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  • 1. Aalto, Daniel
    et al.
    Berkovits, Lauri
    Kansanen, Outi Elina
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Yue, Hong
    John-Nirenberg lemmas for a doubling measure2011Inngår i: Studia Mathematica, ISSN 0039-3223, E-ISSN 1730-6337, Vol. 204, nr 1, s. 21-37Artikkel i tidsskrift (Fagfellevurdert)
    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, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    A Markov Process on Cyclic Words2014Doktoravhandling, med artikler (Annet vitenskapelig)
    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, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Limit points of the iterative scaling procedure2014Inngår i: Annals of Operations Research, ISSN 0254-5330, E-ISSN 1572-9338, Vol. 215, nr 1, s. 15-23Artikkel i tidsskrift (Fagfellevurdert)
    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, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Stationary probability of the identity for the TASEP on a Ring2012Annet (Annet vitenskapelig)
    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, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    TASEP in any Weyl groupManuskript (preprint) (Annet vitenskapelig)
    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, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Linusson, Svante
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Continuous multiline queues and TASEPManuskript (preprint) (Annet vitenskapelig)
  • 7.
    Aas, Erik
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Linusson, Svante
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Continuous multi-line queues and TASEP2018Inngår i: ANNALES DE L INSTITUT HENRI POINCARE D, ISSN 2308-5827, Vol. 5, nr 1, s. 127-152Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, we study a distribution Xi of labeled particles on a continuous ring. It arises in three different ways, all related to the multi-type TASEP on a ring. We prove formulas for the probability density function for some permutations and give conjectures for a larger class. We give a complete conjecture for the probability of two particles i, j being next to each other on the cycle, for which we prove some cases. We also find that two natural events associated to the process have exactly the same probability expressed as a Vandermonde determinant. It is unclear whether this is just a coincidence or a consequence of a deeper connection.

  • 8.
    Aas, Erik
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Sjöstrand, Jonas
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    A product formula for the TASEP on a ring2016Inngår i: Random structures & algorithms (Print), ISSN 1042-9832, E-ISSN 1098-2418, Vol. 48, nr 2, s. 247-259Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 9.
    Abbaszadeh Shahri, Abbas
    et al.
    KTH, Skolan för arkitektur och samhällsbyggnad (ABE), Byggvetenskap.
    Larsson, Stefan
    KTH, Skolan för arkitektur och samhällsbyggnad (ABE), Byggvetenskap, Jord- och bergmekanik.
    Johansson, Fredrik
    KTH, Skolan för arkitektur och samhällsbyggnad (ABE), Byggvetenskap, Jord- och bergmekanik.
    Updated relations for the uniaxial compressive strength of marlstones based on P-wave velocity and point load index test2016Inngår i: INNOVATIVE INFRASTRUCTURE SOLUTIONS, ISSN 2364-4176, Vol. 1, nr 1, artikkel-id UNSP 17Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 10.
    Abdalmoaty, Mohamed
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Learning Stochastic Nonlinear Dynamical Systems Using Non-stationary Linear Predictors2017Licentiatavhandling, monografi (Annet vitenskapelig)
    Abstract [en]

    The estimation problem of stochastic nonlinear parametric models is recognized to be very challenging due to the intractability of the likelihood function. Recently, several methods have been developed to approximate the maximum likelihood estimator and the optimal mean-square error predictor using Monte Carlo methods. Albeit asymptotically optimal, these methods come with several computational challenges and fundamental limitations.

    The contributions of this thesis can be divided into two main parts. In the first part, approximate solutions to the maximum likelihood problem are explored. Both analytical and numerical approaches, based on the expectation-maximization algorithm and the quasi-Newton algorithm, are considered. While analytic approximations are difficult to analyze, asymptotic guarantees can be established for methods based on Monte Carlo approximations. Yet, Monte Carlo methods come with their own computational difficulties; sampling in high-dimensional spaces requires an efficient proposal distribution to reduce the number of required samples to a reasonable value.

    In the second part, relatively simple prediction error method estimators are proposed. They are based on non-stationary one-step ahead predictors which are linear in the observed outputs, but are nonlinear in the (assumed known) input. These predictors rely only on the first two moments of the model and the computation of the likelihood function is not required. Consequently, the resulting estimators are defined via analytically tractable objective functions in several relevant cases. It is shown that, under mild assumptions, the estimators are consistent and asymptotically normal. In cases where the first two moments are analytically intractable due to the complexity of the model, it is possible to resort to vanilla Monte Carlo approximations. Several numerical examples demonstrate a good performance of the suggested estimators in several cases that are usually considered challenging.

  • 11.
    Abdullah Al Ahad, Muhammed
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA.
    Non-linearstates in parallel Blasius boundary layer2014Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    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

  • 12. Abdulle, Assyr
    et al.
    Henning, Patrick
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA.
    Localized orthogonal decomposition method for the wave equation with a continuum of scales2017Inngår i: Mathematics of Computation, ISSN 0025-5718, E-ISSN 1088-6842, Vol. 86, nr 304, s. 549-587Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 13.
    Abedin, Arian
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Ligai, Wolmir
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Automatingand optimizing pile group design using a Genetic Algorithm2018Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    In bridge design, a set of piles is referred to as a pile group. The design process of pile groups employed by many firms is currently manual, time consuming, and produces pile groups that are not robust against placement errors.

    This thesis applies the metaheuristic method Genetic Algorithm to automate and improve the design of pile groups for bridge column foundations. A software is developed and improved by implementing modifications to the Genetic Algorithm. The algorithm is evaluated by the pile groups it produces, using the Monte Carlo method to simulate errors for the purpose of testing the robustness. The results are compared with designs provided by the consulting firm Tyrens AB.

    The software is terminated manually, and generally takes less than half an hour to produce acceptable pile groups. The developed Genetic Algorithm Software produces pile groups that are more robust than the manually designed pile groups to which they are compared, using the Monte Carlo method. However, due to the visually disorganized designs, the pile groups produced by the algorithm may be di cult to get approved by Trafikverket. The software might require further modifications addressing this problem before it can be of practical use.

  • 14.
    Abramson, Nils
    et al.
    KTH, Skolan för industriell teknik och management (ITM), Industriell produktion.
    Boman, J.
    Bonnevier, Björn
    KTH, Skolan för elektro- och systemteknik (EES), Centra, Alfvénlaboratoriet.
    Plane intersections of rotational ellipsoids2006Inngår i: The American mathematical monthly, ISSN 0002-9890, E-ISSN 1930-0972, Vol. 113, nr 4, s. 336-339Artikkel i tidsskrift (Fagfellevurdert)
  • 15. Acker, A.
    et al.
    Henrot, A.
    Poghosyan, M.
    Shahgholian, Henrik
    KTH, Tidigare Institutioner, Matematik.
    The multi-layer free boundary problem for the p-Laplacian in convex domains2004Inngår i: Interfaces and free boundaries (Print), ISSN 1463-9963, E-ISSN 1463-9971, Vol. 6, nr 1, s. 81-103Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 16. Adamaszek, Michal
    et al.
    Barmak, Jonathan Ariel
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    On a lower bound for the connectivity of the independence complex of a graph2011Inngår i: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 311, nr 21, s. 2566-2569Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 17. Adams, Henry
    et al.
    Tausz, Andrew
    Vejdemo-Johansson, Mikael
    KTH, Skolan för datavetenskap och kommunikation (CSC), Datorseende och robotik, CVAP. Institut Jozef Stefan, Slovenia .
    javaPlex: A Research Software Package for Persistent (Co) Homology2014Konferansepaper (Fagfellevurdert)
    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.

  • 18.
    Adelstrand, Carl
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Gavefalk, Sofia
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    In times of regional geopolitical turmoil – Why do some equity funds performbetter than others?2014Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    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.

  • 19. Adiprasito, Karim
    et al.
    Björner, Anders
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Goodarzi, Afshin
    Freie Universität, Germany.
    Face numbers of sequentially Cohen-Macaulay complexes and Betti numbers of componentwise linear ideals2017Inngår i: Journal of the European Mathematical Society (Print), ISSN 1435-9855, E-ISSN 1435-9863, Vol. 19, nr 12, s. 3851-3865Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A numerical characterization is given of the h-triangles of sequentially Cohen-Macaulay simplicial complexes. This result determines the number of faces of various dimensions and codimensions that are possible 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 <= d and shifted pure. (d - 1)-dimensional simplicial complexes.

  • 20. Adiprasito, Karim
    et al.
    Goodarzi, Afshin
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Varbaro, Matteo
    Connectivity of pseudomanifold graphs from an algebraic point of view2015Inngår i: Comptes Rendus Mathematiques de l'Academie des Sciences = Mathematical reports of the academy of science, ISSN 0706-1994, Vol. 353, nr 12, s. 1061-1065Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 21.
    Adler, Jonas
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA.
    GPU Monte Carlo scatter calculations for Cone Beam Computed Tomography2014Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    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.

  • 22.
    Adler, Jonas
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Lunz, Sebastian
    Univ Cambridge, Dept Appl Math & Theoret Phys, Cambridge, England..
    Banach Wasserstein GAN2018Inngår i: Advances in Neural Information Processing Systems 31 (NIPS 2018) / [ed] Bengio, S Wallach, H Larochelle, H Grauman, K CesaBianchi, N Garnett, R, Neural Information Processing Systems (NIPS) , 2018Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Wasserstein Generative Adversarial Networks (WGANs) can be used to generate realistic samples from complicated image distributions. The Wasserstein metric used in WGANs is based on a notion of distance between individual images, which induces a notion of distance between probability distributions of images. So far the community has considered l(2) as the underlying distance. We generalize the theory of WGAN with gradient penalty to Banach spaces, allowing practitioners to select the features to emphasize in the generator. We further discuss the effect of some particular choices of underlying norms, focusing on Sobolev norms. Finally, we demonstrate a boost in performance for an appropriate choice of norm on CIFAR-10 and CelebA.

  • 23.
    Adler, Jonas
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.). Elekta, Box 7593, 103 93 Stockholm, Sweden.
    Ringh, Axel
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Öktem, Ozan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Karlsson, Johan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Learning to solve inverse problems using Wasserstein lossManuskript (preprint) (Annet vitenskapelig)
    Abstract [en]

    We propose using the Wasserstein loss for training in inverse problems. In particular, we consider a learned primal-dual reconstruction scheme for ill-posed inverse problems using the Wasserstein distance as loss function in the learning. This is motivated by miss-alignments in training data, which when using standard mean squared error loss could severely degrade reconstruction quality. We prove that training with the Wasserstein loss gives a reconstruction operator that correctly compensates for miss-alignments in certain cases, whereas training with the mean squared error gives a smeared reconstruction. Moreover, we demonstrate these effects by training a reconstruction algorithm using both mean squared error and optimal transport loss for a problem in computerized tomography.

  • 24.
    Adler, Jonas
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Öktem, Ozan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Solving ill-posed inverse problems using iterative deep neural networks2017Inngår i: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 33, nr 12, artikkel-id 124007Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We propose a partially learned approach for the solution of ill-posed inverse problems with not necessarily linear forward operators. The method builds on ideas from classical regularisation theory and recent advances in deep learning to perform learning while making use of prior information about the inverse problem encoded in the forward operator, noise model and a regularising functional. The method results in a gradient-like iterative scheme, where the 'gradient' component is learned using a convolutional network that includes the gradients of the data discrepancy and regulariser as input in each iteration. We present results of such a partially learned gradient scheme on a non-linear tomographic inversion problem with simulated data from both the Sheep-Logan phantom as well as a head CT. The outcome is compared against filtered backprojection and total variation reconstruction and the proposed method provides a 5.4 dB PSNR improvement over the total variation reconstruction while being significantly faster, giving reconstructions of 512 x 512 pixel images in about 0.4 s using a single graphics processing unit (GPU).

  • 25. Adler, M.
    et al.
    Chhita, S.
    Johansson, Kurt
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    van Moerbeke, P.
    Tacnode GUE-minor processes and double Aztec diamonds2015Inngår i: Probability theory and related fields, ISSN 0178-8051, E-ISSN 1432-2064, Vol. 162, nr 1-2, s. 275-325Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 26. Adler, Mark
    et al.
    Johansson, Kurt
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    van Moerbeke, Pierre
    Double Aztec diamonds and the tacnode process2014Inngår i: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 252, s. 518-571Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 27. Adler, Mark
    et al.
    Johansson, Kurt
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    van Moerbeke, Pierre
    Lozenge Tilings of Hexagons with Cuts and Asymptotic Fluctuations: a New Universality Class2018Inngår i: Mathematical physics, analysis and geometry, ISSN 1385-0172, E-ISSN 1572-9656, Vol. 21, nr 1, artikkel-id 9Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper investigates lozenge tilings of non-convex hexagonal regions and more specifically the asymptotic fluctuations of the tilings within and near the strip formed by opposite cuts in the regions, when the size of the regions tend to infinity, together with the cuts. It leads to a new kernel, which is expected to have universality properties.

  • 28.
    af Klinteberg, Ludvig
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA.
    Computational methods for microfluidics2013Licentiatavhandling, med artikler (Annet vitenskapelig)
    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.

  • 29.
    af Klinteberg, Ludvig
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA.
    Ewald summation for the rotlet singularity of Stokes flow2016Rapport (Annet vitenskapelig)
    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.

  • 30.
    af Klinteberg, Ludvig
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA.
    Fast and accurate integral equation methods with applications in microfluidics2016Doktoravhandling, med artikler (Annet vitenskapelig)
    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.

  • 31.
    af Klinteberg, Ludvig
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA.
    Saffar Shamshirgar, Davoud
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA.
    Tornberg, Anna-Karin
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA.
    Fast Ewald summation for free-space Stokes potentials2017Inngår i: Research in the Mathematical Sciences, ISSN 2197-9847, Vol. 4, nr 1Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 32.
    af Klinteberg, Ludvig
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA.
    Tornberg, Anna-Karin
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA.
    A fast integral equation method for solid particles in viscous flow using quadrature by expansionManuskript (preprint) (Annet vitenskapelig)
    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.

  • 33.
    af Klinteberg, Ludvig
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA. KTH, Skolan för teknikvetenskap (SCI), Centra, Linné Flow Center, FLOW. KTH, Centra, SeRC - Swedish e-Science Research Centre.
    Tornberg, Anna-Karin
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA. KTH, Skolan för teknikvetenskap (SCI), Centra, Linné Flow Center, FLOW. KTH, Centra, SeRC - Swedish e-Science Research Centre.
    A fast integral equation method for solid particles in viscous flow using quadrature by expansion2016Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 326, s. 420-445Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 34.
    af Klinteberg, Ludvig
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA.
    Tornberg, Anna-Karin
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA.
    Adaptive Quadrature by Expansion for Layer Potential Evaluation in Two Dimensions2018Inngår i: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 40, nr 3, s. A1225-A1249Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    When solving partial differential equations using boundary integral equation methods, accurate evaluation of singular and nearly singular integrals in layer potentials is crucial. A recent scheme for this is quadrature by expansion (QBX), which solves the problem by locally approximating the potential using a local expansion centered at some distance from the source boundary. In this paper we introduce an extension of the QBX scheme in two dimensions (2D) denoted AQBX—adaptive quadrature by expansion—which combines QBX with an algorithm for automated selection of parameters, based on a target error tolerance. A key component in this algorithm is the ability to accurately estimate the numerical errors in the coefficients of the expansion. Combining previous results for flat panels with a procedure for taking the panel shape into account, we derive such error estimates for arbitrarily shaped boundaries in 2D that are discretized using panel-based Gauss–Legendre quadrature. Applying our scheme to numerical solutions of Dirichlet problems for the Laplace and Helmholtz equations, and also for solving these equations, we find that the scheme is able to satisfy a given target tolerance to within an order of magnitude, making it useful for practical applications. This represents a significant simplification over the original QBX algorithm, in which choosing a good set of parameters can be hard.

  • 35.
    af Klinteberg, Ludvig
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA.
    Tornberg, Anna-Karin
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA.
    Error estimation for quadrature by expansion in layer potential evaluation2017Inngår i: Advances in Computational Mathematics, ISSN 1019-7168, E-ISSN 1572-9044, Vol. 43, nr 1, s. 195-234Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 36.
    af Klinteberg, Ludvig
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA.
    Tornberg, Anna-Karin
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA.
    Estimation of quadrature errors in layer potential evaluation using quadrature by expansionManuskript (preprint) (Annet vitenskapelig)
    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.

  • 37.
    af Klinteberg, Ludvig
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA.
    Tornberg, Anna-Karin
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA.
    Fast Ewald summation for Stokesian particle suspensions2014Inngår i: International Journal for Numerical Methods in Fluids, ISSN 0271-2091, E-ISSN 1097-0363, Vol. 76, nr 10, s. 669-698Artikkel i tidsskrift (Fagfellevurdert)
    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. 

  • 38.
    Agering, Harald
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    True risk of illiquid investments2018Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    Alternative assets are becoming a considerable portion of global financial markets. Some of these alternative assets are highly illiquid, and as such they may require more intricate methods for calculating risk and performance statistics accurately. Research on hedge funds has established a pattern of risk being understated and various measures of performance being overstated due to illiquidity of the assets. This paper sets out to prove the existence of such bias and presents methods for removing it. Four mathematical methods aiming to adjust statistics for sparse return series were considered, and an implementation was carried out for data on private equity, real estate and infrastructure assets. The results indicate that there are in general substantial adjustments made to the risk and performance statistics of the illiquid assets when using these methods. In particular, the volatility and market exposure were adjusted upwards while manager skill and risk-adjusted performance were adjusted downwards.

  • 39. Aghajani, A.
    et al.
    Razani, Abdolrahman
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.). Department of Mathematics, Faculty of Science, Imam Khomeini International University, Iran .
    Some completeness theorems in the Menger probabilistic metric space2008Inngår i: Applied Sciences: APPS, ISSN 1454-5101, E-ISSN 1454-5101, Vol. 10, s. 1-8Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 40. Agranovsky, M.
    et al.
    Khavinson, D.
    Shapiro, Harold
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Malmheden's theorem revisited2010Inngår i: Expositiones mathematicae, ISSN 0723-0869, E-ISSN 1878-0792, Vol. 28, nr 4, s. 337-350Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 41. Aharonov, Dov
    et al.
    Shapiro, Harold S.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Solynin, Alexander Yu.
    Minimal area problems for functions with integral representation2006Inngår i: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 98, s. 83-111Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 42.
    Ahlberg, Marcus
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Fornander, Eric
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Test Case Prioritization as a Mathematical Scheduling Problem2018Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    Software testing is an extremely important phase of product development where the objective is to detect hidden bugs. The usually high complexity of today’s products makes the testing very resource intensive since numerous test cases have to be generated in order to detect all potential faults. Therefore, improved strategies of the testing process is of high interest for many companies. One area where there exists potential for improvement is the order by which test cases are executed to detect faults as quickly as possible, which in research is known as the test case prioritization problem. In this thesis, an extension to this problem is studied where dependencies between test cases are present and the processing times of the test cases are known. As a first result of the thesis, a mathematical model of the test case prioritization problem with dependencies and known processing times as a mathematical scheduling problem is presented. Three different solution algorithms to this problem are subsequently evaluated: A Sidney decomposition algorithm, an own-designed heuristic algorithm and an algorithm based on Smith’s rule. The Sidney decomposition algorithm outper-formed the others in terms of execution time of the algorithm and objective value of the generated schedule. The evaluation was conducted by simulation with artificial test suites and via a case study in industry through a company in the railway domain.

  • 43.
    Ahlberg, Marcus
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Lilja, Jimmy
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Lageroptimering: Minimera tiden till leverans med begränsat lagerutrymme2016Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    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. 

  • 44.
    Ahlgren, Marcus
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Claims Reserving using Gradient Boosting and Generalized Linear Models2018Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    One fundamental function of an insurance company revolves around calculating the expected claims costs for which the insurer has to compensate its policyholders for. This is the process of claims reserving which is practised by actuaries using statistical methods. Over the last few decades statistical learning methods have become increasingly popular due to their ability to find complex patterns in any type of data. However, they have not been widely adapted within the insurance sector. In this thesis we evaluate the capability of claims reserving with the method of gradient boosting, a non-parametric statistical learning method that has proven to be successful within multiple other disciplines which has made it very popular. The gradient boosting technique is compared with the generalized linear model(GLM) which is widely used for modelling claims. We compare the models by using a claims data set provided by Länsförsäkringar AB which allows us to train the models and evaluate their performance on data not yet seen by the models. The models were implemented using R. The results show that the GLM has a lower prediction error. Also, the gradient boosting method requires more fine tuning to handle claims data properly while the GLM already possesses certain features that makes it suitable for claims reserving without making as many adjustments in the model implementation. The advantage of capturing complex dependencies in data is not fully utilized in this thesis since we only work with 6 predictor variables. It is more likely that gradient boosting can compete with GLM when predicting more complicated claims.

  • 45.
    Ahlgren, Markus
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Internal Market Risk Modelling for Power Trading Companies2015Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    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.

  • 46.
    Ahlin, Filip
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Internal model for spread risk under Solvency II2017Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    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.

  • 47.
    Ahlin, Filip
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Wahlstedt, Anton
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    ESG-investerande och portföljresultat: En studie av ESG-investerande utifrån metoden bäst-i-klassen2015Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Abstract [sv]

    Till följd av en mer globaliserad och industriell omvärld har hållbarhetsfrågor sett till miljö och samhälle blivit en vardaglig rubrik i finansvärlden. Att företag ska ha aktivt arbete mot hållbarhet och ansvarstagande är på så när en självklarhet om inte ett måste. Denna studies syfte är att undersöka ansvarsfullt investerande och portföljresultat. För att analysera detta förhållande fokuserar arbetet på ESG där dess dimensioner inkluderas gemensamt genom optimering, diskussion och slutsats. Arbetet berör hur ESG kan integreras i investeringsprocessen men tyngden av studien och den övergripande frågan angriper diskussionen kring en portföljs resultat vid inkluderande av ESG. Metoder som används är Modern portföljteori kombinerat med implementering av ESG enligt ”bäst-i-klassen”. Studiens resultat leder till slutsatsen att ESG utöver dess positiva effekter, förutsatt en korrekt bedömning, på hållbarhet även är finansiellt argumenterbart för investerare.

  • 48.
    Ahlklo, Yrr
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Lind, Carin
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Modellering och kundprocessanalys av kösystem på Vapiano Sturegatan2016Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Abstract [sv]

    I denna rapport har kösystemet på Vapiano Sturegatan undersökts och analyserats. Restaurangen har problem med långa köer under lunchtid och syftet med denna rapport är att ge förslag på hur man skulle kunna minska dessa.

    De befintliga kösystemet ha modellerats med hjälp av markovsk köteori och approximerats till ett M/M/2-system samt ett M/M/8-system,varavM/M/2-systemet bedömdes vara mest tillförlitligt. Beräkningar av den förväntade tiden i systemet för olika fall ledde till slutsatsen att det bör vara effektivare att öka tillagningskapaciteten på varje betjäningsstation istället för att öppna en ytterligare station.

    Dessutom levereras förslag på alternativa kösystem samt en jämförande analys av tillhörande kundprocesser. För att erhålla ett bättre kundflöde i restaurangen och en smidigare kundprocess för ökat kundvärde kan ett elektroniskt kösystem införas. Om implementering sker noggrant och enligt en väl genomtänkt plan kommer fördelarna med ett sådant system vara många och överträffa dagens befintliga kösystem.

    Rapporten levereras slutligen till Vapiano Sturegatan med förhoppningen att de ska kunna använda den vid planering av restauranger och förändringar i kösystemet

  • 49.
    Ahlqvist, Eric
    KTH, Skolan för teknikvetenskap (SCI).
    Fusion Systems On Finite Groups and Alperin's Theorem2014Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    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.

  • 50.
    Ahlqvist, Eric
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Operations on Étale Sheaves of Sets2016Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    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.

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