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  • 2451.
    Yang, Xiangfeng
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
    Asymptotic expansions for Laplace transforms of Markov processes2018In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 457, no 1, p. 694-721Article in journal (Refereed)
    Abstract [en]

    Let mu(epsilon) be the probability measures on D[0,T] of suitable Markov processes {xi(epsilon)(t)}0 amp;lt;= t amp;lt;= T (possibly with small jumps) depending on a small parameter epsilon amp;gt;0, where D[0,T] denotes the space of all functions on [0, T] which are right continuous with left limits. In this paper we investigate asymptotic expansions for the Laplace transforms integral(D[0,T]) exp{epsilon F-1(x)}mu(epsilon)(dx) as epsilon -amp;gt; 0 for smooth functionals F on D[0,T]. This study not only recovers several well-known results, but more importantly provides new expansions for jump Markov processes. Besides several standard tools such as exponential change of measures and Taylors expansions, the novelty of the proof is to implement the expectation asymptotic expansions on normal deviations which were recently derived in [13]. (c) 2017 Elsevier Inc. All rights reserved.

  • 2452.
    Yang, Xiangfeng
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
    Exact upper tail probabilities of random series2015In: Statistics and Probability Letters, ISSN 0167-7152, E-ISSN 1879-2103, Vol. 99, p. 13-19Article in journal (Refereed)
    Abstract [en]

    In this paper, we obtain new estimates on upper tail probabilities of suitable random series involving a distribution having an exponential tail. These estimates are exact, and the distribution is not heavy-tailed.

  • 2453.
    Yang, Xiangfeng
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
    Large deviations for Markov bridges with jumps2014In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 416, no 1, p. 1-12Article in journal (Refereed)
    Abstract [en]

    In this paper, we consider a family of Markov bridges with jumps constructed from truncated stable processes. These Markov bridges depend on a small parameter h greater than 0, and have fixed initial and terminal positions. We propose a new method to prove a large deviation principle for this family of bridges based on compact level sets, change of measures, duality and various global and local estimates of transition densities for truncated stable processes.

  • 2454.
    Yang, Xiangfeng
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
    On the large deviation principle of generalized Brownian bridges2015In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 430, no 2, p. 845-856Article in journal (Refereed)
    Abstract [en]

    In this paper we consider a family of generalized Brownian bridges with a small noise, which was used by Brennan and Schwartz [3] to model the arbitrage profit in stock index futures in the absence of transaction costs. More precisely, we study the large deviation principle of these generalized Brownian bridges as the noise becomes infinitesimal. (C) 2015 Elsevier Inc. All rights reserved.

  • 2455.
    Ying, Daniel
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Cyclic Trigonal Riemann Surfaces of Genus 42004Licentiate thesis, monograph (Other academic)
    Abstract [en]

    A closed Riemann surface which can be realized as a 3-sheeted covering of the Riemann sphere is called trigonal, and such a covering is called a trigonal morphism. Accola showed that the trigonal morphism is unique for Riemann surfaces of genus g ≥ 5. This thesis will characterize the Riemann surfaces of genus 4 wiht non-unique trigonal morphism. We will describe the structure of the space of cyclic trigonal Riemann surfaces of genus 4.

  • 2456.
    Ying, Daniel
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Klassificering av automorfigrupper på trigonala Riemannytor2003In: Unga matematiker Svenska matematikersamfundets höstmöte,2003, 2003Conference paper (Other academic)
  • 2457.
    Ying, Daniel
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Kubiska riemannytor2004In: Workshop i tillämpad matematik,2004, 2004Conference paper (Other academic)
  • 2458.
    Ying, Daniel
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    On the Moduli Space of Cyclic Trigonal Riemann Surfaces of Genus 42006Doctoral thesis, monograph (Other academic)
    Abstract [en]

    A closed Riemann surface which can be realized as a 3-sheeted covering of the Riemann sphere is called trigonal, and such a covering is called a trigonal morphism. Accola showed that the trigonal morphism is unique for Riemann surfaces of genus g ≥ 5. This thesis characterizes the cyclic trigonal Riemann surfaces of genus 4 with non-unique trigonal morphism using the automorphism groups of the surfaces. The thesis shows that Accola’s bound is sharp with the existence of a uniparametric family of cyclic trigonal Riemann surfaces of genus 4 having several trigonal morphisms. The structure of the moduli space of trigonal Riemann surfaces of genus 4 is also characterized.

    Finally, by using the same technique as in the case of cyclic trigonal Riemann surfaces of genus 4, we are able to deal with p-gonal Riemann surfaces and show that Accola’s bound is sharp for p-gonal Riemann surfaces. Furthermore, we study families of p-gonal Riemann surfaces of genus (p − 1)2 with two p-gonal morphisms, and describe the structure of their moduli space.

  • 2459.
    Zhao, Hongmei
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Lei, Lei
    Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, The Institute of Technology.
    Yuan, Di
    Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, The Institute of Technology.
    Larsson, Torbjörn
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Rönnberg, Elina
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Power efficient uplink scheduling in SC-FDMA: Bounding global optimality by column generation2013In: 2013 IEEE 18th International Workshop on Computer Aided Modeling and Design of Communication Links and Networks (CAMAD, IEEE , 2013, p. 119-123Conference paper (Refereed)
    Abstract [en]

    We study resource allocation in cellular systems and consider the problem of finding a power efficient scheduling in an uplink single carrier frequency division multiple access (SC-FDMA) system with localized allocation of subcarriers, that is, the subcarriers allocated to a user equipment have to be consecutive in the frequency domain in each time slot. This problem is discrete and nonconvex, thus the use of suboptimal algorithms has been a common practice. We leverage the power of mathematical programming in order to approach global optimality or a tight bounding interval confining global optimum, to arrive at an effective scheme for gauging the performance of suboptimal algorithms. Toward this end, we first provide a straightforward integer linear programming formulation, and then an alternative and less trivial, so-called column-oriented, formulation. The latter is solved by column generation, which is a solution technique for large-scale optimization problems with certain characteristics. The computational evaluation demonstrates that the column generation method produces very highquality subcarrier allocations that either coincide with the global optimum or enable an extremely sharp bounding interval. Hence the approach serves well for the purpose of benchmarking results for large-scale instances of power efficient SC-FDMA scheduling.

  • 2460.
    Zhao, Yixin
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
    On the Integration of Heuristics with Column-Oriented Models for Discrete Optimization2016Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Column-oriented models are today common in the eld of discrete optimization, and there is an increasing interest in using such models as a basis for heuristic solution methods. The common theme of this work is to explore some possibilities to integrate heuristic principles and column-oriented models for discrete optimization problems.

    In the rst paper, we consider a resource allocation problem for cellular systems. We propose a strong column-oriented formulation and a corresponding column generation method, as well as an enhanced column generation scheme for this problem. The enhanced scheme is composed of a stabilization technique, an approximate column generation principle, and, for nding integer solutions, a heuristic that is embedded in the column generation scheme.

    The second paper provides a new and strong convexied formulation of the xed charge transportation problem. This formulation is obtained by integrating the concepts of Lagrangian decomposition and column generation. It is shown both theoretically and practically that this integration yields a formulation which is stronger than three other convexied formulations of the problem.

    List of papers
    1. Power efficient uplink scheduling in SC-FDMA: benchmarking by column generation
    Open this publication in new window or tab >>Power efficient uplink scheduling in SC-FDMA: benchmarking by column generation
    Show others...
    2016 (English)In: Optimization and Engineering, ISSN 1389-4420, E-ISSN 1573-2924, Vol. 17, no 4, p. 695-725Article in journal (Refereed) Published
    Abstract [en]

    We study resource allocation in cellular systems and consider the problem of finding a power efficient scheduling in an uplink single carrier frequency division multiple access system. Due to the discrete nature of this problem and its computational difficulty, particularly in a real-time setting, the use of suboptimal algorithms is common practice. We aim at an effective way of gauging the performance of suboptimal algorithms by finding tight bounds on the global optimum. Toward this end, we first provide a basic integer linear programming formulation. Then we propose a significantly stronger column-oriented formulation and a corresponding column generation method, as well as an enhanced column generation scheme. The latter extends the first scheme through the inclusion of a stabilization technique, an approximate column generation principle, and a tailored heuristic that is embedded in the column generation scheme to find high-quality though not necessarily global optimal solutions. The computational evaluation demonstrates that compared with a poor performance by the integer linear programming formulation, the column generation method can produce near-optimal schedules that enable a sharp bounding interval. The enhanced column generation method significantly sharpens the bounding interval. Hence the column generation approach serves well for the purpose of benchmarking results for large-scale instances.

    Place, publisher, year, edition, pages
    Springer-Verlag New York, 2016
    Keywords
    Localized SC-FDMA, Stabilized column generation, Power minimization, Integer linear programming, Uplink scheduling, Matheuristic
    National Category
    Mathematics
    Identifiers
    urn:nbn:se:liu:diva-127355 (URN)10.1007/s11081-015-9304-z (DOI)000387857500004 ()
    Note

    Funding agencies: Research School in Interdisciplinary Mathematics at Linkoping University; Excellence Center at Linkoping - Lund in Information Technology, Centrum for Industriell Informationsteknologi, Linkoping University, EC FP7 Marie Curie Project [318992]; Chinese Sc

    Available from: 2016-04-22 Created: 2016-04-22 Last updated: 2019-08-06Bibliographically approved
    2. Power efficient uplink scheduling in SC-FDMA: Bounding global optimality by column generation
    Open this publication in new window or tab >>Power efficient uplink scheduling in SC-FDMA: Bounding global optimality by column generation
    Show others...
    2013 (English)In: 2013 IEEE 18th International Workshop on Computer Aided Modeling and Design of Communication Links and Networks (CAMAD, IEEE , 2013, p. 119-123Conference paper, Published paper (Refereed)
    Abstract [en]

    We study resource allocation in cellular systems and consider the problem of finding a power efficient scheduling in an uplink single carrier frequency division multiple access (SC-FDMA) system with localized allocation of subcarriers, that is, the subcarriers allocated to a user equipment have to be consecutive in the frequency domain in each time slot. This problem is discrete and nonconvex, thus the use of suboptimal algorithms has been a common practice. We leverage the power of mathematical programming in order to approach global optimality or a tight bounding interval confining global optimum, to arrive at an effective scheme for gauging the performance of suboptimal algorithms. Toward this end, we first provide a straightforward integer linear programming formulation, and then an alternative and less trivial, so-called column-oriented, formulation. The latter is solved by column generation, which is a solution technique for large-scale optimization problems with certain characteristics. The computational evaluation demonstrates that the column generation method produces very highquality subcarrier allocations that either coincide with the global optimum or enable an extremely sharp bounding interval. Hence the approach serves well for the purpose of benchmarking results for large-scale instances of power efficient SC-FDMA scheduling.

    Place, publisher, year, edition, pages
    IEEE, 2013
    Series
    International Workshop on Computer Aided Modeling and Design of Communication Links and Networks (CAMAD), ISSN 2378-4865 ; 2013
    National Category
    Mathematics
    Identifiers
    urn:nbn:se:liu:diva-106237 (URN)10.1109/CAMAD.2013.6708101 (DOI)
    Conference
    2013 IEEE 18th International Workshop on Computer Aided Modeling and Design of Communication Links and Networks (CAMAD)
    Available from: 2014-04-29 Created: 2014-04-29 Last updated: 2018-06-25
  • 2461.
    Zhao, Yixin
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
    Larsson, Torbjörn
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
    Rönnberg, Elina
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
    A Large Neighbourhood Search Principle for Column-Oriented Models: Theoretical Derivation and Example Applications2016In: Matheuristics 2016: Proceedings of the Sixth International Workshop on Model-based Metaheuristics / [ed] V. Maniezzo and T. Stutzle, Bruxelles, Belgium: IRIDIA , 2016Conference paper (Refereed)
  • 2462.
    Zhao, Yixin
    et al.
    Nanjing University of Science and Technology, School of Automation.
    Larsson, Torbjörn
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
    Rönnberg, Elina
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
    An integer programming column generation principlefor heuristic search methods2019In: International Transactions in Operational Research, ISSN 0969-6016, E-ISSN 1475-3995, Vol. 27, no 1, p. 665-695Article in journal (Refereed)
    Abstract [en]

    There is an increasing interest in integrating column generation and heuristic approaches to efficiently solve large-scale discrete optimisation problems. We contribute in this direction. Based on the insights from Lagrangian duality theory, we present an auxiliary problem that can be used for finding near-optimal solutions to a discrete column-oriented model. The structure of this auxiliary problem makes it suitable for being addressed with a heuristic search method involving column generation. To this end, we suggest a large neighbourhood search strategy where the repair step is to solve a column generation type subproblem. The suggested search strategy and mathematical models involved need to be tailored to the problem structure. To illustrate important design options and computational behaviour, four applications are studied: bin packing, generalised assignment, a resource allocation problem and the fixed-charge transportation problem.

  • 2463.
    Zhao, Yixin
    et al.
    Nanjing University of Science and Technology, School of Automation.
    Larsson, Torbjörn
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
    Rönnberg, Elina
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
    Pardalos, Panos
    University of Florida, Department of Industrial and System Engineering.
    The fixed charge transportation problem: a strong formulation based on Lagrangian decomposition and column generation2018In: Journal of Global Optimization, ISSN 0925-5001, E-ISSN 1573-2916, Vol. 72, no 3, p. 517-538Article in journal (Refereed)
    Abstract [en]

    A new and strong convexified formulation of the fixed charge transportation problem is provided. This formulation is obtained by integrating the concepts of Lagrangian decomposition and column generation. The decomposition is made by splitting the shipping variables into supply and demand side copies, while the columns correspond to extreme flow patterns for single sources or sinks. It is shown that the combination of Lagrangian decomposition and column generation provides a formulation whose strength dominates those of three other convexified formulations of the problem. Numerical results illustrate that our integrated approach has the ability to provide strong lower bounds. The Lagrangian decomposition yields a dual problem with an unbounded set of optimal solutions. We propose a regularized column generation scheme which prioritizes an optimal dual solution with a small 1-norm. We further demonstrate numerically that information gained from the strong formulation can also be used for constructing a small-sized core problem which yields high-quality upper bounds.

  • 2464.
    Zhao, Yixin
    et al.
    Nanjing Univ Sci and Technol, Peoples R China.
    Larsson, Torbjörn
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
    Yuan, Di
    Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering.
    Rönnberg, Elina
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
    Lei, Lei
    Linköping University, Department of Science and Technology. Linköping University, Faculty of Science & Engineering.
    Correction: Power efficient uplink scheduling in SC-FDMA: benchmarking by column generation (vol 17, pg 695, 2016)2019In: Optimization and Engineering, ISSN 1389-4420, E-ISSN 1573-2924, Vol. 20, no 3, p. 959-959Article in journal (Other academic)
    Abstract [en]

    At the time of the final publication of the paper, in December 2016, Yixin Zhaos affiliation had changed.

  • 2465.
    Zhao, Yixin
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
    Larsson, Torbjörn
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
    Yuan, Di
    Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering.
    Rönnberg, Elina
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
    Lei, Lei
    Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering.
    Power efficient uplink scheduling in SC-FDMA: benchmarking by column generation2016In: Optimization and Engineering, ISSN 1389-4420, E-ISSN 1573-2924, Vol. 17, no 4, p. 695-725Article in journal (Refereed)
    Abstract [en]

    We study resource allocation in cellular systems and consider the problem of finding a power efficient scheduling in an uplink single carrier frequency division multiple access system. Due to the discrete nature of this problem and its computational difficulty, particularly in a real-time setting, the use of suboptimal algorithms is common practice. We aim at an effective way of gauging the performance of suboptimal algorithms by finding tight bounds on the global optimum. Toward this end, we first provide a basic integer linear programming formulation. Then we propose a significantly stronger column-oriented formulation and a corresponding column generation method, as well as an enhanced column generation scheme. The latter extends the first scheme through the inclusion of a stabilization technique, an approximate column generation principle, and a tailored heuristic that is embedded in the column generation scheme to find high-quality though not necessarily global optimal solutions. The computational evaluation demonstrates that compared with a poor performance by the integer linear programming formulation, the column generation method can produce near-optimal schedules that enable a sharp bounding interval. The enhanced column generation method significantly sharpens the bounding interval. Hence the column generation approach serves well for the purpose of benchmarking results for large-scale instances.

  • 2466.
    Zhu, Yurong
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
    Large Deviations on Longest Runs2016Student paper other, 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    The study on the longest stretch of consecutive successes in \random" trials dates back to 1916 when the German philosopher Karl Marbe wrote a paper concerning the longest stretch of consecutive births of children of the same sex as appearing in the birth register of a Bavarian town. The result was actually used by parents to \predict" the sex of their children. The longest stretch of same-sex births during that time in 200 thousand birth registrations was actually 17 t log2(200 103): During the past century, the research of longest stretch of consecutive successes (longest runs) has found applications in various areas, especially in the theory of reliability. The aim of this thesis is to study large deviations on longest runs in the setting of Markov chains. More precisely, we establish a general large deviation principle for the longest success run in a two-state (success or failure) Markov chain. Our tool is based on a recent result regarding a general large deviation for the longest success run in Bernoulli trails. It turns out that the main ingredient in the proof is to implement several global and local estimates of the cumulative distribution function of the longest success run.

  • 2467.
    Zikrin, Spartak
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Large-Scale Optimization Methods with Application to Design of Filter Networks2014Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Nowadays, large-scale optimization problems are among those most challenging. Any progress in developing methods for large-scale optimization results in solving important applied problems more effectively. Limited memory methods and trust-region methods represent two ecient approaches used for solving unconstrained optimization problems. A straightforward combination of them deteriorates the efficiency of the former approach, especially in the case of large-scale problems. For this reason, the limited memory methods are usually combined with a line search. We develop new limited memory trust-region algorithms for large-scale unconstrained optimization. They are competitive with the traditional limited memory line-search algorithms.

    In this thesis, we consider applied optimization problems originating from the design of lter networks. Filter networks represent an ecient tool in medical image processing. It is based on replacing a set of dense multidimensional lters by a network of smaller sparse lters called sub-filters. This allows for improving image processing time, while maintaining image quality and the robustness of image processing.

    Design of lter networks is a nontrivial procedure that involves three steps: 1) choosing the network structure, 2) choosing the sparsity pattern of each sub-filter and 3) optimizing the nonzero coecient values. So far, steps 1 and 2 were mainly based on the individual expertise of network designers and their intuition. Given a sparsity pattern, the choice of the coecients at stage 3 is related to solving a weighted nonlinear least-squares problem. Even in the case of sequentially connected lters, the resulting problem is of a multilinear least-squares (MLLS) type, which is a non-convex large-scale optimization problem. This is a very dicult global optimization problem that may have a large number of local minima, and each of them is singular and non-isolated. It is characterized by a large number of decision variables, especially for 3D and 4D lters.

    We develop an effective global optimization approach to solving the MLLS problem that reduces signicantly the computational time. Furthermore, we  develop efficient methods for optimizing sparsity of individual sub-filters  in lter networks of a more general structure. This approach offers practitioners a means of nding a proper trade-o between the image processing quality and time. It allows also for improving the network structure, which makes automated some stages of designing lter networks.

    List of papers
    1. On Efficiently Combining Limited Memory and Trust-Region Techniques
    Open this publication in new window or tab >>On Efficiently Combining Limited Memory and Trust-Region Techniques
    2013 (English)Report (Other academic)
    Abstract [en]

    Limited memory quasi-Newton methods and trust-region methods represent two efficient approaches used for solving unconstrained optimization problems. A straightforward combination of them deteriorates the efficiency of the former approach, especially in the case of large-scale problems. For this reason, the limited memory methods are usually combined with a line search. We show how to efficiently combine limited memory and trust-region techniques. One of our approaches is based on the eigenvalue decomposition of the limited memory quasi-Newton approximation of the Hessian matrix. The decomposition allows for finding a nearly-exact solution to the trust-region subproblem defined by the Euclidean norm with an insignificant computational overhead compared with the cost of computing the quasi-Newton direction in line-search limited memory methods. The other approach is based on two new eigenvalue-based norms. The advantage of the new norms is that the trust-region subproblem is separable and each of the smaller subproblems is easy to solve. We show that our eigenvalue-based limited-memory trust-region methods are globally convergent. Moreover, we propose improved versions of the existing limited-memory trust-region algorithms. The presented results of numerical experiments demonstrate the efficiency of our approach which is competitive with line-search versions of the L-BFGS method.

    Place, publisher, year, edition, pages
    Linköping: Linköping University Electronic Press, 2013. p. 33
    Series
    LiTH-MAT-R, ISSN 0348-2960 ; 2013:13
    Keywords
    Unconstrained Optimization; Large-scale Problems; Limited Memory Methods;
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:liu:diva-102005 (URN)LiTH-MAT-R--2013/13--SE (ISRN)
    Available from: 2013-11-26 Created: 2013-11-26 Last updated: 2016-01-12Bibliographically approved
    2. Global search strategies for solving multilinear least-squares problems
    Open this publication in new window or tab >>Global search strategies for solving multilinear least-squares problems
    2012 (English)In: Sultan Qaboos University Journal for Science, ISSN 1027-524X, Vol. 17, no 1, p. 12-21Article in journal (Refereed) Published
    Abstract [en]

    The multilinear least-squares (MLLS) problem is an extension of the linear leastsquares problem. The difference is that a multilinear operator is used in place of a matrix-vector product. The MLLS is typically a large-scale problem characterized by a large number of local minimizers. It originates, for instance, from the design of filter networks. We present a global search strategy that allows for moving from one local minimizer to a better one. The efficiency of this strategy is illustrated by results of numerical experiments performed for some problems related to the design of filter networks.

    Place, publisher, year, edition, pages
    Sultan Qaboos University, 2012
    Keywords
    Global optimization; Global search strategies; Multilinear least-squares; Filter
    National Category
    Computational Mathematics Medical Image Processing
    Identifiers
    urn:nbn:se:liu:diva-78918 (URN)
    Available from: 2012-08-28 Created: 2012-06-25 Last updated: 2015-09-03Bibliographically approved
    3. Sparsity Optimization in Design of Multidimensional Filter Networks
    Open this publication in new window or tab >>Sparsity Optimization in Design of Multidimensional Filter Networks
    2013 (English)Report (Other academic)
    Abstract [en]

    Filter networks is a powerful tool used for reducing the image processing time, while maintaining its reasonably high quality.They are composed of sparse sub-filters whose low sparsity ensures fast image processing.The filter network design is related to solvinga sparse optimization problem where a cardinality constraint bounds above the sparsity level.In the case of sequentially connected sub-filters, which is the simplest network structure of those considered in this paper, a cardinality-constrained multilinear least-squares (MLLS) problem is to be solved. If to disregard the cardinality constraint, the MLLS is typically a large-scale problem characterized by a large number of local minimizers. Each of the local minimizers is singular and non-isolated.The cardinality constraint makes the problem even more difficult to solve.An approach for approximately solving the cardinality-constrained MLLS problem is presented.It is then applied to solving a bi-criteria optimization problem in which both thetime and quality of image processing are optimized. The developed approach is extended to designing filter networks of a more general structure. Its efficiency is demonstrated by designing certain 2D and 3D filter networks. It is also compared with the existing approaches.

    Place, publisher, year, edition, pages
    Linköping: Linköping University Electronic Press, 2013. p. 21
    Series
    LiTH-MAT-R, ISSN 0348-2960 ; 2013:16
    Keywords
    Sparse optimization; Cardinality Constraint; Multicriteria Optimization; Multilinear Least-Squares Problem; Filter networks; Medical imaging
    National Category
    Computational Mathematics Medical Image Processing Signal Processing
    Identifiers
    urn:nbn:se:liu:diva-103915 (URN)LiTH-MAT-R-2013/16-SE (ISRN)
    Available from: 2014-02-03 Created: 2014-02-03 Last updated: 2016-11-24Bibliographically approved
  • 2468.
    Äng, Oscar
    et al.
    Linköping University, Department of Mathematics. Linköping University, Faculty of Science & Engineering.
    Trygg, Alexander
    Linköping University, Department of Mathematics. Linköping University, Faculty of Science & Engineering.
    Planering av stränggjutningsproduktion: En heruistisk metod2017Independent thesis Basic level (degree of Bachelor), 10,5 credits / 16 HE creditsStudent thesis
    Abstract [en]

    This study aims to investigate if it is possible to use a heuristic method to create feasible solution in a Cast Batching Problem at SSAB. The problem occurs when different kinds of steel should be cast during the same day. Depending on which order the groups of different steel is placed different amounts of waste is produced, the goal is to minimize this waste. Earlier work has been done on this problem and resulted in a mathematical model to create feasible solutions to this problem. In practice the time it takes to create good solutions are long and the question is if it is possible to use a heuristic method to generate good solutions in a shorter amount of time.

    Drawing upon inspiration from metaheuristics such as Variable Neighbourhood Search, Simualted Annealing and Tabu Search multiple heuristics have been created, implemented and evaluated against the mathematical model. One of the heuristics perform better than the mathematical model does in 10 minutes. The result from the mathematical model after 60 minutes is slightly better than the heuristic, but the results are similar. With regards to running time the heuristic takes considerably less time than 10 minutes.

  • 2469.
    Åberg, Johnny
    Linköping University, Department of Mathematics. Linköping University, Faculty of Science & Engineering.
    Programmering i Ma1c: ett specialanpassat utbildningsmaterial för lösning av sannolikhetsproblem2019Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    From July 1st 2018 solving mathematical problems with computer programming is included in mathematics in Swedish upper secondary school. This study tries to make a reasonable interpretation of the unclear wording in the new curriculum and develops a customized educational material for the programming part of the course based on the interpretation. The material consists of a projector presentation and a booklet with excercises, focuses on probability problems, has been tried in three minor and unsystematic trials, is not fully tested and needs to be further improved. Given the study´s interpretatio, and 9 hours of teaching in programming, there are good reasons to suspect that the pupils will not learn how to solve mathematical problems with computer programming due to shortage of time.

  • 2470.
    Ålund, Oskar
    et al.
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    A provably stable, non-iterative domain decomposition technique for the advection-diffusion equation2016Report (Other academic)
    Abstract [en]

    We describe an efficient, non-iterative domain decomposition approach for the onedimensional advection–diffusion equation based on the Summation-by-Parts technique in both time and space. A fully discrete multidomain analogue of the continuous equation is formulated and a linear system consisting only of the solution components involved in the coupling between the subdomain interfaces is isolated. Once the coupling system is solved, the full solution is found by computing linear combinations of known vectors, weighted by the coupling components. Both stability and invertibility of the discrete scheme is proved using standard Summation-by-Parts procedures.

    In a numerical study we show that perfunctory implementations of monodomain Summation-by-Parts based time integration can be improved upon significantly. Using our proposed method we are able to reduce execution time and memory footprint by up to 80% and 95% respectively. Similar improvements in execution time is shown also when compared against explicit Runge–Kutta time integration.

  • 2471.
    Ålund, Oskar
    et al.
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    A Stable Domain Decomposition Technique for Advection–Diffusion Problems2018In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 77, no 2, p. 755-774Article in journal (Refereed)
    Abstract [en]

    The use of implicit methods for numerical time integration typically generates very large systems of equations, often too large to fit in memory. To address this it is necessary to investigate ways to reduce the sizes of the involved linear systems. We describe a domain decomposition approach for the advection–diffusion equation, based on the Summation-by-Parts technique in both time and space. The domain is partitioned into non-overlapping subdomains. A linear system consisting only of interface components is isolated by solving independent subdomain-sized problems. The full solution is then computed in terms of the interface components. The Summation-by-Parts technique provides a solid theoretical framework in which we can mimic the continuous energy method, allowing us to prove both stability and invertibility of the scheme. In a numerical study we show that single-domain implementations of Summation-by-Parts based time integration can be improved upon significantly. Using our proposed method we are able to compute solutions for grid resolutions that cannot be handled efficiently using a single-domain formulation. An order of magnitude speed-up is observed, both compared to a single-domain formulation and to explicit Runge–Kutta time integration.

  • 2472.
    Ålund, Oskar
    et al.
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    A stable, high order accurate and efficient hybrid method for flow calculations in complex geometries2018In: 2018 AIAA Aerospace Sciences Meeting, AIAA SciTech Forum, (AIAA 2018-1096), American Institute of Aeronautics and Astronautics, 2018, no 210059, p. 1-9Conference paper (Refereed)
    Abstract [en]

    The suitability of a discretization method is highly dependent on the shape of the domain. Finite difference schemes are typically efficient, but struggle with complex geometry, while finite element methods are expensive but well suited for complex geometries. In this paper we propose a provably stable hybrid method for a 2D advection–diffusion problem, using a class of inner product compatible projection operators to couple the non-conforming grids that arise due to varying the discretization method throughout the domain.

  • 2473.
    Ålund, Oskar
    et al.
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Encapsulated high order difference operators on curvilinear non-conforming grids2019In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 385, p. 209-224Article in journal (Refereed)
    Abstract [en]

    Constructing stable difference schemes on complex geometries is an arduous task. Even fairly simple partial differential equations end up very convoluted in their discretized form, making them difficult to implement and manage. Spatial discretizations using so called summation-by-parts operators have mitigated this issue to some extent, particularly on rectangular domains, making it possible to formulate stable discretizations in a compact and understandable manner. However, the simplicity of these formulations is lost for curvilinear grids, where the standard procedure is to transform the grid to a rectangular one, and change the structure of the original equation. In this paper we reinterpret the grid transformation as a transformation of the summation-by-parts operators. This results in operators acting directly on the curvilinear grid. Together with previous developments in the field of nonconforming grid couplings we can formulate simple, implementable, and provably stable schemes on general nonconforming curvilinear grids. The theory is applicable to methods on summation-by-parts form, including finite differences, discontinuous Galerkin spectral element, finite volume, and flux reconstruction methods. Time dependent advection–diffusion simulations corroborate the theoretical development.

    The full text will be freely available from 2021-02-26 12:23
  • 2474.
    Åslund, Jan
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Asymptotic analysis of junctions in multi-structures2002Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    A multi-structure is a compound domain that consists of several substructures such as solid bodies, thin shells and slender rods. In this thesis we consider different mixed boundary value problems in multi-structures. In the formulations of these problems a small perturbation parameter c is introduced, e.g., the thickness of a shell. The common objective of the papers in this thesis is to analyse the junctions between the substructures and to construct the asymptotics of the solution as ε tends to zero.

  • 2475.
    Österberg, Sofia
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Motiverad för matematik?: En litteraturstudie om yttre och inre faktorers påverkan på gymnasieelevers motivation i skolmatematik2014Independent thesis Advanced level (degree of Master (Two Years)), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    När jag har varit ute i gymnasieskolan på praktik har jag mött elever med väldigt olika attityder och inställningar till matematik. Dessa attityder kan ha följt med eleverna länge, då de möter matematiken för första gången i förskolan. När eleverna sedan når gymnasiet är de olika motiverade för att lära sig matematik och som lärare kan det vara svårt att veta hur man ska motivera sina elever till att lära sig matematik. Syftet med denna litteraturstudie är att sammanställa och analysera vilka yttre- och intre faktorer som påverkar elevers motivation i ämnet matematik, för att sedan kunna diskutera vad dessa faktorer kan ha för inverkan på elever motivation på gymnasiet.

    Litteraturstudien visar att det finns flertalet yttre- och inre faktorer som kan påverka elevers motivation för att lära sig matematik under skolgången och att det finns olika teorier om när elevers motivation för att lära sig matematik sjunker. Dessa faktorer har olika stor påverkan på elevernas motivation på gymnasiet och de flesta av faktorerna kommer att kunna påverka eleverna även när de går på gymnasiet. Utifrån varje faktor framgår det hur det påverkar eleverna och därför också vad man som lärare kan göra för att höja elevernas motivation för att lära sig ämnet matematik.

  • 2476.
    Österholm, Magnus
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    A metacognitive perspective on reading mathe-matical texts: Students’ beliefs and criteria for comprehension2006Manuscript (preprint) (Other academic)
  • 2477.
    Österholm, Magnus
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    A reading comprehension perspective on problem solving2006In: Developing and researching quality in mathematics teaching and learning : proceedings of MADIF 5 : the 5th Swedish Mathematics Education Research Seminar, Malmö, January 24-25, 2006 / [ed] Christer Bergsten and Barbro Grevholm, Linköping: Svensk förening för matematikdidaktisk forskning (SMDF) , 2006, p. 136-145Conference paper (Refereed)
    Abstract [en]

    The purpose of this paper is to discuss the bi-directional relationship between reading comprehension and problem solving, i.e. how reading comprehension can affect and become an integral part of problem solving, and how it can be affected by the mathematical text content or by the mathematical situation when the text is read. Based on theories of reading comprehension and a literature review it is found that the relationship under study is complex and that the reading process can affect as well as act as an integral part of the problem solving process but also that not much research has focused on this relationship.

  • 2478.
    Österholm, Magnus
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Characterizing reading comprehension of mathematical texts2006In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 63, no 3, p. 325-346Article in journal (Refereed)
    Abstract [en]

    This study compares reading comprehension of three different texts: two mathematical texts and one historical text. The two mathematical texts both present basic concepts of group theory, but one does it using mathematical symbols and the other only uses natural language. A total of 95 upper secondary and university students read one of the mathematical texts and the historical text. Before reading the texts, a test of prior knowledge for both mathematics and history was given and after reading each text, a test of reading comprehension was given. The results reveal a similarity in reading comprehension between the mathematical text without symbols and the historical text, and also a difference in reading comprehension between the two mathematical texts. This result suggests that mathematics in itself is not the most dominant aspect affecting the reading comprehension process, but the use of symbols in the text is a more relevant factor. Although the university students had studied more mathematics courses than the upper secondary students, there was only a small and insignificant difference between these groups regarding reading comprehension of the mathematical text with symbols. This finding suggests that there is a need for more explicit teaching of reading comprehension for texts including symbols.

  • 2479.
    Österholm, Magnus
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Epistemological beliefs and communication in mathematics education at upper secondary and university levels2009In: Perspectives on mathematical knowledge. Proceedings of MADIF 6, the 6th Swedish Mathematics Education Research Seminar, Stockholm, January 29-30, 2008 / [ed] Christer Bergsten, Barbro Grevholm, Thomas Lingefjärd, Linköping: Svensk förening för matematikdidaktisk forskning (SMDF) , 2009, p. 132-134Conference paper (Other academic)
  • 2480.
    Österholm, Magnus
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Kognitiva och metakognitiva perspektiv på läsförståelse inom matematik2006Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    There seems to exist a general belief that one needs to learn specifically how to read mathematical texts, that is, a need to develop a special kind of reading ability for such texts. However, this belief does not seem to be based on research results since it does not exist much research that focus on reading comprehension in mathematics.

    The main purpose of this dissertation is to examine whether a reader needs special types of knowledge or abilities in order to read mathematical texts. Focus is on students’ reading of different kinds of texts that contain mathematics from introductory university level. The reading of mathematical texts is studied from two different perspectives, on the one hand a cognitive perspective, where reading abilities and content knowledge are studied in relation to reading comprehension, and on the other a metacognitive perspective, where focus is on beliefs and how a reader determines whether a text has been understood or not.

    Three empirical studies together with theoretical discussions, partly based on two literature surveys, are included in this dissertation. The literature surveys deal with properties of mathematical texts and reading in relation to problem solving. The empirical studies compare the reading of different types of texts, partly mathematical texts with texts with content from another domain and partly different types of mathematical texts, where focus is on the use of symbols and texts focusing on conceptual or procedural knowledge. Furthermore, students’ beliefs about their own reading comprehension and about texts and reading in general in mathematics are studied, in particular whether these beliefs are connected to reading comprehension.

    The results from the studies in this dissertation show that the students seem to use a special type of reading ability for mathematical texts; to focus on symbols in a text. For mathematical texts without symbols, a more general reading ability is used, that is, a type of ability also used for texts with content from another domain. The special type of reading ability used for texts including symbols affects the reading comprehension differently depending on whether the text focuses on conceptual or procedural knowledge. Compared to the use of the more general reading ability, the use of the special reading ability creates a worse reading comprehension.

    There seems to exist a need to focus on reading and reading comprehension in mathematics education since results in this dissertation show that courses at the upper secondary level (course E) and at the university level (in algebra and analysis) do not affect the special reading ability. However, the mentioned results show that this focus on reading does not necessarily need to be about learning to read mathematical texts in a special manner but to use an existing, more general, reading ability also for mathematical texts.

    Results from the metacognitive perspective show a difference between conscious aspects, such as regarding beliefs and reflections about comprehension, and unconscious aspects, such as the more automatic processes that make a reader understand a text, where also metacognitive processes are active. In particular, beliefs, which have been examined through a questionnaire, do not have a clear and independent effect on reading comprehension.

    From the texts used in these studies and the participating students, there seems not do be a general need to view the reading of mathematical texts as a special kind of process that demands special types of reading abilities. Instead, the development of a special type of reading ability among students could be caused by a lack of experiences regarding a need to read different types of mathematical texts where similarities with reading in general can be highlighted and used.

    List of papers
    1. A reading comprehension perspective on problem solving
    Open this publication in new window or tab >>A reading comprehension perspective on problem solving
    2006 (English)In: Developing and researching quality in mathematics teaching and learning : proceedings of MADIF 5 : the 5th Swedish Mathematics Education Research Seminar, Malmö, January 24-25, 2006 / [ed] Christer Bergsten and Barbro Grevholm, Linköping: Svensk förening för matematikdidaktisk forskning (SMDF) , 2006, p. 136-145Conference paper, Published paper (Refereed)
    Abstract [en]

    The purpose of this paper is to discuss the bi-directional relationship between reading comprehension and problem solving, i.e. how reading comprehension can affect and become an integral part of problem solving, and how it can be affected by the mathematical text content or by the mathematical situation when the text is read. Based on theories of reading comprehension and a literature review it is found that the relationship under study is complex and that the reading process can affect as well as act as an integral part of the problem solving process but also that not much research has focused on this relationship.

    Place, publisher, year, edition, pages
    Linköping: Svensk förening för matematikdidaktisk forskning (SMDF), 2006
    Series
    Skrifter från Svensk förening för matematikdidaktisk forskning, ISSN 1651-3274 ; 5
    National Category
    Other Mathematics Didactics
    Identifiers
    urn:nbn:se:liu:diva-14116 (URN)91-973934-4-4 (ISBN)
    Conference
    MADIF 5, the 5th Swedish mathematics education research seminar, January 24-25, Malmö, Sweden
    Available from: 2012-04-18 Created: 2006-11-10 Last updated: 2012-04-18Bibliographically approved
    2. Characterizing reading comprehension of mathematical texts
    Open this publication in new window or tab >>Characterizing reading comprehension of mathematical texts
    2006 (English)In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 63, no 3, p. 325-346Article in journal (Refereed) Published
    Abstract [en]

    This study compares reading comprehension of three different texts: two mathematical texts and one historical text. The two mathematical texts both present basic concepts of group theory, but one does it using mathematical symbols and the other only uses natural language. A total of 95 upper secondary and university students read one of the mathematical texts and the historical text. Before reading the texts, a test of prior knowledge for both mathematics and history was given and after reading each text, a test of reading comprehension was given. The results reveal a similarity in reading comprehension between the mathematical text without symbols and the historical text, and also a difference in reading comprehension between the two mathematical texts. This result suggests that mathematics in itself is not the most dominant aspect affecting the reading comprehension process, but the use of symbols in the text is a more relevant factor. Although the university students had studied more mathematics courses than the upper secondary students, there was only a small and insignificant difference between these groups regarding reading comprehension of the mathematical text with symbols. This finding suggests that there is a need for more explicit teaching of reading comprehension for texts including symbols.

    Keywords
    literacy, mathematical texts, mental representation, reading comprehension, symbols, university, upper secondary level
    National Category
    Other Mathematics Didactics
    Identifiers
    urn:nbn:se:liu:diva-14117 (URN)10.1007/s10649-005-9016-y (DOI)
    Available from: 2006-11-10 Created: 2006-11-10 Last updated: 2017-12-13
    3. Metacognition and reading - criteria for comprehension of mathematics texts
    Open this publication in new window or tab >>Metacognition and reading - criteria for comprehension of mathematics texts
    2006 (English)In: Proceedings of the 30th conference of the International group for the psychology of mathematics education / [ed] J. Novotná, H. Moraová, M. Krátká and N. Stehlíková, Prague: The International Group for the Psychology of Mathematics Education , 2006, Vol. 4, p. 289-296Conference paper, Published paper (Other academic)
    Abstract [en]

    This study uses categories of comprehension criteria to examine students’ reasons for stating that they do, or do not, understand a given mathematics text. Nine student teachers were individually interviewed, where they read a text and commented on their comprehension, in particular, why they felt they did, or did not, understand the text. The students had some difficulties commenting on their comprehension in this manner, something that can be due to that much of comprehension monitoring, when criteria for comprehension are used, might be operating at an unconscious cognitive level. Some specific aspects of mathematics texts are examined, such as the symbolic language and conceptual and procedural understanding.

    Place, publisher, year, edition, pages
    Prague: The International Group for the Psychology of Mathematics Education, 2006
    Series
    PME Conference Proceedings, ISSN 0771-100X
    National Category
    Other Mathematics Didactics
    Identifiers
    urn:nbn:se:liu:diva-14118 (URN)000281571400037 ()
    Conference
    Conference of the International Group for the Psychology of Mathematics Education, 16 – 21 July, Prague, Czech Republic
    Available from: 2010-02-16 Created: 2009-03-18 Last updated: 2012-08-16Bibliographically approved
    4. A metacognitive perspective on reading mathe-matical texts: Students’ beliefs and criteria for comprehension
    Open this publication in new window or tab >>A metacognitive perspective on reading mathe-matical texts: Students’ beliefs and criteria for comprehension
    2006 (English)Manuscript (preprint) (Other academic)
    National Category
    Didactics Other Mathematics
    Identifiers
    urn:nbn:se:liu:diva-52953 (URN)
    Available from: 2010-01-14 Created: 2010-01-14 Last updated: 2010-02-24
  • 2481.
    Österholm, Magnus
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Learning mathematics by reading - a study of students interacting with a text2003Report (Other academic)
    Abstract [en]

    This study investigates the situation when students on their own read a new mathematical text, and solve problems relevant to the text. The students worked together in pairs on a given text, about the absolute value of real numbers, with a video camera recording their activity. First, the students were instructed to read and discuss the text without any given tasks. Thereafter, the students were given exercises relevant to the text, and they were allowed to keep the text and use it when working with these exercises. Two pairs of students participated, all of them on their last year on the natural science programme at the Swedish upper secondary school. The observations reveal a variety of different activities among the students, and some questions also arise that would be interesting to examine in more detail.

  • 2482.
    Österholm, Magnus
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Learning mathematics by reading - a study of students interacting with a text2003In: Nordic pre-conference to ICME 10, 2003Conference paper (Other academic)
  • 2483.
    Österholm, Magnus
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Läsa matematiska texter: Förståelse och lärande i läsprocessen2004Licentiate thesis, monograph (Other academic)
    Abstract [sv]

    Denna avhandling behandlar läsning av matematiska texter; hur och vad man förstår och lär sig vid läsningen. Fokus ligger på läsprocessen, det vill säga själva läsandet av texten och vad man förstår efter att läst igenom texten. Huvudsyftet är att studera specifika aspekter i läsandet av just matematiska texter för att testa och utveckla en befintlig, allmän teori kring läsprocessen. Speciellt studeras användningen av symboler i matematiska texter och hur detta kan påverka läsprocessen. Avhandlingen byggs upp av teoretiska diskussioner kring läsning av matematiska texter samt en empirisk studie bland gymnasieelever och universitetsstuderande.

    De teoretiska diskussionerna utgår bland annat från en litteraturstudie kring förekommande påståenden om speciella egenskaper hos matematiska texter, och speciellt diskuteras läsning av symboler och algebraiska uttryck.

    Den empiriska studien (med 106 deltagare) använde tre olika texter; en historietext om ryska revolutionen samt två matematiktexter om gruppteori. Matematiktexterna behandlar samma sak som gruppteori, men skillnaden mellan dem är att den ena använder matematiska symboler i sin presentation medan den andra inte alls använder symboler. Varje deltagare fick läsa en utav matematiktexterna samt historietexterna, och fick efter varje text besvara frågor om textens innehåll.

    Den grupp av personer som läste matematiktexten utan symboler har bättre resultat på frågor om texten än den grupp som läste texten med symboler. Detta verkar kunna bero på oförmåga att artikulera symboler vid läsning av texten samt att avkodningsförmågan inte verkar kunna utnyttjas på samma sätt för texten med symboler. Läsning av matematiska texter med symboler är alltså ganska speciellt och man kan behöva lära sig hur man läser sådana texter. Däremot verkar det finnas många likheter med läsning av matematiska texter utan symboler och historietexten. Det matematiska innehållet verkar alltså inte i någon större omfattning påverka läsprocessen, utan hur detta innehåll presenteras är en viktig aspekt.

    I de teoretiska diskussionerna ges förslag på hur läsning av matematiska symboler kan infogas i den allmänna teorin för läsprocessen. Överlag finns dock ingen anledning att se läsning av matematiska texter som någon speciell typ av process som skiljer sig från läsning av andra texter. Den allmänna teorin för läsprocessen kan därmed fungera som teoretisk grund även för läsförståelse av matematiska texter, möjligen med föreslaget tillägg om matematiska symboler.

  • 2484.
    Österholm, Magnus
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Metacognition and reading - criteria for comprehension of mathematics texts2006In: Proceedings of the 30th conference of the International group for the psychology of mathematics education / [ed] J. Novotná, H. Moraová, M. Krátká and N. Stehlíková, Prague: The International Group for the Psychology of Mathematics Education , 2006, Vol. 4, p. 289-296Conference paper (Other academic)
    Abstract [en]

    This study uses categories of comprehension criteria to examine students’ reasons for stating that they do, or do not, understand a given mathematics text. Nine student teachers were individually interviewed, where they read a text and commented on their comprehension, in particular, why they felt they did, or did not, understand the text. The students had some difficulties commenting on their comprehension in this manner, something that can be due to that much of comprehension monitoring, when criteria for comprehension are used, might be operating at an unconscious cognitive level. Some specific aspects of mathematics texts are examined, such as the symbolic language and conceptual and procedural understanding.

  • 2485.
    Österholm, Magnus
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Reading mathematical texts: cognitive processes and mental representations2004Conference paper (Refereed)
  • 2486.
    Özarslan, Evren
    et al.
    Linköping University, Department of Biomedical Engineering, Division of Biomedical Engineering. Linköping University, Faculty of Science & Engineering.
    Yolcu, Cem
    Linköping University, Department of Biomedical Engineering, Division of Biomedical Engineering. Linköping University, Faculty of Science & Engineering.
    Herberthson, Magnus
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Division of Biomedical Engineering. Linköping University, Faculty of Science & Engineering. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Westin, Carl-Fredrik
    Linköping University, Department of Biomedical Engineering, Division of Biomedical Engineering. Linköping University, Faculty of Science & Engineering. Laboratory for Mathematics in Imaging, Department of Radiology, Brigham and Women’s Hospital, Harvard Medical School, Boston, MA, USA.
    Influence of the Size and Curvedness of Neural Projections on the Orientationally Averaged Diffusion MR Signal2018In: Frontiers in Physics, E-ISSN 2296-424X, Vol. 6, p. 1-10, article id 17Article in journal (Refereed)
    Abstract [en]

    Neuronal and glial projections can be envisioned to be tubes of infinitesimal diameter as far as diffusion magnetic resonance (MR) measurements via clinical scanners are concerned. Recent experimental studies indicate that the decay of the orientationally-averaged signal in white-matter may be characterized by the power-law, Ē(q) ∝ q−1, where q is the wavenumber determined by the parameters of the pulsed field gradient measurements. One particular study by McKinnon et al. [1] reports a distinctively faster decay in gray-matter. Here, we assess the role of the size and curvature of the neurites and glial arborizations in these experimental findings. To this end, we studied the signal decay for diffusion along general curves at all three temporal regimes of the traditional pulsed field gradient measurements. We show that for curvy projections, employment of longer pulse durations leads to a disappearance of the q−1 decay, while such decay is robust when narrow gradient pulses are used. Thus, in clinical acquisitions, the lack of such a decay for a fibrous specimen can be seen as indicative of fibers that are curved. We note that the above discussion is valid for an intermediate range of q-values as the true asymptotic behavior of the signal decay is Ē(q) ∝ q−4 for narrow pulses (through Debye-Porod law) or steeper for longer pulses. This study is expected to provide insights for interpreting the diffusion-weighted images of the central nervous system and aid in the design of acquisition strategies.

  • 2487.
    Özarslan, Evren
    et al.
    Linköping University, Department of Biomedical Engineering, Division of Biomedical Engineering. Linköping University, Faculty of Science & Engineering.
    Yolcu, Cem
    Linköping University, Department of Biomedical Engineering, Division of Biomedical Engineering. Linköping University, Faculty of Science & Engineering.
    Herberthson, Magnus
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Westin, Carl-Fredrik
    Linköping University, Department of Biomedical Engineering, Division of Biomedical Engineering. Linköping University, Faculty of Science & Engineering. Laboratory for Mathematics in Imaging, Department of Radiology, Harvard Medical School, Brigham and Women's Hospital, Boston, MA, United States.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Division of Biomedical Engineering. Linköping University, Faculty of Science & Engineering.
    Effective Potential for Magnetic Resonance Measurements of Restricted Diffusion2017In: Frontiers in Physics, E-ISSN 2296-424X, Vol. 5, article id 68Article in journal (Refereed)
    Abstract [en]

    The signature of diffusive motion on the NMR signal has been exploited to characterize the mesoscopic structure of specimens in numerous applications. For compartmentalized specimens comprising isolated subdomains, a representation of individual pores is necessary for describing restricted diffusion within them. When gradient waveforms with long pulse durations are employed, a quadratic potential profile is identified as an effective energy landscape for restricted diffusion. The dependence of the stochastic effective force on the center-of-mass position is indeed found to be approximately linear (Hookean) for restricted diffusion even when the walls are sticky. We outline the theoretical basis and practical advantages of our picture involving effective potentials.

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