system to be solved in M log M time, where M is the number of particles. This framework is suitable for simulations of large particle systems, and can be used for studying e.g. porous media models.

  • 26.
    af Klinteberg, Ludvig
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Tornberg, Anna-Karin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    A fast integral equation method for solid particles in viscous flow using quadrature by expansion2016In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 326, 420-445 p.Article in journal (Refereed)
    Abstract [en]

    Boundary integral methods are advantageous when simulating viscous flow around rigid particles, due to the reduction in number of unknowns and straightforward handling of the geometry. In this work we present a fast and accurate framework for simulating spheroids in periodic Stokes flow, which is based on the completed double layer boundary integral formulation. The framework implements a new method known as quadrature by expansion (QBX), which uses surrogate local expansions of the layer potential to evaluate it to very high accuracy both on and off the particle surfaces. This quadrature method is accelerated through a newly developed precomputation scheme. The long range interactions are computed using the spectral Ewald (SE) fast summation method, which after integration with QBX allows the resulting system to be solved in M log M time, where M is the number of particles. This framework is suitable for simulations of large particle systems, and can be used for studying e.g. porous media models.

    The full text will be freely available from 2018-09-09 10:45
  • 27.
    af Klinteberg, Ludvig
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Tornberg, Anna-Karin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Error estimation for quadrature by expansion in layer potential evaluation2017In: Advances in Computational Mathematics, ISSN 1019-7168, E-ISSN 1572-9044, Vol. 43, no 1, 195-234 p.Article in journal (Refereed)
    Abstract [en]

    In boundary integral methods it is often necessary to evaluate layer potentials on or close to the boundary, where the underlying integral is difficult to evaluate numerically. Quadrature by expansion (QBX) is a new method for dealing with such integrals, and it is based on forming a local expansion of the layer potential close to the boundary. In doing so, one introduces a new quadrature error due to nearly singular integration in the evaluation of expansion coefficients. Using a method based on contour integration and calculus of residues, the quadrature error of nearly singular integrals can be accurately estimated. This makes it possible to derive accurate estimates for the quadrature errors related to QBX, when applied to layer potentials in two and three dimensions. As examples we derive estimates for the Laplace and Helmholtz single layer potentials. These results can be used for parameter selection in practical applications.

  • 28.
    af Klinteberg, Ludvig
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Tornberg, Anna-Karin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Estimation of quadrature errors in layer potential evaluation using quadrature by expansionManuscript (preprint) (Other academic)
    Abstract [en]

    In boundary integral methods it is often necessary to evaluate layer potentials on or close to the boundary, where the underlying integral is difficult to evaluate numerically. Quadrature by expansion (QBX) is a new method for dealing with such integrals, and it is based on forming a local expansion of the layer potential close to the boundary. In doing so, one introduces a new quadrature error due to nearly singular integration in the evaluation of expansion coefficients. Using a method based on contour integration and calculus of residues, the quadrature error of nearly singular integrals can be accurately estimated. This makes it possible to derive accurate estimates for the quadrature errors related to QBX, when applied to layer potentials in two and three dimensions. As examples we derive estimates for the Laplace and Helmholtz single layer potentials. These results can be used for parameter selection in practical applications.

  • 29.
    af Klinteberg, Ludvig
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Tornberg, Anna-Karin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Fast Ewald summation for Stokesian particle suspensions2014In: International Journal for Numerical Methods in Fluids, ISSN 0271-2091, E-ISSN 1097-0363, Vol. 76, no 10, 669-698 p.Article in journal (Refereed)
    Abstract [en]

    We present a numerical method for suspensions of spheroids of arbitrary aspect ratio, which sediment under gravity. The method is based on a periodized boundary integral formulation using the Stokes double layer potential. The resulting discrete system is solved iteratively using generalized minimal residual accelerated by the spectral Ewald method, which reduces the computational complexity to O(N log N), where N is the number of points used to discretize the particle surfaces. We develop predictive error estimates, which can be used to optimize the choice of parameters in the Ewald summation. Numerical tests show that the method is well conditioned and provides good accuracy when validated against reference solutions. 

  • 30. Aghajani, A.
    et al.
    Razani, Abdolrahman
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). Department of Mathematics, Faculty of Science, Imam Khomeini International University, Iran .
    Some completeness theorems in the Menger probabilistic metric space2008In: Applied Sciences: APPS, ISSN 1454-5101, E-ISSN 1454-5101, Vol. 10, 1-8 p.Article in journal (Refereed)
    Abstract [en]

    In this article, some new completeness theorems in probabilistic normed space are proved. Moreover, the existence of a constrictive Monger probabilistic normed space is shown.

  • 31. Agranovsky, M.
    et al.
    Khavinson, D.
    Shapiro, Harold
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Malmheden's theorem revisited2010In: Expositiones mathematicae, ISSN 0723-0869, Vol. 28, no 4, 337-350 p.Article in journal (Refereed)
    Abstract [en]

    In 1934 Malmheden [16] discovered an elegant geometric algorithm for solving the Dirichlet problem in a ball. Although his result was rediscovered independently by Duffin (1957) [8] 23 years later, it still does not seem to be widely known. In this paper we return to Malmheden's theorem, give an alternative proof of the result that allows generalization to polyharmonic functions and, also, discuss applications of his theorem to geometric properties of harmonic measures in balls in R-n.

  • 32. Aharonov, Dov
    et al.
    Shapiro, Harold S.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Solynin, Alexander Yu.
    Minimal area problems for functions with integral representation2006In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 98, 83-111 p.Article in journal (Refereed)
    Abstract [en]

    We study the minimization problem for the Dirichlet integral in some standard classes of analytic functions. In particular, we solve the minimal area a(2)-problern for convex functions and for typically real functions. The latter gives a new solution to the minimal area a(2)-problem for the class S of normalized univalent functions in the unit disc.

  • 33.
    Ahlberg, Marcus
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Lilja, Jimmy
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Lageroptimering: Minimera tiden till leverans med begränsat lagerutrymme2016Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    This thesis presents a study in mathematical optimization of the inventory routine at the company Aktiebolaget Kronborsten. The thesis establishes a general optimization problem identified at Kronborstens inventory routine. The identified problem is to find the optimal mix between products in the finished goods inventory, which minimizes the expected time until delivery.

    The proposed model assumes that orders and manufacturing follow a stochastic process. With these assumptions the inventory and manufacturing are represented as several independent Markov processes. From the stationary distribution of these processes a function was identified for the expected time until delivery for a given solution. The identified function had convex properties which made it possible to solve the optimization problem using the marginal allocation algorithm.

    The mathematical problem is followed by a chapter about the costs related to storage. The purpose of this chapter is to help Kronborsten to valuate their options and consequences of strategical decisions about the inventory levels. 

  • 34.
    Ahlgren, Markus
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Internal Market Risk Modelling for Power Trading Companies2015Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Since the financial crisis of 2008, the risk awareness has increased in the -financial sector. Companies are regulated with regards to risk exposure. These regulations are driven by the Basel Committee that formulates broad supervisory standards, guidelines and recommends statements of best practice in banking supervision. In these regulations companies are regulated with own funds requirements for market risks.

    This thesis constructs an internal model for risk management that, according to the "Capital Requirements Regulation" (CRR) respectively the "Fundamental Review of the Trading Book" (FRTB), computes the regulatory capital requirements for market risks. The capital requirements according to CRR and FRTB are compared to show how the suggested move to an expected shortfall (ES) based model in FRTB will affect the capital requirements. All computations are performed with data that have been provided from a power trading company to make the results fit reality. In the results, when comparing the risk capital requirements according to CRR and FRTB for a power portfolio with only linear assets, it shows that the risk capital is higher using the value-at-risk (VaR) based model. This study shows that the changes in risk capital mainly depend on the different methods of calculating the risk capital according to CRR and FRTB respectively and minor on the change of risk measure.

  • 35.
    Ahlin, Filip
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Internal model for spread risk under Solvency II2017Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In May 2009 the European Commission decided on new regulations regarding solvency among insurance firms, the Solvency II Directive. The directive aims to strengthen the connection between the requirement of solvency and risks for insurance firms. The directive partly consists of a market risk module, in which a credit spread risk is a sub category.

    In this thesis a model for credit spread risk is implemented. The model is an extended version of the Jarrow, Lando and Turnbull model (A Markov Model for theTerm Structure of Credit Risk Spreads, 1997) as proposed by Dubrana (A Stochastic Model for Credit Spreads under a Risk-Neutral Framework through the use of an Extended Version of the Jarrow, Lando and Turnbull Model, 2011). The implementation includes the calibration of a stochastic credit risk driver as well as a simulation of bond returns with the allowance of credit transitions and defaults.

    The modeling will be made with the requirements of the Solvency II Directive in mind. Finally, the result will be compared with the Solvency II standard formula for the spread risk sub-module.

  • 36.
    Ahlin, Filip
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Wahlstedt, Anton
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    ESG-investerande och portföljresultat: En studie av ESG-investerande utifrån metoden bäst-i-klassen2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    As a result of a more globalized and industrial world, sustainability issues in terms of the environment and society has become an everyday heading in the financial world. The fact that companies should work actively towards sustainability and accountability is today a necessity rather than a choice. The purpose of this study is to research responsible investment (RI) and portfolio performance. To examine this relationship the study focuses on ESG where its dimensions will be included jointly through optimization, discussion and conclusion. The report outlines how ESG can be integrated into the investment process, but the weight of the study addresses the discussion of a portfolio's performance at the inclusion of ESG. Methods used are Modern Portfolio Theory (MPT) combined with the implementation of ESG according to "best-in-class". The results of the study lead towards the conclusion that ESG in addition to its positive effects, provided an accurate assessment, on sustainability also is financially arguable for investors.

  • 37.
    Ahlklo, Karin
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Lind, Carin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Modellering och kundprocessanalys av kösystem på Vapiano Sturegatan2016Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    In this Bachelorthesis, the queuing system of Vapiano Sturegatan has been analysed. The customers of the restaurant experience long waiting times during lunchtime, which is a problem Vapiano Sturegatan  recognises. The purpose of this report is to suggest and analyse possible improvements of the queueing system in order to reduce this problem.

    The current queuing system was approximated with markovian queuing models. Both an M/M/2-and an M/M/8-approach were considered, which of the M/M/2-model was deemed most reliable. The expected time in the system was calculated for different modications of Vapiano Sturegatan's current queuing system setup. They led to the conclusion that adding capacity to every serving station would be the best improvement to their current system, instead of adding an extra station. Furthermore, other queuing systems are considered and analysed from a customer process perspective. To improve the flow of customers in the restaurant, this report suggests an electronic queuing system. As long as the suggested system is implemented with careful planning and evaluation, the advantages of the electronic system exceed the benefit of simplicity of the current queuing system.

    This thesis will be delivered to Vapiano Sturegatan. The authors hope that the results can beneficial in the planning of future restaurants and changes of the queuing system.

  • 38.
    Ahlqvist, Eric
    KTH, School of Engineering Sciences (SCI).
    Fusion Systems On Finite Groups and Alperin's Theorem2014Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    Let G be a group and P a Sylow p-subgroup of G. A fusion system of G on P, denoted by FP (G), is the category with objects; subgroups of P, and morphisms induced by conjugation in G. This thesis gives a brief introduction to the theory fusion systems.

    Two classical theorems of Burnside and Frobenius are stated and proved. These theorems may be seen as a starting point of the theory of fusion systems, even though the axiomatic foundation is due to Puig in the early 1990's.

    An abstract fusion system F on a p-group P is dened and the notion of a saturated fusion system is discussed. It turns out that the fusion system of any nite group is saturated, but the converse; that a saturated fusion system is realizable on a nite group, is not always true.

    Two versions of Alperin's fusion theorem are stated and proved. The first one is the classical formulation of Alperin and the second one, due to Puig, a version stated in the language of fusion systems. The differences between these two are investigated.

    The fusion system F of GL2 (3) on the Sylow 2-subgroup isomorphicto SD16 is determined and the subgroups generating F are found.

  • 39.
    Ahlqvist, Eric
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Operations on Étale Sheaves of Sets2016Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Rydh showed in 2011 that any unramified morphism ƒof algebraic spaces (algebraic stacks) has a canonical and universal factorization through an algebraic space (algebraic stack) called the étale envelope of ƒ, where the first morphism is a closed immersion and the second is étale. We show that when ƒ is étale then the étale envelope can be described by applying the left adjoint of the pullback of ƒ to the constant sheaf defined by a pointed set with two elements. When ƒ is a monomorphism locally of finite type we have a similar construction using the direct image with proper support.

  • 40.
    Ahmadi-Djam, Adrian
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Belfrage Nordström, Sean
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Forecasting Non-Maturing Liabilities2017Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    With ever increasing regulatory pressure financial institutions are required to carefully monitor their liquidity risk. This Master thesis focuses on asserting the appropriateness of time series models for forecasting deposit volumes by using data from one undisclosed financial institution. Holt-Winters, Stochastic Factor, ARIMA and ARIMAX models are considered with the latter being the one with best out-of-sample performance. The ARIMAX model is appropriate for forecasting deposit volumes on a 3 to 6 month horizon with seasonality accounted for through monthly dummy variables. Explanatory variables such as market volatility and interest rates do improve model accuracy but vastly increases complexity due to the simulations needed for forecasting.

  • 41.
    Ahmed, Ilyas
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Importance Sampling for Least-Square Monte Carlo Methods2016Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Pricing American style options is challenging due to early exercise opportunities. The conditional expectation in the Snell envelope, known as the continuation value is approximated by basis functions in the Least-Square Monte Carlo-algorithm, giving robust estimation for the options price. By change of measure in the underlying Geometric Brownain motion using Importance Sampling, the variance of the option price can be reduced up to 9 times. Finding the optimal estimator that gives the minimal variance requires careful consideration on the reference price without adding bias in the estimator. A stochastic algorithm is used to find the optimal drift that minimizes the second moment in the expression of the variance after change of measure. The usage of Importance Sampling shows significant variance reduction in comparison with the standard Least-Square Monte Carlo. However, Importance Sampling method may be a better alternative for more complex instruments with early exercise opportunity.

  • 42.
    Ahmed, Shoaib
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Topology optimization of load-carryingstructures using three different typesof finite elements2013Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This thesis deals with topology optimization of load-carrying structures, in particular compliance minimization subject to a constraint on the total amount of material to be used. The main purpose of the work was to compare the following three types of finite elements for the above topology optimization problems: Four node square elements with bilinear shape functions, nine node square elements with quadratic shape functions, and six node hexagonal elements with Wachspress shape functions. The SIMP approach (Solid Isotropic Material with Penalization) was used to model the topology optimization problem for different load and support conditions, and the method of moving asymptotes (MMA) was used to solve the formulated optimization problems. On the considered test problems, it turned out that the results obtained by using six node hexagonal elements were in general better than the corresponding results using nine node square elements which in turn were better than the results using four node square elements. The price paid for the improvements were increased computation times.

  • 43.
    Ait Ali, Abderrahman
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Transport Science, Transport Planning, Economics and Engineering.
    Lindberg, Per Olov
    KTH.
    Nilsson, Jan-Eric
    Eliasson, Jonas
    Aronsson, Martin
    Disaggregation in Bundle Methods: Application to the Train Timetabling Problem2017Conference paper (Refereed)
    Abstract [en]

    Bundle methods are often used to solve dual problems that arise from Lagrangian relaxations of large scale optimization problems. An example of such problems is the train timetabling problem. This paper focuses on solving a dual problem that arises from Lagrangian relaxation of a train timetabling optimization program. The dual problem is solved using bundle methods. We formulate and compare the performances of two different bundle methods: the aggregate method, which is a standard method, and a new, disaggregate, method which is proposed here. The two methods were tested on realistic train timetabling scenarios from the Iron Ore railway line. The numerical results show that the new disaggregate approach generally yields faster convergence than the standard aggregate approach.

  • 44.
    Ait-Ali, Abderrahman
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Integration of Production Scheduling and Energy Management: Software Development2015Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Demand-Side Management concepts have the potential to positively impact the financial as well as the environmental aspects of energy-intensive industries. More specifically, they allow reducing the energy cost for the industrial plants by dealing with energy-availability fluctuations.

    In this context, efficient frameworks for scheduling with energy awareness have been studied and showed potential to reduce the overall energy bill for energy-intensive industries, for instance stainless steel and paper plants. Those frameworks usually combine scheduling and energy optimization into one monolithic system. This work investigates the possibility of integrating the two systems by specific exchange of signals, while keeping the scheduling model separated from the energy-cost optimization model. Such integration means that the pre-existent schedulers and energy optimizers could be easily modified and reused without re-implementing the whole new system.

    Two industrial problems with different scheduling approaches are studied. The first problem is about pulp and paper production which uses the Resource Task Network (RTN) scheduling approach. The second one is about stainless steel production which is based on a bi-level heuristic implementation of an improved energy-aware scheduler. This work presents the decomposition methods that are available in literature and their application to the two industrial problems. Besides an improvement in the RTN approach for handling storages, this thesis describes a prototype implementation of the energy-aware RTN scheduler for paper and pulp production. Furthermore, this work investigates the performance of the application of different decomposition methods on different problem instances.

    The numerical case studies show that even though the decomposition decreases the solution quality compared to the monolithic system, it still gives good solutions within an acceptable duration with the advantage of having two separate pre-existent systems which are simply exchanging signals.

  • 45.
    Ait-Lakbir, Hanane
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Study and Industrialization of Computational Methods for Orbital Maneuvers2016Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    The use of electric propulsion is a watershed in the space field. Indeed, due to its eÿciency in term of mass consumption, the actors of the space industries see in this piece of technology a means to manufacture lighter satellites and to launch them at lower cost. To face with this new market, industries need to develop new tools to handle these satellites and their missions. This report will elaborate on the methods used to compute maneuvers for all-electric spacecraft.

    One of the main phases during satellite operations is maneuvering to ensure on the one hand a correct configuration to achieve the mission and on the other hand the integrity of the satellite. The present work is focused on the computation of the orbital maneuvers during the early phase of the mission: orbit raising. Due to the characteristics of electric propulsion, an overall approach provided by the application of the optimal control theory is required to compute these maneuvers performed by low-thrust engines. This report will develop the use of an indirect method based on the Pontryagin minimum principle. Two types of problems related to the constraints during the space missions are presented. Because electric maneuvers are longer than chemical maneuvers, it is usually necessary to seek to minimize the duration of a maneuver. The second interesting performance is the remaining propellant mass to achieve the mission: therefore, the minimization of the mass consumption during the maneuver is the second performance considered in the report.

    During the internship, a JAVA implementation of the resolution of these two problems has been done. The report will present the preliminary results as well as the encountered difficulties and some possible solutions.

  • 46.
    Aittokoski, Timo
    et al.
    Department of Mathematical Information Technology, University of Jyväskylä, Finland.
    Miettinen, Kaisa
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Cost Effective Simulation-Based Multiobjective Optimization in Performance of Internal Combustion Engine2008In: Engineering optimization (Print), ISSN 0305-215X, Vol. 40, no 7, 593-612 p.Article in journal (Refereed)
    Abstract [en]

    Solving real-life engineering problems requires often multiobjective, global, and efficient (in terms of objective function evaluations) treatment. In this study, we consider problems of this type by discussing some drawbacks of the current methods and then introduce a new population-based multiobjective optimization algorithm UPS-EMOA which produces a dense (not limited to the population size) approximation of the Pareto-optimal set in a computationally effective manner.

  • 47. Aka, Menny
    et al.
    Breuillard, Emmanuel
    Rosenzweig, Lior
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    de Saxce, Nicolas
    Diophantine properties of nilpotent Lie groups2015In: Compositio Mathematica, ISSN 0010-437X, E-ISSN 1570-5846, Vol. 151, no 6, 1157-1188 p.Article in journal (Refereed)
    Abstract [en]

    A finitely generated subgroup F of a real Lie group G is said to be Diophantine if there is beta > 0 such that non-trivial elements in the word ball B-Gamma(n) centered at 1 is an element of F never approach the identity of G closer than broken vertical bar Br(n)broken vertical bar(-beta). A Lie group G is said to be Diophantine if for every k >= 1 a random k-tuple in G generates a Diophantine subgroup. Semi-simple Lie groups are conjectured to be Diophantine but very little is proven in this direction. We give a characterization of Diophantine nilpotent Lie groups in terms of the ideal of laws of their Lie algebra. In particular we show that nilpotent Lie groups of class at most 5, or derived length at most 2, as well as rational nilpotent Lie groups are Diophantine. We also find that there are non-Diophantine nilpotent and solvable (non-nilpotent) Lie groups.

  • 48. Aka, Menny
    et al.
    Breuillard, Emmanuel
    Rosenzweig, Lior
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    de Saxce, Nicolas
    On metric Diophantine approximation in matrices and Lie groups2015In: Comptes rendus. Mathematique, ISSN 1631-073X, Vol. 353, no 3, 185-189 p.Article in journal (Refereed)
    Abstract [en]

    We study the Diophantine exponent of analytic submanifolds of m x n real matrices, answering questions of Beresnevich, Kleinbock, and Margulis. We identify a family of algebraic obstructions to the extremality of such a submanifold, and give a formula for the exponent when the submanifold is algebraic and defined over Q. We then apply these results to the determination of the Diophantine exponent of rational nilpotent Lie groups.

  • 49.
    Alam, Amit
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Inas, Yakub
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Analys av reporäntans påverkan på prissättningen av bostäder: Slår reporänteförändringar lika mycket på bostäder av olika storlek?2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    The aim of this study is to investigate whether changes of the repo rate has diverse effects on apartments of different sizes, targeting specific areas in Stockholm. A conclusion, that the effect of the repo rate differs for apartments of different sizes, was made based on regression analysis and hypothesis testing. The housing market is characterized by vast shifts and the repo rate has reached a historical low-point of -0.25 per cent. It is reflected upon how the central bank’s steering interest rate actually impacts the prices on the housing market and whether it has distinct effects on apartments of different sizes. Apartments sold between years 2005-2015 have been analyzed where the gravity of the repo rate has been taken into consideration and if its significance varies amongst apartments of different sizes. Important parameters concerning apartment prices have been utilized in the constructed model.

  • 50. Alberts, Tom
    et al.
    Binder, Ilia
    Viklund, Fredrik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    A Dimension Spectrum for SLE Boundary Collisions2016In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 343, no 1, 273-298 p.Article in journal (Refereed)
    Abstract [en]

    We consider chordal SLE curves for , where the intersection of the curve with the boundary is a random fractal of almost sure Hausdorff dimension . We study the random sets of points at which the curve collides with the real line at a specified "angle" and compute an almost sure dimension spectrum describing the metric size of these sets. We work with the forward SLE flow and a key tool in the analysis is Girsanov's theorem, which is used to study events on which moments concentrate. The two-point correlation estimates are proved using the direct method.

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