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  • 51.
    Andersson-Evelönn, Emma
    et al.
    Umeå universitet, Medicinska fakulteten, Institutionen för medicinsk biovetenskap, Patologi.
    Vidman, Linda
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Källberg, David
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik. Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Landfors, Mattias
    Umeå universitet, Medicinska fakulteten, Institutionen för medicinsk biovetenskap, Patologi.
    Liu, Xijia
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Ljungberg, Börje
    Umeå universitet, Medicinska fakulteten, Institutionen för kirurgisk och perioperativ vetenskap, Urologi och andrologi.
    Hultdin, Magnus
    Umeå universitet, Medicinska fakulteten, Institutionen för medicinsk biovetenskap, Patologi.
    Degerman, Sofie
    Umeå universitet, Medicinska fakulteten, Institutionen för medicinsk biovetenskap, Patologi. Umeå universitet, Medicinska fakulteten, Institutionen för klinisk mikrobiologi.
    Rydén, Patrik
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Combining epigenetic and clinicopathological variables improves prognostic prediction in clear cell Renal Cell CarcinomaManuskript (preprint) (Övrigt vetenskapligt)
  • 52.
    Andren, Daniel
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Markström, Klas
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    The bivariate ising polynomial of a graph2009Ingår i: Discrete Applied Mathematics, ISSN 0166-218X, E-ISSN 1872-6771, Vol. 157, nr 11, s. 2515-2524Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we discuss the two variable Ising polynomials in a graph theoretical setting. This polynomial has its origin in physics as the partition function of the Ising model with an external field. We prove some basic properties of the Ising polynomial and demonstrate that it encodes a large amount of combinatorial information about a graph. We also give examples which prove that certain properties, such as the chromatic number, are not determined by the Ising polynomial. Finally we prove that there exist large families of non-isomorphic planar triangulations with identical Ising polynomial. (C) 2009 Published by Elsevier B.V.

  • 53. Andren, Lina J.
    et al.
    Casselgren, Carl Johan
    Markström, Klas
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Restricted completion of sparse partial Latin squares2019Ingår i: Combinatorics, probability & computing, ISSN 0963-5483, E-ISSN 1469-2163, Vol. 28, nr 5, s. 675-695Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    An n × n partial Latin square P is called α-dense if each row and column has at most αn non-empty cells and each symbol occurs at most αn times in P. An n × n array A where each cell contains a subset of {1,…, n} is a (βn, βn, βn)-array if each symbol occurs at most βn times in each row and column and each cell contains a set of size at most βn. Combining the notions of completing partial Latin squares and avoiding arrays, we prove that there are constants α, β > 0 such that, for every positive integer n, if P is an α-dense n × n partial Latin square, A is an n × n (βn, βn, βn)-array, and no cell of P contains a symbol that appears in the corresponding cell of A, then there is a completion of P that avoids A; that is, there is a Latin square L that agrees with P on every non-empty cell of P, and, for each i, j satisfying 1 ≤ i, j ≤ n, the symbol in position (i, j) in L does not appear in the corresponding cell of A.

  • 54.
    Andren, Lina J.
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Casselgren, Carl Johan
    Öhman, Lars-Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Avoiding Arrays of Odd Order by Latin Squares2013Ingår i: Combinatorics, probability & computing, ISSN 0963-5483, E-ISSN 1469-2163, Vol. 22, nr 2, s. 184-212Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We prove that there is a constant c such that, for each positive integer k, every (2k + 1) x (2k + 1) array A on the symbols 1, ... , 2k + 1 with at most c(2k + 1) symbols in every cell, and each symbol repeated at most c(2k + 1) times in every row and column is avoidable; that is, there is a (2k + 1) x (2k + 1) Latin square S on the symbols 1, ... , 2k + 1 such that, for each i, j is an element of {1, ... , 2k + 1}, the symbol in position (i, j) of S does not appear in the corresponding cell in Lambda. This settles the last open case of a conjecture by Haggkvist. Using this result, we also show that there is a constant rho, such that, for any positive integer n, if each cell in an n x n array B is assigned a set of m <= rho n symbols, where each set is chosen independently and uniformly at random from {1, ... , n}, then the probability that B is avoidable tends to 1 as n -> infinity.

  • 55.
    Andrén, Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    On the Ising problem and some matrix operations2007Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    The first part of the dissertation concerns the Ising problem proposed to Ernst Ising by his supervisor Wilhelm Lenz in the early 20s. The Ising model, or perhaps more correctly the Lenz-Ising model, tries to capture the behaviour of phase transitions, i.e. how local rules of engagement can produce large scale behaviour.

    Two decades later Lars Onsager solved the Ising problem for the quadratic lattice without an outer field. Using his ideas solutions for other lattices in two dimensions have been constructed. We describe a method for calculating the Ising partition function for immense square grids, up to linear order 320 (i.e. 102400 vertices).

    In three dimensions however only a few results are known. One of the most important unanswered questions is at which temperature the Ising model has its phase transition. In this dissertation it is shown that an upper bound for the critical coupling Kc, the inverse absolute temperature, is 0.29 for the tree dimensional cubic lattice.

    To be able to get more information one has to use different statistical methods. We describe one sampling method that can use simple state generation like the Metropolis algorithm for large lattices. We also discuss how to reconstruct the entropy from the model, in order to obtain parameters as the free energy.

    The Ising model gives a partition function associated with all finite graphs. In this dissertation we show that a number of interesting graph invariants can be calculated from the coefficients of the Ising partition function. We also give some interesting observations about the partition function in general and show that there are, for any N, N non-isomorphic graphs with the same Ising partition function.

    The second part of the dissertation is about matrix operations. We consider the problem of multiplying them when the entries are elements in a finite semiring or in an additively finitely generated semiring. We describe a method that uses O(n3 / log n) arithmetic operations.

    We also consider the problem of reducing n x n matrices over a finite field of size q using O(n2 / logq n) row operations in the worst case.

  • 56.
    Andrén, Lina J.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Avoidability by Latin squares of arrays of even orderManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    We prove that for any k and any 2k × 2k array A such that no cell in A contains more than   k/2550 symbols, and no symbol occurs more than k/2550 times in any row or column, there is a Latin square such that no 2550cell in the Latin square contains a symbol that occurs in the corresponding cell in A. This proves a conjecture of Häggkvist [8] in the special case of arrays with even side.

  • 57.
    Andrén, Lina J.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Avoidability of random arraysManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    An n×n array that in each cell contains a subset of the symbols 1, . . . , n is avoidable if there exists a Latin square of order n such that no cell in the Latin square contains a symbol which belongs to the set of symbols in the corresponding cell of the array. Some results on deterministic conditions for avoidability of arrays have been found, but here we study the problem of having an array with randomly assigned subsets of C in its cells. This is equivalent to the problem of list-edge-coloring  with randomly assigned lists from the set {1, . . . , n}. We show that an array where each symbol appears in each cell with probability p will be avoidable with very high probability even if p is such that the expected number of symbols forbidden in each cell is slightly higher than what deterministic theorems can prove is avoidable.

  • 58.
    Andrén, Lina J.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Avoiding (m, m, m)-arrays of order n = 2kManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    An (m, m, m)-array of order n is an n × n array such that each cell is assigned a set of at most m symbols from {1,...,n} such that no symbol occurs more than m times in any row or column. An (m,m,m)- array is called avoidable if there exists a Latin square such that no cell in the Latin square contains a symbol that also belongs to the set assigned to the corresponding cell in the array. We show that there is a constant γ such that if m ≤ γ2k, then any (m,m,m)-array of order 2k is avoidable. Such a constant γ has been conjectured to exist for all n by Häggkvist.

  • 59.
    Andrén, Lina J
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Avoiding (m, m, m)-arrays of order n=2(k)2012Ingår i: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 19, nr 1, s. P63-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    An (m, m, m)-array of order n is an n x n array such that each cell is assigned a set of at most m symbols from f 1,...,n g such that no symbol occurs more than m times in any row or column. An (m, m, m)-array is called avoidable if there exists a Latin square such that no cell in the Latin square contains a symbol that also belongs to the set assigned to the corresponding cell in the array. We show that there is a constant gamma such that if m <= gamma 2(k) and k >= 14, then any (m, m, m)-array of order n = 2(k) is avoidable. Such a constant gamma has been conjectured to exist for all n by Haggkvist.

  • 60.
    Andrén, Lina J.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    On Latin squares and avoidable arrays2010Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [sv]

    Denna avhandling inehåller de fyra nedan uppräknade artiklarna, samt en översikt av forskningsområdet.

    I Lina J. Andrén: Avoiding (m, m, m)-arrays of order n = 2k

    II Lina J. Andrén: Avoidability of random arrays

    III Lina J. Andrén: Avoidability by Latin squares of arrays with even order

    IV Lina J. Andrén, Carl Johan Casselgren and Lars-Daniel Öhman: Avoiding arrays of odd order by Latin squares

    Artikel I, III och IV behandlar en förmodan av Häggkvist, som säger att det finns en konstant c sådan att för varje positivt heltal n gäller att om m ≤ cn så finns för varje n × n array A av delmängder till {1, . . . ,n} sådan att ingen cell i A i innehåller fler än m symboler, och ingen symbol förekommer i fler än m celler i någon av raderna eller kolumnerna, så finns en latinsk kvadrat L sådan att ingen cell i L innehåller en symbol som förekommer i motsvarande cell i A. En sådan latinsk kvadrat sägs undvika A. Artikel I innehåller ett bevis av förmodan i specialfallet n = 2k. Artikel III använder och utökar metoderna i Artikel I till ett bevis av förmodan för alla latinska kvadrater av jämn ordning. Förmodan visas slutligen för samtliga ordningar i Artikel IV, där bevismetoden liknar den som finns i i Artikel I och III tillsammans med en omfärgningssats. Artikel II behandlar en annan aspekt av problemet genom att undersöka vad ett deterministiskt resultat om existens av latinska kvadrater som undviker en viss typ av array säger om arrayer där mängderna tilldelas slumpmässigt.

  • 61.
    Andrén, Lina J.
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Casselgren, Carl Johan
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Öhman, Lars-Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Avoiding arrays of odd order by Latin squaresManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    We prove that there exists a constant c such that for each pos- itive integer k every (2k+1)×(2k+1) array A on the symbols 1,...,2k+1 with at most c(2k + 1) symbols in every cell, and each symbol repeated at most c(2k+1) times in every row and column is avoidable; that is, there is a (2k+1)×(2k+1) Latin square S on the symbols 1,...,2k+1 such that for each cell (i, j) in S the symbol in (i, j) does not appear in the corresponding cell in A. This settles the last open case of a conjecture by Häggkvist.

  • 62.
    Angelov, Angel G.
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Methods for interval-censored data and testing for stochastic dominance2018Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    This thesis includes four papers: the first three of them are concerned with methods for interval-censored data, while the forth paper is devoted to testing for stochastic dominance.

    In many studies, the variable of interest is observed to lie within an interval instead of being observed exactly, i.e., each observation is an interval and not a single value. This type of data is known as interval-censored. It may arise in questionnaire-based studies when the respondent gives an answer in the form of an interval without having pre-specified ranges. Such data are called self-selected interval data. In this context, the assumption of noninformative censoring is not fulfilled, and therefore the existing methods for interval-censored data are not necessarily applicable.

    A problem of interest is to estimate the underlying distribution function. There are two main approaches to this problem: (i) parametric estimation, which assumes a particular functional form of the distribution, and (ii) nonparametric estimation, which does not rely on any distributional assumptions. In Paper A, a nonparametric maximum likelihood estimator for self-selected interval data is proposed and its consistency is shown. Paper B suggests a parametric maximum likelihood estimator. The consistency and asymptotic normality of the estimator are proven.

    Another interesting problem is to infer whether two samples arise from identical distributions. In Paper C, nonparametric two-sample tests suitable for self-selected interval data are suggested and their properties are investigated through simulations.

    Paper D concerns testing for stochastic dominance with uncensored data. The paper explores a testing problem which involves four hypotheses, that is, based on observations of two random variables X and Y, one wants to discriminate between four possibilities: identical survival functions, stochastic dominance of X over Y, stochastic dominance of Y over X, or crossing survival functions. Permutation-based tests suitable for two independent samples and for paired samples are proposed. The tests are applied to data from an experiment concerning the individual's willingness to pay for a given environmental improvement.

  • 63.
    Angelov, Angel G.
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Nonparametric two-sample tests for informatively interval-censored dataManuskript (preprint) (Övrigt vetenskapligt)
  • 64.
    Angelov, Angel G.
    et al.
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Ekström, Magnus
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Maximum likelihood estimation for survey data with informative interval censoring2019Ingår i: AStA Advances in Statistical Analysis, ISSN 1863-8171, E-ISSN 1863-818X, Vol. 103, nr 2, s. 217-236Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Interval-censored data may arise in questionnaire surveys when, instead of being asked to provide an exact value, respondents are free to answer with any interval without having pre-specified ranges. In this context, the assumption of noninformative censoring is violated, and thus, the standard methods for interval-censored data are not appropriate. This paper explores two schemes for data collection and deals with the problem of estimation of the underlying distribution function, assuming that it belongs to a parametric family. The consistency and asymptotic normality of a proposed maximum likelihood estimator are proven. A bootstrap procedure that can be used for constructing confidence intervals is considered, and its asymptotic validity is shown. A simulation study investigates the performance of the suggested methods.

  • 65.
    Angelov, Angel G.
    et al.
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Ekström, Magnus
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Nonparametric estimation for self-selected interval data collected through a two-stage approach2017Ingår i: Metrika (Heidelberg), ISSN 0026-1335, E-ISSN 1435-926X, Vol. 80, nr 4, s. 377-399Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Self-selected interval data arise in questionnaire surveys when respondents are free to answer with any interval without having pre-specified ranges. This type of data is a special case of interval-censored data in which the assumption of noninformative censoring is violated, and thus the standard methods for interval-censored data (e.g. Turnbull's estimator) are not appropriate because they can produce biased results. Based on a certain sampling scheme, this paper suggests a nonparametric maximum likelihood estimator of the underlying distribution function. The consistency of the estimator is proven under general assumptions, and an iterative procedure for finding the estimate is proposed. The performance of the method is investigated in a simulation study.

  • 66.
    Angelov, Angel G.
    et al.
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Ekström, Magnus
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik. Department of Forest Resource Management, Swedish University of Agricultural Sciences, Umeå, Sweden.
    Kriström, Bengt
    Department of Forest Economics, Swedish University of Agricultural Sciences, Umeå, Sweden.
    Nilsson, Mats E.
    Gösta Ekman Laboratory, Department of Psychology, Stockholm University, Stockholm, Sweden.
    Four-decision tests for stochastic dominance, with an application to environmental psychophysics2019Ingår i: Journal of mathematical psychology (Print), ISSN 0022-2496, E-ISSN 1096-0880, Vol. 93, artikel-id 102281Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    If the survival function of a random variable X lies to the right of the survival function of a random variable Y, then X is said to stochastically dominate Y. Inferring stochastic dominance is particularly complicated because comparing survival functions raises four possible hypotheses: identical survival functions, dominance of X over Y, dominance of Y over X, or crossing survival functions. In this paper, we suggest four-decision tests for stochastic dominance suitable for paired samples. The tests are permutation-based and do not rely on distributional assumptions. One-sided Cramér–von Mises and Kolmogorov–Smirnov statistics are employed but the general idea may be utilized with other test statistics. The power to detect dominance and the different types of wrong decisions are investigated in an extensive simulation study. The proposed tests are applied to data from an experiment concerning the individual’s willingness to pay for a given environmental improvement.

  • 67.
    Angelov, Angel G.
    et al.
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Ekström, Magnus
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Kriström, Bengt
    Umeå universitet, Samhällsvetenskapliga fakulteten, Centrum för miljö- och naturresursekonomi (CERE). Department of Forest Economics, Swedish University of Agricultural Sciences.
    Nilsson, Mats E.
    Gösta Ekman Laboratory, Department of Psychology, Stockholm University.
    Testing for stochastic dominance: Procedures with four hypothesesManuskript (preprint) (Övrigt vetenskapligt)
  • 68.
    Angervall, Petra
    et al.
    Inst. i pedagogik och specialpedagogik, Göteborgs universitet.
    Gustafsson, Jan
    Inst. i pedagogik och specialpedagogik, Göteborgs universitet.
    Silfver, Eva
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för naturvetenskapernas och matematikens didaktik. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Umeå forskningscentrum för matematikdidaktik (UFM).
    Policy and governance in academic networks2011Konferensbidrag (Refereegranskat)
  • 69.
    Anton, Rikard
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Convergence of an exponential method for the stochastic Schrödinger equation with power-law nonlinearityManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    A temporal approximation of the stochastic Schrödinger equation with a power-law nonlinearity and driven by multiplicative Ito noise is considered. Observe that the nonlinearity is not globally Lipschitz continuous and, in general, the exact solution cannot be assumed to remain bounded for all times. The first of these issues is handled by considering a truncated version of the equation. The second issue is handled by working with stopping times and random time intervals, on which the solution is almost surely bounded. For the time integration we use a stochastic exponential method. This exponential method has the advantage of being explicit and it does not suffer any CFL-type step size restrictions in general. In this work we prove almost sure convergence and convergence in probability, accompanied by convergence orders of 1/2- and 1/2, respectively. We also find that the regularity assumptions required on the noise and initial value are less restrictive for the convergence of the exponential scheme, compared to the Crank-Nicolson scheme. In addition, we provide numerical experiments that illustrate our theoretical results.

  • 70.
    Anton, Rikard
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Exponential integrators for stochastic partial differential equations2018Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    Stochastic partial differential equations (SPDEs) have during the past decades become an important tool for modeling systems which are influenced by randomness. Because of the complex nature of SPDEs, knowledge of efficient numerical methods with good convergence and geometric properties is of considerable importance. Due to this, numerical analysis of SPDEs has become an important and active research field.

    The thesis consists of four papers, all dealing with time integration of different SPDEs using exponential integrators. We analyse exponential integrators for the stochastic wave equation, the stochastic heat equation, and the stochastic Schrödinger equation. Our primary focus is to study strong order of convergence of temporal approximations. However, occasionally, we also analyse space approximations such as finite element and finite difference approximations. In addition to this, for some SPDEs, we consider conservation properties of numerical discretizations.

    As seen in this thesis, exponential integrators for SPDEs have many benefits over more traditional integrators such as Euler-Maruyama schemes or the Crank-Nicolson-Maruyama scheme. They are explicit and therefore very easy to implement and use in practice. Also, they are excellent at handling stiff problems, which naturally arise from spatial discretizations of SPDEs. While many explicit integrators suffer step size restrictions due to stability issues, exponential integrators do not in general.

    In Paper 1 we consider a full discretization of the stochastic wave equation driven by multiplicative noise. We use a finite element method for the spatial discretization, and for the temporal discretization we use a stochastic trigonometric method. In the first part of the paper, we prove mean-square convergence of the full approximation. In the second part, we study the behavior of the total energy, or Hamiltonian, of the wave equation. It is well known that for deterministic (Hamiltonian) wave equations, the total energy remains constant in time. We prove that for stochastic wave equations with additive noise, the expected energy of the exact solution grows linearly with time. We also prove that the numerical approximation produces a small error in this linear drift.

    In the second paper, we study an exponential integrator applied to the time discretization of the stochastic Schrödinger equation with a multiplicative potential. We prove strong convergence order 1 and 1/2 for additive and multiplicative noise, respectively. The deterministic linear Schrödinger equation has several conserved quantities, including the energy, the mass, and the momentum. We first show that for Schrödinger equations driven by additive noise, the expected values of these quantities grow linearly with time. The exponential integrator is shown to preserve these linear drifts for all time in the case of a stochastic Schrödinger equation without potential. For the equation with a multiplicative potential, we obtain a small error in these linear drifts.

    The third paper is devoted to studying a full approximation of the one-dimensional stochastic heat equation. For the spatial discretization we use a finite difference method and an exponential integrator is used for the temporal approximation. We prove mean-square convergence and almost sure convergence of the approximation when the coefficients of the problem are assumed to be Lipschitz continuous. For non-Lipschitz coefficients, we prove convergence in probability.

    In Paper 4 we revisit the stochastic Schrödinger equation. We consider this SPDE with a power-law nonlinearity. This nonlinearity is not globally Lipschitz continuous and the exact solution is not assumed to remain bounded for all times. These difficulties are handled by considering a truncated version of the equation and by working with stopping times and random time intervals. We prove almost sure convergence and convergence in probability for the exponential integrator as well as convergence orders of ½ − 𝜀, for all 𝜀 > 0, and 1/2, respectively.

  • 71.
    Anton, Rikard
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Cohen, David
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik. Department of Mathematics, University of Innsbruck, A–6020 Innsbruck, Austria.
    Exponential integrators for stochastic Schrödinger equations driven by Itô noise2018Ingår i: Journal of Computational Mathematics, ISSN 0254-9409, E-ISSN 1991-7139, Vol. 36, nr 2, s. 276-309Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study an explicit exponential scheme for the time discretisation of stochastic Schr¨odinger Equations Driven by additive or Multiplicative Itô Noise. The numerical scheme is shown to converge with strong order 1 if the noise is additive and with strong order 1/2 for multiplicative noise. In addition, if the noise is additive, we show that the exact solutions of the linear stochastic Schr¨odinger equations satisfy trace formulas for the expected mass, energy, and momentum (i. e., linear drifts in these quantities). Furthermore, we inspect the behaviour of the numerical solutions with respect to these trace formulas. Several numerical simulations are presented and confirm our theoretical results.

  • 72.
    Anton, Rikard
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Cohen, David
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik. Univ Innsbruck, Dept Math, Innsbruck, Austria.
    Larsson, Stig
    Wang, Xiaojie
    Full discretization of semilinear stochastic wave equations driven by multiplicative noise2016Ingår i: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 54, nr 2, s. 1093-1119Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A fully discrete approximation of the semilinear stochastic wave equation driven by multiplicative noise is presented. A standard linear finite element approximation is used in space, and a stochastic trigonometric method is used for the temporal approximation. This explicit time integrator allows for mean-square error bounds independent of the space discretization and thus does not suffer from a step size restriction as in the often used Stormer-Verlet leapfrog scheme. Furthermore, it satisfies an almost trace formula (i.e., a linear drift of the expected value of the energy of the problem). Numerical experiments are presented and confirm the theoretical results.

  • 73.
    Anton, Rikard
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Cohen, David
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Quer-Sardanyons, Lluis
    A fully discrete approximation of the one-dimensional stochastic heat equation2018Ingår i: IMA Journal of Numerical Analysis, ISSN 0272-4979, E-ISSN 1464-3642Artikel i tidskrift (Övrigt vetenskapligt)
    Abstract [en]

    A fully discrete approximation of the one-dimensional stochastic heat equation driven by multiplicative space–time white noise is presented. The standard finite difference approximation is used in space and a stochastic exponential method is used for the temporal approximation. Observe that the proposed exponential scheme does not suffer from any kind of CFL-type step size restriction. When the drift term and the diffusion coefficient are assumed to be globally Lipschitz this explicit time integrator allows for error bounds in Lq(&#x03A9;)" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline-table; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">Lq(Ω)Lq(Ω)⁠, for all q&#x2A7E;2" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline-table; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">q⩾2q⩾2⁠, improving some existing results in the literature. On top of this we also prove almost sure convergence of the numerical scheme. In the case of nonglobally Lipschitz coefficients, under a strong assumption about pathwise uniqueness of the exact solution, convergence in probability of the numerical solution to the exact solution is proved. Numerical experiments are presented to illustrate the theoretical results.

  • 74.
    Antonsen Åberg, Andreas
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Development and evaluation of stress tests: Utilizing stress tests to complement the current ex-ante analysis at Second Swedish National Pension Fund2017Självständigt arbete på avancerad nivå (masterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
    Abstract [sv]

    På den finansiella marknaden förekommer termen stresstester med jämna mellanrum, där vissa institutioner har det som krav och andra har det som ett frivilligt sätt att komplettera prediktioner. Stresstester används för att mäta hur robust ett finansiellt instrument eller en portfölj är i olika scenarion, där utmaningen blir att konstruera ett stresstest som är relevant och tillräckligt extremt. Målet med arbetet är att studera olika stresstestmetoder som ska kunna bli tillämpade hos Andra AP-fonden (AP2) i samband med deras prediktion av marknadsrisker. Två olika metoder implementeras med olika scenarion och således utförs unika analyser för respektive metod. Därav jämförs inte metoderna mot varandra utan varje metod analyseras individuellt med för- och nackdelar utifrån valet av metod och typen av scenarion. Resultatet för den första metoden, historiskt stresstest, påvisar att portföljen som stressas skulle minska i värde under det specificerade scenariot. För den andra metoden, koherent stresstest, varierar resultatet för de olika scenarierna. 

  • 75.
    Appelblad, Mats
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Solvenskrav och riskhantering enligt Solvens II: Implementering av de nya riskbaserade solvensreglerna på ett skadeförsäkringsbolag2014Självständigt arbete på avancerad nivå (yrkesexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
    Abstract [en]

    The insurance industryis challengedby major changesthrough internationalizationand thusgrowingcompetitionwithmore optionsand greater availabilityfor customers.Solvency II, a new regulatoryframework and anew standard forinsurance companies,is therefore implemented in a steptowardsa more competitive Europeaninsurancemarket. Solvency II will result in extensive structural changes for many insurance companies. Newstandards andinternal models must also be implemented by the companies. Solvency IIhasa tightening effect on thesolvency capital requirements forinsurance companies. At the same time it also leads tomajor changesandincreased demandon risk management andinternal control, alongside with demands fordisclosure of informationto the market. The purposeof this thesis isthereforeto develop aSolvency IImodel with solvency capital requirements, SCR, and own risk and solvency assessment, ORSA,for a small, fictitious, non-life insurancecompany.The thesis iscovered byfour parts, whereeach of themis a partof developingthe non-life insurance company. The modelis implementedin association withthe consulting firmtheFinancialCompliance Group, FCG, inStockholm and willprovide insight into theSolvency II, its meaning, andhow the frameworkcan be implementedin practice.The modelingis doneprimarilyin Excel. Matlab and VBA, the programming language integrated in Excel, is also used for the implementation. The result shows that market risk is the largest part of the total solvency capital requirement related to the non-life insurance company. The size and allocation of the assets of the insurance company has a direct impact on the size of the capital requirement for market risk. The counterparty credit rating, probability of default, also has a crucial effect on the size of the capital requirement. The outcome in both the base scenario and the stressed scenario in the ORSA show the importance of companies simulating a future solvency situation. They can thereby get an idea of ​​how the business reacts to market changes. The combination of assets in the asset portfolio that generates the minimum SCR is the portfolio with the lowest return and the lowest risk profile. This approach also results in a high solvency ratio. Conversely, the portfolio with the highest yield also implies a maximum level of risk. More weight allocated in assets with high returns and variance generates a higher SCR and thereby a lower solvency ratio. The insurance company can benefit from the strategy with a high return on the asset portfolio in prosperous times with positive market trends. Conversely, more weight allocated to assets with low returns generates a lower SCR and a higher solvency ratio. This approach is preferable when the market suffers from negative trends. The solvency ratio is further affected by changes in the value of both assets and liabilities. A decrease in interest rates results in an increase of the technical provisions which in turn leads to a reduction in own funds and solvency ratio. The same effect arises when the total value of assets is reduced. The thesis also showed the importance of reallocating the assets in the asset portfolio. This is particularly palpable in times when the value of assets suffers from downward trends. Reallocation of the assets will reduce the risk of falling solvency ratio and thereby the risk that the company will become insolvent.

  • 76.
    Araujo-Cabarcas, Juan Carlos
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Reliable hp finite element computations of scattering resonances in nano optics2019Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    Eigenfrequencies are commonly studied in wave propagation problems, as they are important in the analysis of closed cavities such as a microwave oven. For open systems, energy leaks into infinity and therefore scattering resonances are used instead of eigenfrequencies. An interesting application where resonances take an important place is in whispering gallery mode resonators.

    The objective of the thesis is the reliable and accurate approximation of scattering resonances using high order finite element methods. The discussion focuses on the electromagnetic scattering resonances in metal-dielectric nano-structures using a Drude-Lorentz model for the description of the material properties. A scattering resonance pair satisfies a reduced wave equationand an outgoing wave condition. In this thesis, the outgoing wave condition is replaced by a Dirichlet-to-Neumann map, or a Perfectly Matched Layer. For electromagnetic waves and for acoustic waves, the reduced wave equation is discretized with finite elements. As a result, the scattering resonance problem is transformed into a nonlinear eigenvalue problem.

    In addition to the correct approximation of the true resonances, a large number of numerical solutions that are unrelated to the physical problem are also computed in the solution process. A new method based on a volume integral equation is developed to remove these false solutions.

    The main results of the thesis are a novel method for removing false solutions of the physical problem, efficient solutions of non-linear eigenvalue problems, and a new a-priori based refinement strategy for high order finite element methods. The overall material in the thesis translates into a reliable and accurate method to compute scattering resonances in physics and engineering.

  • 77.
    Araujo-Cabarcas, Juan Carlos
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Campos, Carmen
    Engström, Christian
    Roman, Jose E.
    Computation of scattering resonances in absorptive and dispersive media with applications to metal-dielectric nano-structuresManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    In this paper we consider scattering resonance computations in optics when the resonators consist of frequency dependent and lossy materials, such as metals at optical frequencies. The proposed computational approach combines a novel hp-FEM strategy, based on dispersion analysis for complex frequencies, with a fast implementation of the nonlinear eigenvalue solver NLEIGS.Numerical computations illustrate that the pre-asymptotic phase is significantly reduced compared to standard uniform h and p strategies. Moreover, the efficiency grows with the refractive index contrast, which makes the new strategy highly attractive for metal-dielectric structures. The hp-refinement strategy together with the efficient parallel code result in highly accurate approximations and short runtimes on multi processor platforms.

  • 78.
    Araujo-Cabarcas, Juan Carlos
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Engström, Christian
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    On spurious solutions in finite element approximations of resonances in open systems2017Ingår i: Computers and Mathematics with Applications, ISSN 0898-1221, E-ISSN 1873-7668, Vol. 74, nr 10, s. 2385-2402Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, we discuss problems arising when computing resonances with a finite element method. In the pre-asymptotic regime, we detect for the one dimensional case, spurious solutions in finite element computations of resonances when the computational domain is truncated with a perfectly matched layer (PML) as well as with a Dirichlet-to-Neumann map (DtN). The new test is based on the Lippmann–Schwinger equation and we use computations of the pseudospectrum to show that this is a suitable choice. Numerical simulations indicate that the presented test can distinguish between spurious eigenvalues and true eigenvalues also in difficult cases.

  • 79.
    Araujo-Cabarcas, Juan Carlos
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Engström, Christian
    Removal of spurious solutions encountered in Helmholtz scattering resonance computations in R^dManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    In this paper we consider a sorting scheme for the removal of spurious scattering resonant pairs in two-dimensional electromagnetic problems and in three-dimensional acoustic problems. The novel sorting scheme is based on a Lippmann-Schwinger type of volume integral equation and can therefore be applied to graded material properties as well as piece-wise constant material properties. For TM/TE polarized electromagnetic waves and for acoustic waves, we compute first approximations of scattering resonances with finite elements. Then, we apply the novel sorting scheme to the computed eigenpairs and use it to remove spurious solutions in electromagnetic and acoustic scattering resonances computations at low computational cost. Several test cases with Drude-Lorentz dielectric resonators as well as with graded material properties are considered.

  • 80.
    Araujo-Cabarcas, Juan Carlos
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Engström, Christian
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Jarlebring, Elias
    Royal Institute of Technology.
    Efficient resonance computations for Helmholtz problems based on a Dirichlet-to-Neumann map2018Ingår i: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 330, s. 177-192Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We present an efficient procedure for computing resonances and resonant modes of Helmholtz problems posed in exterior domains. The problem is formulated as a nonlinear eigenvalue problem (NEP), where the nonlinearity arises from the use of a Dirichlet-to-Neumann map, which accounts for modeling unbounded domains. We consider a variational formulation and show that the spectrum consists of isolated eigenvalues of finite multiplicity that only can accumulate at infinity. The proposed method is based on a high order finite element discretization combined with a specialization of the Tensor Infinite Arnoldi method (TIAR). Using Toeplitz matrices, we show how to specialize this method to our specific structure. In particular we introduce a pole cancellation technique in order to increase the radius of convergence for computation of eigenvalues that lie close to the poles of the matrix-valued function. The solution scheme can be applied to multiple resonators with a varying refractive index that is not necessarily piecewise constant. We present two test cases to show stability, performance and numerical accuracy of the method. In particular the use of a high order finite element discretization together with TIAR results in an efficient and reliable method to compute resonances.

  • 81.
    Arnqvist, Per
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Allowing Left Truncated and Censored Fertility Data in the Normal Waiting Model1995Rapport (Övrigt vetenskapligt)
    Abstract [en]

    Models describing marital fertility are under consideration. In Arnqvist (Research Report 2, Mathematical Statistics, Umeå University), a normal approximation of the waiting model was introduced. In this report a modification of the normal approximation is suggested. This specification allows the data to be left truncated and censored, which gives the possibility to apply the normally approximated waiting model in datasets as from the United Nations World Fertility Services. The model is appropriate except for extremely high fertility intensities, when it gives rise to bias in the parameter estimations. In this case, therefore, a bootstrap method is suggested to estimate and correct the bias. This means that the normal approximated waiting model is a good competitor to the well known Poisson or Coale-Trussell model. It also uses an understandable fertility specification.

  • 82.
    Arnqvist, Per
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Approximation of the waiting model1995Rapport (Övrigt vetenskapligt)
    Abstract [en]

    In an attempt to estimate the level of family planning in a population, Coale-Trussell suggested an intensity model based on five year summarized data as given in the reports of the United Nations. Their model is denoted Coale-Trussell model. To make inference in the model, it was assumed that the pregnancy data in the model followed a Poisson process. In Arnqvist (research report 1, 1995, Mathematical Statistics, Umeå University), a modification of the Poisson assumption in the intensity model was suggested, introducing waiting time after the pregnancies. The resulting model was named the waiting model. The aim of this paper is to compare the Coale-Trussell model with the waiting model when data of the form given in UN World Fertility Surveys are used (Table 1). By using a normal approximation of the first two moments of the number of pregnancies, the asymptotic variance of the estimators of the interesting parameters is given. Simulation studies show that the Coale-Trussell model and the normal approximation model both approximate the lower intensities in the waiting model well. However, the Coale-Trussell model gives essentially biased estimates of the intensities for high birth intensities.

  • 83.
    Arnqvist, Per
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Aspects of the Coale-Trussell Model1995Rapport (Övrigt vetenskapligt)
    Abstract [en]

    Coale-Trussell model for marital fertility is investigated. The assumption that the data follow a Poisson model is invalidated by empirical evidence. The data are less spread than assumed, which indicates a point process which is undersdispersed relative to the Poisson model. By generalizing the Poisson model, by using a more realistic assumption about spacing between births, eg. allowing for a constant delay after each birth, we produce a better and more natural descripton of human reproduction.

  • 84.
    Arnqvist, Per
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Functional clustering methods and marital fertility modelling2017Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    This thesis consists of two parts.The first part considers further development of a model used for marital fertility, the Coale-Trussell's fertility model, which is based on age-specific fertility rates. A new model is suggested using individual fertility data and a waiting time after pregnancies. The model is named the waiting model and can be understood as an alternating renewal process with age-specific intensities. Due to the complicated form of the waiting model and the way data is presented, as given in the United Nation Demographic Year Book 1965, a normal approximation is suggested together with a normal approximation of the mean and variance of the number of births per summarized interval. A further refinement of the model was then introduced to allow for left truncated and censored individual data, summarized as table data. The waiting model suggested gives better understanding of marital fertility and by a simulation study it is shown that the waiting model outperforms the Coale-Trussell model when it comes to estimating the fertility intensity and to predict the mean and variance of the number of births for a population.

    The second part of the thesis focus on developing functional clustering methods.The methods are motivated by and applied to varved (annually laminated) sediment data from lake Kassj\"on in northern Sweden. The rich but complex information (with respect to climate) in the varves, including the shapes of the seasonal patterns, the varying varve thickness, and the non-linear sediment accumulation rates makes it non-trivial to cluster the varves. Functional representations, smoothing and alignment are functional data tools used to make the seasonal patterns comparable.Functional clustering is used to group the seasonal patterns into different types, which can be associated with different weather conditions.

    A new non-parametric functional clustering method is suggested, the Bagging Voronoi K-mediod Alignment algorithm, (BVKMA), which simultaneously clusters and aligns spatially dependent curves. BVKMA is used on the varved lake sediment, to infer on climate, defined as frequencies of different weather types, over longer time periods.

    Furthermore, a functional model-based clustering method is proposed that clusters subjects for which both functional data and covariates are observed, allowing different covariance structures in the different clusters. The model extends a model-based functional clustering method proposed by James and Suger (2003). An EM algorithm is derived to estimate the parameters of the model.

  • 85.
    Arnqvist, Per
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Bigler, Christian
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för ekologi, miljö och geovetenskap.
    Renberg, Ingemar
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för ekologi, miljö och geovetenskap.
    Sjöstedt de Luna, Sara
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Functional clustering of varved lake sediment to reconstruct past seasonal climate2016Ingår i: Environmental and Ecological Statistics, ISSN 1352-8505, E-ISSN 1573-3009, Vol. 23, nr 4, s. 513-529Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Annually laminated (varved) lake sediments constitutes excellent environmental archives, and have the potential to play an important role for understanding past seasonal climate with their inherent annual time resolution and within-year seasonal patterns. We propose to use functional data analysis methods to extract the relevant information with respect to climate reconstruction from the rich but complex information in the varves, including the shapes of the seasonal patterns, the varying varve thickness, and the non-linear sediment accumulation rates. In particular we analyze varved sediment from lake Kassjon in northern Sweden, covering the past 6400 years. The properties of each varve reflect to a large extent weather conditions and internal biological processes in the lake the year that the varve was deposited. Functional clustering is used to group the seasonal patterns into different types, that can be associated with different weather conditions. The seasonal patterns were described by penalized splines and clustered by the k-means algorithm, after alignment. The observed (within-year) variability in the data was used to determine the degree of smoothing for the penalized spline approximations. The resulting clusters and their time dynamics show great potential for seasonal climate interpretation, in particular for winter climate changes.

  • 86.
    Arnqvist, Per
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Sjösted de Luna, Sara
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Model based functional clustering of varved lake sedimentsManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    Climate and environmental changes are today widely discussed, and in particular the impact of human activity. To understand variations in past climate over longer time periods, historical documents, year rings from trees, ice cores from glaciers as well as lake and sea sediments are being used.In this paper we introduce a model based functional cluster analysis, giving us possibility to use both the functional form and covariates in our analysis. It also allow us to model the dependency of the chosen basis coefficients and the covariates. We also allow for different covariance structure within each cluster and give suggestions on how to determine how many clusters to use.In particular we analyze varved sediment from lake Kassjön (N Sweden) which cover more than 6400 years.

  • 87.
    Arvidsson, Dan
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Cross-Platform Modelling for Human Activity Recognition System2018Självständigt arbete på avancerad nivå (magisterexamen), 10 poäng / 15 hpStudentuppsats (Examensarbete)
    Abstract [en]

    Human activity recognition (HAR) systems have a large set of potential applications in healthcare, e.g. fall detection and tracking physical activities. HAR systems based on wearable sensors have gained the most attraction, due to smartphones having these sensors embedded in them. This makes them a great candidate for collecting human activity sensor data. By utilizing the smartphone sensors, no other sensors need to be supplied and instead only a mobile application needs to be supplied. However, this comes with a trade-off, sensors embedded in smartphones display specific heterogeneity and biases, depending on platform and price range. Normally in such a scenario, multiple HAR systems have to be built and trained for each device. This is both a time consuming effort and gives no guarantees that the different systems will have similar activity recognition accuracy. Therefore, in this thesis, a HAR system is constructed, where classification methods and filtering techniques are explored and evaluated, in an effort to give some guidelines for how to construct a HAR system, that can be embedded in multiple platforms. This study shows that when considering a few common activities, this HAR system performs well even when sensor data is collected from multiple sources. Ensemble method AdaBoost, in combination with decision trees, gives the overall best performance. Filtering techniques, such as Butterworth and Chebyshev performs better than constant- and linear detrending. This is primarily due to their ability to distinguish between low frequency activities, such as standing and sitting. The best result in this study was given when combining Chebyshev filtering and AdaBoosted decision trees, with a F-score of 0.9877.

  • 88.
    Arvidsson, Dan
    et al.
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Westerlund, Fredrik
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Fjärranalys av skog med multivariata modeller2016Självständigt arbete på grundnivå (kandidatexamen), 10 poäng / 15 hpStudentuppsats (Examensarbete)
  • 89.
    Arvidsson, Per
    et al.
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Snickars, Samuel
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Molekylär klassificering av tjocktarmscancer: PAM-klusteranalys för identifiering av undergrupper2012Självständigt arbete på grundnivå (kandidatexamen), 10 poäng / 15 hpStudentuppsats (Examensarbete)
    Abstract [sv]

    Huvudsyftet med denna studie är att med hjälp av klusteranalys dela in en mängd tjocktarmscancerfall i undergrupper baserat på deras molekylära egenskaper. Materialet som används tillhandahålls av en forskningsgrupp vid Patologi, Institutionen för medicinsk biovetenskap, Umeå universitet, och består efter viss bearbetning av 455 observationer vilket är en större datamängd än flera liknande studier. De molekylära variabler som ligger till grund för klusterindelningen är nivån på CIMP (CpG Island Methylator Phenotype), MSI (Mikrosatellitinstabillitet), BRAF- och KRAS-mutationer. Dessa är kategoriska variabler och därför används PAM (Partitioning Around Medoids) som är en särskild klusterteknik lämpad vid data på varierade variabelnivåer. I det slutliga resultatet fås fyra undergrupper som representeras av olika kombinationer av utfallen på ovannämnda variabler. Klustren utvärderas bland annat genom att jämföra överlevnadstiden för varje kluster, och det visar sig att två av klustren skiljer sig signifikant åt i detta avseende. Även andra patientrelaterade och tumörspecifika egenskaper kopplas samman till de olika cancertyperna och testas om de förekommer i varierande utsträckning. Var någonstans tumören är placerad är till exempel signifikant skilt mellan grupperna. Klusteranalyser är explorativa redskap så valet av variabler och sedermera tolkningar av resultat kan vara komplicerade och kräva stor sakkunskap.

  • 90.
    Asratian, Armen S.
    et al.
    Linköping University, Linköping, Sweden.
    Casselgren, Carl Johan
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Vandenbussche, Jennifer
    Southern Polytechnic State University, Marietta, Georgia.
    West, Douglas B.
    University of Illinois, Urbana, Illinois.
    Proper path-factors and interval edge-coloring of (3,4)-biregular bigraphs2009Ingår i: Journal of Graph Theory, ISSN 0364-9024, E-ISSN 1097-0118, Vol. 61, nr 2, s. 88-97Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    An interval coloring of a graph G is a proper coloring of E(G) by positive integers such that the colors on the edges incident to any vertex are consecutive. A (3,4)-biregular bigraph is a bipartite graph in which each vertex of one part has degree 3 and each vertex of the other has degree 4; it is unknown whether these all have interval colorings. We prove that G has an interval coloring using 6 colors when G is a (3,4)-biregular bigraph having a spanning subgraph whose components are paths with endpoints at 3-valent vertices and lengths in {2, 4, 6, 8}. We provide several sufficient conditions for the existence of such a subgraph.

  • 91. Atroshi, Isam
    et al.
    Lyrén, Per-Erik
    Umeå universitet, Samhällsvetenskapliga fakulteten, Institutionen för tillämpad utbildningsvetenskap.
    Gummesson, Christina
    Responsiveness of the 6-item CTS symptoms scale in carpal tunnel syndrome2010Konferensbidrag (Övrigt vetenskapligt)
  • 92.
    Atroshi, Isam
    et al.
    Department of Clinical Sciences, Lund University, Lund, Sweden.
    Lyrén, Per-Erik
    Umeå universitet, Samhällsvetenskapliga fakulteten, Beteendevetenskapliga mätningar.
    Gummesson, Christina
    Department of Health Sciences, Division of Physiotherapy, Lund University, 22100 Lund, Sweden.
    The 6-item CTS symptoms scale: a brief outcomes measure for carpal tunnel syndrome2009Ingår i: Quality of Life Research, ISSN 0962-9343, E-ISSN 1573-2649, Vol. 18, nr 3, s. 347-358Artikel i tidskrift (Refereegranskat)
  • 93. Atroshi, Isam
    et al.
    Lyrén, Per-Erik
    Umeå universitet, Samhällsvetenskapliga fakulteten, Institutionen för tillämpad utbildningsvetenskap.
    Ornstein, Ewald
    Gummesson, Christina
    Responsiveness of the 6-item CTS Symptoms Scale as a brief outcome measure in carpal tunnel syndrome2010Konferensbidrag (Refereegranskat)
  • 94. Avelin, Benny
    et al.
    Hed, Lisa
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Persson, Håkan
    A Note on the Hyperconvexity of Pseudoconvex Domains Beyond Lipschitz Regularity2015Ingår i: Potential Analysis, ISSN 0926-2601, E-ISSN 1572-929X, Vol. 43, nr 3, s. 531-545Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We show that bounded pseudoconvex domains that are Holder continuous for all alpha < 1 are hyperconvex, extending the well-known result by Demailly (Math. Z. 194(4) 519-564, 1987) beyond Lipschitz regularity.

  • 95. Avelin, Benny
    et al.
    Hed, Lisa
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Persson, Håkan
    Approximation of plurisubharmonic functions2016Ingår i: Complex Variables and Elliptic Equations, ISSN 1747-6933, E-ISSN 1747-6941, Vol. 61, nr 1, s. 23-28Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We extend a result by Fornaaess and Wiegerinck [Ark. Mat. 1989;27:257-272] on plurisubharmonic Mergelyan type approximation to domains with boundaries locally given by graphs of continuous functions.

  • 96.
    Avelin, Benny
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Lundström, Niklas L.P.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Nyström, Kaj
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Boundary estimates for solutions to operators of p-Laplace type with lower order terms2011Ingår i: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 250, nr 1, s. 264-291Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we study the boundary behavior of solutions to equations of the form∇⋅A(x,∇u)+B(x,∇u)=0, in a domain ΩRn, assuming that Ω is a δ-Reifenberg flat domain for δ sufficiently small. The function A is assumed to be of p-Laplace character. Concerning B, we assume that |∇ηB(x,η)|⩽c|η|p−2, |B(x,η)|⩽c|η|p−1, for some constant c, and that B(x,η)=|η|p−1B(x,η/|η|), whenever xRn, ηRn∖{0}. In particular, we generalize the results proved in J. Lewis et al. (2008) [12] concerning the equation ∇⋅A(x,∇u)=0, to equations including lower order terms.

  • 97.
    Avelin, Benny
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Lundström, Niklas L.P.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Nyström, Kaj
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Optimal doubling, reifenberg flatness and operators of p-laplace type2011Ingår i: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 74, nr 17, s. 5943-5955Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, we consider equations of p-Laplace type of the form A(x,u)=0. Concerning A we assume, for p∈(1,) fixed, an appropriate ellipticity type condition, Hölder continuity in x and that A(x,η)=|η|p−1A(x,η/|η|) whenever xRn and ηRn∖{0}. Let ΩRn be a bounded domain, let D be a compact subset of Ω. We say that is the A-capacitary function for D in Ω if on D, on Ω in the sense of and in ΩD in the weak sense. We extend to RnΩ by putting on RnΩ. Then there exists a unique finite positive Borel measure on Rn, with support in Ω, such that In this paper, we prove that if Ω is Reifenberg flat with vanishing constant, then for every τ, 0<τ≤1. In particular, we prove that is an asymptotically optimal doubling measure on Ω.

  • 98. Babb, Penny
    et al.
    Zhang, Li-Chun
    Allin, Paul
    Wallgren, Anders
    Wallgren, Britt
    Blunt, Gordon
    Garrett, Andrew
    Murtagh, Fionn
    Smith, Peter W. F.
    Elliott, Duncan
    Nason, Guy
    Powell, Ben
    Moore, Jamie C.
    Durrant, Gabriele B.
    Smith, Paul A.
    Chambers, Raymond L.
    Herzberg, Agnes M.
    Pilling, Mark
    Appleby, Wendy
    Barnett, Arthur
    Bhansali, Rajendra
    Bharadwaj, Neeraj
    Dong, Yuexiao
    van den Brakel, J. A.
    Budd, Lisa
    Doidge, James
    Gilbert, Ruth
    Francis, Brian
    Frisoli, Kayla
    Nugent, Rebecca
    Garcia Perez, Francisco Javier
    Lara, Libia
    Porcu, Emilio
    Henry, Sarah
    Hunt, Ian
    Ieva, Francesca
    Gasperoni, Francesca
    Jansson, Ingegerd
    Kumar, Kuldeep
    Longford, Nick
    Manninen, Asta
    Mateu, Jorge
    McNicholas, Paul D.
    McNicholas, Sharon M.
    Tait, Peter A.
    Mehew, Jenny
    Oberski, Daniel L.
    Ruiz, Marcelo
    Yohai, Victor J.
    Zamar, Ruben
    Stehlik, Milan
    Stehlikova, Silvia
    Nunez Soza, Ludy
    Towers, Jude
    Wijayatunga, Priyantha
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Statistical challenges of administrative and transaction data: Discussion on the paper by Hand2018Ingår i: Journal of the Royal Statistical Society: Series A (Statistics in Society), ISSN 0964-1998, E-ISSN 1467-985X, Vol. 181, nr 3, s. 578-605Artikel i tidskrift (Övrigt vetenskapligt)
  • 99.
    Backlund, Ulf
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Envelopes of holomorphy for bounded holomorphic functions1992Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    Some problems concerning holomorphic continuation of the class of bounded holo­morphic functions from bounded domains in Cn that are domains of holomorphy are solved. A bounded domain of holomorphy Ω in C2 with nonschlicht H°°-envelope of holomorphy is constructed and it is shown that there is a point in D for which Glea­son’s Problem for H°°(Ω) cannot be solved. Furthermore a proof of the existence of a bounded domain of holomorphy in C2 for which the volume of the H°°-envelope of holomorphy is infinite is given. The idea of the proof is to put a family of so-called ”Sibony domains” into the unit bidisk by a packing procedure and patch them together by thin neighbourhoods of suitably chosen curves.

    If H°°(Ω) is the Banach algebra of bounded holomorphic functions on a bounded domain Ω in Cn and if p is a point in Ω, then the following problem is known as Gleason’s Problem for Hoo(Ω) :

    Is the maximal ideal in H°°(Ω) consisting of functions vanishing at p generated

    by (z1 -p1) , ... ,   (zn - pn) ?

    A sufficient condition for solving Gleason’s Problem for 77°° (Ω) for all points in Ω is given. In particular, this condition is fulfilled by a convex domain Ω with Lip1+e boundary (0 < e < 1) and thus generalizes a theorem of S.L.Leibenson. It is also proved that Gleason’s Problem can be solved for all points in certain unions of two polydisks in C2. One of the ideas in the methods of proof is integration along specific polygonal lines.

    Certain properties of some open sets defined by global plurisubharmonic func­tions in Cn are studied. More precisely, the sets Du = {z e Cn : u(z) < 0} and Eh = {{z,w) e Cn X C : h(z,w) < 1} are considered where ti is a plurisubharmonic function of minimal growth and h≠0 is a non-negative homogeneous plurisubharmonic function. (That is, the functions u and h belong to the classes L(Cn) and H+(Cn x C) respectively.) It is examined how the fact that Eh and the connected components of Du are H°°-domains of holomorphy is related to the structure of the set of disconti­nuity points of the global defining functions and to polynomial convexity. Moreover it is studied whether these notions are preserved under a certain bijective mapping from L(Cn) to H+(Cn x C). Two counterexamples are given which show that polynomial convexity is not preserved under this bijection. It is also proved, for example, that if Du is bounded and if the set of discontinuity points of u is pluripolar then Du is of type H°°.

    A survey paper on general properties of envelopes of holomorphy is included. In particular, the paper treats aspects of the theory for the bounded holomorphic functions. The results for the bounded holomorphic functions are compared with the corresponding ones for the holomorphic functions.

  • 100. Backlund, Ulf
    et al.
    Carlsson, Linus
    Fällström, Anders
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Persson, Håkan
    Semi-Bloch Functions in Several Complex Variables2016Ingår i: Journal of Geometric Analysis, ISSN 1050-6926, E-ISSN 1559-002X, Vol. 26, nr 1, s. 463-473Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Let M be an n-dimensional complex manifold. A holomorphic function f : M -> C is said to be semi-Bloch if for every lambda is an element of C the function g(lambda) = exp(lambda f(z)) is normal on M. We characterize semi-Bloch functions on infinitesimally Kobayashi non-degenerate M in geometric as well as analytic terms. Moreover, we show that on such manifolds, semi-Bloch functions are normal.

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