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  • 1. Ahlkrona, Josefin
    et al.
    Lötstedt, Per
    Kirchner, Nina
    Stockholm University, Faculty of Science, Department of Physical Geography.
    Zwinger, Thomas
    Dynamically coupling the non-linear Stokes equations with the shallow ice approximation in glaciology: Description and first applications of the ISCAL method2016In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 308, p. 1-19Article in journal (Refereed)
    Abstract [en]

    We propose and implement a new method, called the Ice Sheet Coupled Approximation Levels (ISCAL) method, for simulation of ice sheet flow in large domains during long time-intervals. The method couples the full Stokes (FS) equations with the Shallow Ice Approximation (SIA). The part of the domain where SIA is applied is determined automatically and dynamically based on estimates of the modeling error. For a three dimensional model problem, ISCAL computes the solution substantially faster with a low reduction in accuracy compared to a monolithic FS. Furthermore, ISCAL is shown to be able to detect rapid dynamic changes in the flow. Three different error estimations are applied and compared. Finally, ISCAL is applied to the Greenland Ice Sheet on a quasi-uniform grid, proving ISCAL to be a potential valuable tool for the ice sheet modeling community.

  • 2.
    Atle, Andreas
    Stockholm University, Faculty of Science, Numerical Analysis and Computer Science(NADA) (together with KTH).
    Approximations of Integral Equations for WaveScattering2006Doctoral thesis, monograph (Other academic)
    Abstract [en]

    Wave scattering is the phenomenon in which a wave field interacts with physical objects. An incoming wave is scattered at the surface of the object and a scattered wave is produced. Common practical cases are acoustic, electromagnetic and elastic wave scattering. The numerical simulation of the scattering process is important, for example, in noise control, antenna design, prediction of radar cross sections and nondestructive testing.

    Important classes of numerical methods for accurate simulation of scattering are based on integral representations of the wave fields and theses representations require the knowledge of potentials on the surfaces of the scattering objects. The potential is typically computed by a numerical approximation of an integral equation that is defined on the surface. We first develop such numerical methods in time domain for the scalar wave equation. The efficiency of the techniques are improved by analytic quadrature and in some cases by local approximation of the potential.

    Most scattering simulations are done for harmonic or single frequency waves. In the electromagnetic case the corresponding integral equation method is called the method of moments. This numerical approximation is computationally very costly for high frequency waves. A simplification is suggested by physical optics, which directly gives an approximation of the potential without the solution of an integral equation. Physical optics is however only accurate for very high frequencies.

    In this thesis we improve the accuracy in the physical optics approximation of scalar waves by basing the computation of the potential on the theory of radiation boundary conditions. This theory describes the local coupling of derivatives in the wave field and if it is applied at the surface of the scattering object it generates an expression for the unknown potential. The full wave field is then computed as for other integral equation methods.

    The new numerical techniques are analyzed mathematically and their efficiency is established in a sequence of numerical experiments. The new on surface radiation conditions give, for example, substantial improvement in the estimation of the scattered waves in the acoustic case. This numerical experiment corresponds to radar cross-section estimation in the electromagnetic case.

  • 3.
    Boman, Jan
    Stockholm University, Faculty of Science, Department of Mathematics.
    Datortomografins matematik: Om en matematisk teori med många nya tillämpningar2008In: Normat, ISSN ISSN 0801-3500, Vol. 56, no 4, p. 177-187Article in journal (Refereed)
  • 4.
    Eriksson, Henrik
    et al.
    Kungliga Teknikiska Högskolan.
    Eriksson, Kimmo
    Stockholm University, Faculty of Humanities, Centre for the Study of Cultural Evolution.
    Conjugacy of Coxeter elements2009In: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 16, no 2, p. -R4Article in journal (Refereed)
    Abstract [en]

    For a Coxeter group (W, S), a permutation of the set S is called a Coxeter word and the group element represented by the product is called a Coxeter element. Moving the first letter to the end of the word is called a rotation and two Coxeter elements are rotation equivalent if their words can be transformed into each other through a sequence of rotations and legal commutations. We prove that Coxeter elements are conjugate if and only if they are rotation equivalent. This was known for some special cases but not for Coxeter groups in general.

  • 5.
    Eriksson, Kimmo
    et al.
    Stockholm University, Faculty of Humanities, Centre for the Study of Cultural Evolution.
    Sjöstrand, Jonas
    Stockholm University, Faculty of Humanities, Centre for the Study of Cultural Evolution.
    On two theorems of Quinzii and rent controlled housing allocation in Sweden2007In: International Journal of Game Theory, ISSN 0020-7276, E-ISSN 1432-1270, Vol. 9, no 3, p. 515-526Article in journal (Refereed)
  • 6.
    Eriksson, Kimmo
    et al.
    Stockholm University, Faculty of Humanities, Centre for the Study of Cultural Evolution.
    Sjöstrand, Jonas
    Stockholm University, Faculty of Humanities, Centre for the Study of Cultural Evolution.
    Strimling, Pontus
    Stockholm University, Faculty of Humanities, Centre for the Study of Cultural Evolution.
    Optimal Expected Rank in a Two-Sided Secretary Problem2007In: Operations Research, ISSN 0030-364X, Vol. 55, no 5, p. 921-931Article in journal (Refereed)
    Abstract [en]

    In a two-sided version of the famous secretary problem, employers search for a secretary at the same time as secretaries search for an employer. Nobody accepts being put on hold, and nobody is willing to take part in more than N interviews. Preferences are independent, and agents seek to optimize the expected rank of the partner they obtain among the N potential partners. We find that in any subgame perfect equilibrium, the expected rank grows as the square root of N (whereas it tends to a constant in the original secretary problem). We also compute how much agents can gain by cooperation.

  • 7.
    Eriksson, Kimmo
    et al.
    Stockholm University, Faculty of Humanities, Centre for the Study of Cultural Evolution.
    Strimling, Pontus
    Stockholm University, Faculty of Humanities, Centre for the Study of Cultural Evolution.
    Biases for acquiring information individually rather than socially2009In: Journal of Evolutionary Psychology, ISSN 0737-4828, Vol. 7, no 4, p. 309-329Article in journal (Refereed)
    Abstract [en]

    We discuss theoretical and empirical arguments for a human bias to acquire information individually rather than socially. In particular, we argue that when other people can be observed, information collection is a public good and hence some of the individual variation in the choice between individual and social learning can be explained by variation in social value orientation. We conducted two experimental studies, based on the game Explore & Collect, to test the predictions that (1) socially and individually acquired information of equal objective value are treated differently, and (2) prosocial subjects tend to spend more effort than selfish subjects on individual acquiring of information. Both predictions were supported.

  • 8.
    Eriksson, Kimmo
    et al.
    Stockholm University, Faculty of Humanities, Centre for the Study of Cultural Evolution.
    Strimling, Pontus
    Stockholm University, Faculty of Humanities, Centre for the Study of Cultural Evolution.
    Partner Search Heuristics in the Lab:: Stability of Matchings Under Various Preference Structures2009In: Adaptive Behavior, ISSN 1059-7123, E-ISSN 1741-2633, Vol. 17, no 6, p. 524-536Article in journal (Refereed)
    Abstract [en]

    When agents search for partners, the outcome is a matching. K. Eriksson and O. Häggström (2008) defined a measure of instability of matchings and proved that under a certain partner search heuristic, outcomes are likely to have low instability. They also showed that with regards to stability, the preference structure known as common preferences lie somewhere in between the extreme cases of homotypic and antithetical preferences. Following up on this theoretical work, we let human subjects search for a good partner in a computer game where preferences were set to be either common, homotypic, or antithetical. We find that total search effort and instability of the outcome vary in the predicted ways with the preference structure and the number of agents. A set of simulations show that these results are consistent with a model where agents use a simple search heuristic with a slight possibility of error.

  • 9.
    Hagdahl, Stefan
    Stockholm University, Faculty of Science, Numerical Analysis and Computer Science(NADA) (together with KTH).
    Hybrid Methods for Computational Electromagnetics in Frequency Domain2005Doctoral thesis, monograph (Other academic)
    Abstract [en]

    In this thesis we study hybrid numerical methods to be used in computational electromagnetics. The purpose is to address a wide frequency range relative to a given geometry. We also focus on efficient and robust numerical algorithms for computing the so called Smooth Surface Diffraction predicted by Geometrical Theory of Diffraction (GTD). We restrict the presentation to frequency domain scattering problems.

    The hybrid methods consist in combinations of Boundary Element Methods and asymptotic methods. Three hybrids will be presented. One of them has been developed from a theoretical idea to an industrial code. The two other hybrids will be presented mainly from a theoretical perspective.

    To be able to compute the Smooth Surface Diffracted field we introduce a numerical method that is to be used with surface curvature sensitive meshing, complemented with auxiliary data taken from a geometry database. By using two geometry representations we can show first order convergence and we then achieve an efficient and robust numerical algorithm. This numerical algorithm may be an essential part of an GTD implementation which in its turn is a component in the hybrid methods.

    As a background to our new techiniques we will also give short introductions to the Boundary Element Method and the Geometrical Theory of Diffraction from a theoretical and implementational point of view.

  • 10.
    Hedman, Maria
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Att hitta matematiken i förskolan2010Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    I och med att man nu håller på att införa en reviderad läroplan för förskolan där bl.a matematiken får en större plats ville jag se hur förskolorna i dag arbetar med matematiken utifrån den läroplan som gäller idag. Syftet med min studie är att ta reda på hur pedagoger synliggör och arbetar med matematiken i förskolan. Är det i planerade aktiviteter eller i den fria leken som matematiken kommer in och hur befäster man barnens kunskaper så att det verkligen blir en bestående kunskap? Jag har valt att i min studie intervjua fem förskollärare från fem olika enskilt drivna förskolor med lite olika inriktningar. Jag har främst tittat på hur de planerar sin verksamhet utifrån läroplanens strävansmål i matematik och hur de lär barnen taluppfattningen. Jag har också tittat på hur de dokumenterar barnens lärande och hur detta synliggörs för föräldrarna. Jag har även tittat på hur de stödjer och uppmuntrar barn som är ointresserade av matematik och hur de stödjer och uppmuntrar barn som är mycket intresserade av matematik. 

    I min studie har jag valt att dela in materialet i det som är pedagogiskt planerade aktiviteter och de aktiviteter som är mer spontana. Resultatet visar att även de förskolor som inte fokuserar på matematiken arbetar med taluppfattningen i framförallt rutinsituationerna så som dukning och påklädning och i den fria leken. 

  • 11. Holmström, Kenneth
    et al.
    Petersson, Jöran
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    A review of the parameter estimation problem of fitting positive exponential sums to empirical data2002In: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 126, no 1, p. 31-61Article in journal (Refereed)
    Abstract [en]

    Exponential sum models are used frequently: in heat diffusion, diffusion of chemical compounds, time series in medicine, economics, physical sciences and technology. Thus it is important to find good methods for the estimation of parameters in exponential sums. In this paper we review and discuss results from the last forty years of research. There are many different ways of estimating parameters in exponential sums and model a fit criterion, which gives a valid result from the fit. We find that a good choice is a weighted two-norm objective function, with weights based on the maximum likelihood (ML) criterion. If the number of exponential terms is unknown, statistical methods based on an information criterion or cross-validation can be used to determine the optimal number. It is suitable to use hybrid Gauss–Newton (GN) and quasi-Newton algorithms to find the unknown parameters in the constrained weighted nonlinear least-squares (NLLS) problem formulated using an maximal likelihood (ML) objective function. The problem is highly ill conditioned and it is crucial to find good starting values for the parameters. To find the initial parameter values, a modified Prony method or a method based upon rewriting partial sums as geometrical sums is proposed.

  • 12.
    Höglund, Thomas
    Stockholm University, Faculty of Science, Department of Mathematics.
    Mathematical Asset Management2008Book (Refereed)
    Abstract [en]

    The book presents an accessible and practical introduction to financial derivatives and portfolio selection while also acting as a basis for further study in mathematical finance.

  • 13.
    Höhna, Sebastian
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Sahlin, Kristoffer
    Royal Institute of Technology (KTH).
    Burnin Estimation and Convergence AssessmentManuscript (preprint) (Other academic)
    Abstract [en]

    Estimating the burnin length and assessing convergence purely from the output of an MCMC run is increasingly important in Bayesian phylogenetic inference. Previously, methods for estimating the burnin and assessing convergence have been ad-hoc, such as the minimum number of effective samples or the deviation in split frequencies. In this paper we compare the currently used methods to convergence assessment methods from the mathematical literature, namely the Geweke test and the Heidelberger-Welch test. The latter two show strong advantages in being statistically consistent and unbiased. Statistical consistency and unbiasedness was verified on simulated data with known posterior distributions. Both methods consider convergence as the Null hypothesis. The Null hypothesis is rejected based on standard p-values, which are easier to interpret than a threshold as used by the eeffective sample size. We extend these convergence assessment methods for single and multiple chains. Furthermore, we test the performance of the convergence assessment methods on an empirical dataset and conclude that tests for convergence to the same stationary distribution from independent runs are most adequate. Additionally,we developed an automatic procedure that finds the optimal burnin in the cases we studied. All methods we tested are implemented in the open source software RevBayes (http://www.revbayes.net/).

  • 14.
    Johansson, Christer
    Stockholm University, Faculty of Science, Numerical Analysis and Computer Science(NADA) (together with KTH).
    Numerical methods for waveguide modelling2006Doctoral thesis, monograph (Other academic)
    Abstract [en]

    Waveguides are used to transmit electromagnetic signals. Their geometry is typically long and slender. This particular shape can be used in the design of efficient computational methods. Only special modes are transmitted and eigenvalue and eigenvector analysis becomes important.

    We develop finite-element systems for solving electromagnetic field problems in time and frequency domain for closed waveguide cross-sections filled with various materials. The frequency domain discretization of the cross-section for the waveguide produces an algebraic eigenvalue problem. A general program based on Arnoldi's method and ARPACK has been written using node and edge elements to approximate the field. A serious problem with standard node elements is the occurrence of spurious solutions due to improper modeling of the null space of the curl operator. Edge elements remove such non physical spurious solutions.

    Numerical examples are given for homogeneous and inhomogeneous waveguides. The homogeneous results are compared to analytical solutions to demonstrate that the right order of convergence is achieved.

    Computations on more complicated inhomogeneous waveguides with and without striplines, are compared to results found in the literature together with grid convergence studies. We also give examples where corner singularities are addressed with $hp$-adaptive methods.

    The code is used in an industrial environment, together with 3-D time and frequency domain solvers for Maxwell's equations on general domains. For the full 3-D time domain simulations, cross section simulations are used as input on an artificial boundary that we define as a waveguide port. The excitation is done by a Huygens' surface and the backscattered field is taken care of by an unsplit perfectly matched layer. The results have been compared to what analytical input would give.

  • 15. Kurina, Galina A.
    et al.
    Smirnova, E. V.
    Zhou, Yishao
    Stockholm University, Faculty of Science, Department of Mathematics.
    Optimal control in feedback form for linear-quadratic problem with intermediate data2007In: Proceedings of Mathematical Department. Issue 11 (new series). Voronezh State University, Scientific book, Voronezh, Russia , 2007, p. 121-127Chapter in book (Other academic)
    Abstract [en]

    This paper deals with a non-standard linear quadratic problem with intermediate points data. The existence of optimal feedback control is proven and an explicit expression of the feedback law is given.

  • 16.
    Ogembo, Sara
    et al.
    Stockholm University, Faculty of Social Sciences, Department of Special Education.
    Gradin, Carina
    Stockholm University, Faculty of Social Sciences, Department of Special Education.
    Matematik lust eller olust: Hur elever i grundskolans tidigare år ser på matematik & matematikundervisning 2009Independent thesis Advanced level (degree of Master (One Year)), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Syftet med uppsatsen har varit att undersöka hur elever ser på ämnet matematik och matematikundervisning. Vår ambition har även varit att få syn på vad elever finner lustfyllt och mindre lustfyllt med matematiken och matematikundervisning.

    Utgångspunkten till det valda ämnet är att många elever som slutar grundskolan inte når upp till betyget Godkänd i matematik (SOU, 2004). Med hjälp av enkätfrågor ställda till 30 stycken elever i år 4, varav 7 elever som ingår i en mindre undervisningsgrupp under matematiklektioner, försökte vi finna svar på våra frågor. De 7 elever som ingår i den mindre undervisningsgruppen har även svarat på enkäten utifrån hur de upplevde matematiklektionerna när de var integrerade i den stora undervisningsgruppen. Vårt syfte med detta har varit att göra en jämförelse mellan de olika gruppernas upplevelse.

    Resultatet av enkätundersökningen visade att majoriteten av eleverna i den mindre undervisningsgruppen tycker att matematik är "så där", vilket handlar om att eleverna upplevde matematik både som roligt och tråkigt. Hälften av dessa elever tyckte inte om matematikundervisningen när de ingick i stor undervisningsgrupp, men som de däremot gör när de ingår i liten undervisningsgrupp. Drygt hälften av eleverna i stor undervisningsgrupp tycker om matematik och hälften av dessa elever gav svaret att de tycker om matematiklektionerna, andra hälften tyckte ”så där” om matematiklektionerna.

    I litteraturstudien kom vi bland annat i kontakt med Sjöbergs studie (2006) där 13 elever som efter avslutad grundskola inte nått upp till betyget godkänd i matematik, fick ge sin syn på varför de ansåg att de hamnat i matematiksvårigheter. En annan studie som också visade intresse var Engström (2006) som i sin avhandling har tittat på hur datorn kan användas som redskap i matematikundervisning.

    Det framkom även i litteraturstudien att orsakerna till elevers matematiksvårigheter kan orsakas av vilken förmåga som läraren har att förmedla matematikkunskaper till elever. Vi alla är olika och lär oss på olika sätt. Samt att miljön har en stor inverkan.

     

  • 17.
    Parszyk, Ing-Marie
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Är det jag eller matteläraren som inte fattar?: Unga vuxna väletablerade och interner med utländsk familjebakgrund berättar om matematikens betydelse för självkänslan i (skol)livet2009Book (Other academic)
  • 18.
    Partridge, Daniel
    et al.
    Stockholm University, Faculty of Science, Department of Applied Environmental Science (ITM).
    Tunved, Peter
    Stockholm University, Faculty of Science, Department of Applied Environmental Science (ITM).
    Vrugt, Jasper
    Ekman, Annica
    Stockholm University, Faculty of Science, Department of Meteorology .
    Sorooshian, Armin
    Roelofs, Geert-Jan
    Jonsson, Haf
    A study of marine stratocumulus clouds using an inverse modelling approachManuscript (preprint) (Other academic)
    Abstract [en]

    This paper presents a Bayesian inverse modelling approach to simultaneously assess the ability of a pseudo-adiabatic cloud parcel model to match in-situ measurements of the droplet size distribution in a cloud as well as model parameters describing the updraft and different aerosol microphysical properties (herein termed calibration parameters). Our methodology is tested using observations from two clean (average accumulation mode number concentration < 60 cm-3) and two polluted clouds (average accumulation mode number concentration > 100 cm-3) observed during the Marine Stratus/Stratocumulus Experiment (MASE II) campaign. Our framework capitalizes on recent developments in Markov Chain Monte Carlo (MCMC) simulation and retrieves the most likely parameter values and their underlying posterior probability density function. This distribution provides necessary information to efficiently and in a statistically robust manner, assess both the global sensitivity of aerosol physiochemical and meteorological parameters, and the suitability of cloud parcel models to comprehensively describe the evolution of cloud droplet size distributions in stratocumulus clouds.

    We demonstrate that the updraft velocity is the most important calibration parameter for describing the observed droplet distribution for each cloud case, corroborating previous findings. The accumulation mode number, shape and size are found to be more important than chemistry except for the most polluted conditions (average accumulation mode number concentration ~455 cm-3). This highlights that conditions exist for marine stratocumulus clouds in which an accurate description of the aerosol chemistry is a pre-requisite for the accurate representation of cloud microphysical properties.

    Overall, the MCMC algorithm successfully matches the observed droplet size distribution for each cloud case. In doing so, however, the subsequent agreement between the derived and measured calibration parameters is generally poor. An important result from this analysis is that for certain calibration parameters, consistent patterns of deviation were found in the posterior distributions for all the clouds included in this study. This finding indicates that either there is systematic sampling or averaging artefacts in our observations, or our pseudo-adiabatic cloud parcel model omits or consistently misrepresents processes and/or parameter(s) required to accurately simulate the droplet size distributions of the observed marine stratocumulus. By repeating our inverse methodology with more calibration parameters of which current measurements are uncertain (surface tension, mass accommodation coefficient), we find that it is likely that the process description within the current formulation of the pseudo-adiabatic cloud model used in this study misses a dynamical process rather than parameter(s).

  • 19.
    Pettersson, Astrid
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Bedömning av elevers kunskapsutveckling2010In: Forskning om undervisning och lärande, ISSN 2000-9674, no 4, p. 59-60Article in journal (Other academic)
  • 20.
    Pettersson, Astrid
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Bedömning av kunskap för lärande och undervisning: - en grund för ökat kunnande2010In: Forskning om undervisning och lärande, ISSN 2000-9674, no 3, p. 7-19Article in journal (Other academic)
  • 21.
    Pettersson, Astrid
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Ingemansson, Ingmar
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Matematiken i PISA2010In: Rustad att möta framtiden? PISA 2009 om 15-åringars läsförståelse och kunskaper i matematik och naturvetenskap, Stockholm: Skolverket , 2010, p. 97-112Chapter in book (Other academic)
  • 22.
    Pettersson, Astrid
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Olofsson, Gunilla
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Kjellström, Katarina
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Ingemansson, Ingmar
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Hallén, Stina
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Björklund Boistrup, Lisa
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Alm, Lena
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Bedömning av kunskap - för lärande och undervisning i matematik2010Book (Other academic)
  • 23.
    Pettersson, Astrid
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Skytt, Anette
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Genomförandet av ämnesprov för årskurs 3, 20092010In: Ämnesproven i grundskolans årskurs 3: en redovisning av utprovningsomgången 20, Stockholm: Skolverket , 2010, , p. 12p. 14-27Chapter in book (Other academic)
  • 24.
    Pettersson, Astrid
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Skytt, Anette
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Hur gick det? Ämnesprov i matematik för årskurs 3, 20092010In: Nämnaren, ISSN 0348-2723, no 2, p. 3-9Article in journal (Other (popular science, discussion, etc.))
  • 25.
    Rullgård, Hans
    Stockholm University, Faculty of Science, Department of Mathematics. Matematik.
    An explicit inversion formula for the exponential Radon transform using data from 180 degrees2004In: Arkiv för Matematik, ISSN 0004-2080, Vol. 42, no 2, p. 353-362Article in journal (Refereed)
    Abstract [en]

    We derive a direct inversion formula for the exponential Radon transform. Our formula requires only the values of the transform over an 180° range of angles. It is an explicit formula, except that it involves a holomorphic function for which an explicit expression has not been found. In practice, this function can be approximated by an easily computed polynomial of rather low degree.

  • 26.
    Rullgård, Hans
    Stockholm University, Faculty of Science, Department of Mathematics. Matematik.
    Stability of the inverse problem for the attenuated Radon transform with 180 degrees data2004In: Inverse Problems, Vol. 20, no 3, p. 781-797Article in journal (Refereed)
    Abstract [en]

    We consider the inverse problem for the attenuated Radon transform in two dimensions. It has recently been shown that this problem has a unique solution when the attenuation function is Hölder continuous, even with limited angle data. In this paper, we study stability of the inverse problem, with data from a 180° range of angles. We show that when the attenuation function is Hölder continuous and the support of the original function f is restricted to a given compact set, the Hölder norm of f with exponent -1/2 can be estimated in terms of the L2 norm of the attenuated Radon transform of f. We also obtain new stability results for the forward problem, that is, estimates of the norm of the Radon transform in terms of norms of the original function and the attenuation function.

  • 27.
    Rullgård, Hans
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics. Matematik.
    Öktem, Ozan
    Skoglund, Ulf
    A component-wise iterated relative entropy regularization method with updated prior and regularization parameter2007In: Inverse Problems, Vol. 23, no 5, p. 2121-2139Article in journal (Refereed)
    Abstract [en]

    We present a componentwise iterated relative entropy regularization method (COMET) where the prior and regularization parameter could be updated in the iterates. Such a reconstruction method could be useful for multicomponent inverse problems, such as the one occurring in electron tomography. The paper also contains a brief introduction to regularization theory with emphasis on variational based regularization methods, and we rigorously prove that the tolerance-based entropy reconstruction method that occurs in the COMET iterates is a regularization method. We conclude by showing examples of COMET applied to electron tomography data.

  • 28.
    Wahlund, Björn
    et al.
    Department of Clinical Neuroscience, Division of Psychiatry, Karolinska Institutet, Karolinska Hospital Huddinge, Stockholm, Sweden..
    Klonowski, Wlodzimierz
    Nalecz Institute of Biocybernetics and Biomedical Engineering, Polish Academy of Sciences, Warsaw, Poland..
    Stepien, Paweł
    Nalecz Institute of Biocybernetics and Biomedical Engineering, Polish Academy of Sciences, Warsaw, Poland..
    Stepien, Robert
    Nalecz Institute of Biocybernetics and Biomedical Engineering, Polish Academy of Sciences, Warsaw..
    von Rosen, Tatjana
    Stockholm University, Faculty of Social Sciences, Department of Statistics.
    von Rosen, Dietrich
    The Department of Energy and Technology, SLU, Sweden.
    EEG data, fractal dimension and multivariate statistics2010In: Journal of Computer Science and Engineering, ISSN 2043-9091, Vol. 3, no 1, p. 10-16Article in journal (Refereed)
    Abstract [en]

    The objective of this paper is to discuss the concept of Inverse Problem, i.e. how to obtain information via data about a complex mathematical model. We propose that by merging ideas from applied mathematics with ideas from multivariate statistical inference it is possible to find solutions or good approximation of many complex scientific problems.

  • 29.
    Yin, Ge
    et al.
    Stockholm University, Faculty of Science, Department of Environmental Science and Analytical Chemistry.
    Danielsson, Sara
    Dahlberg, Anna-Karin
    Zhou, Yihui
    Stockholm University, Faculty of Science, Department of Environmental Science and Analytical Chemistry.
    Qiu, Yanling
    Stockholm University, Faculty of Science, Department of Environmental Science and Analytical Chemistry.
    Nyberg, Elisabeth
    Bignert, Anders
    Sampling designs for contaminant temporal trend analyses using sedentary species exemplified by the snails (Bellamya aeruginosa) and (Viviparus viviparus)Manuscript (preprint) (Other academic)
1 - 29 of 29
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