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  • 2451.
    Wästlund, Johan
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Perfect packings of squares using the stack-pack strategy2003Ingår i: Discrete & Computational Geometry, ISSN 0179-5376, E-ISSN 1432-0444, Vol. 29, nr 4, s. 625-631Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider the problem of packing an infinite set of square tiles into a finite number of rectangular boxes. We introduce a simple packing strategy that we call stack-pack. Using this strategy, we prove that if 1/2 < t < 2/3, then the squares of side n-t, for positive integers n, can be packed into some finite collection of square boxes of the same area ? (2r) as the total area of the tiles.

  • 2452.
    Wästlund, Johan
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Random Assignment Problems2003Ingår i: Random Structures and Algorithms,2003, 2003Konferensbidrag (Övrigt vetenskapligt)
  • 2453.
    Wästlund, Johan
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    The variance and higher moments in the random assignment problem2005Rapport (Övrigt vetenskapligt)
    Abstract [en]

    We obtain exact formulas for all moments of the cost Cn of the inimum assignment in the complete bipartite graph Kn,n with independent exp(1) edge costs. In particular we prove that as n tends to infinity, the variance of Cn is c/n+O(1/n2), where c = 4ζ(2)-4ζ(3), or approximately 1.7715.

  • 2454.
    Wästlund, Johan
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Two-person symmetric whist2005Rapport (Övrigt vetenskapligt)
    Abstract [en]

    The game of two-person whist is played with a deck of cards. Each card belongs to a suit, and each suit is totally ordered. The cards are distributed between the two players so that each player receives the same number of cards. Hence both players have complete information about the deal. Play proceeds in tricks, with the obligation to follow suit, as in many real-world card games.

    We study the symmetric case of this game, that is, we assume that in each suit, the two players have the same number of cards. Under this assumption, the second player in each trick will always be able to follow suit.

    We show how to assign a value from a certain semigroup to each single-suit card distribution in such a way that the outcome of a multisuit deal under optimal play is determined by the sum of the values of the individual suit. This allows us to play a deal perfectly, provided that we can compute the values of its single-suit components. Although we do not have an efficient algorithm for doing this in general, we give methods that will allow us to find the value of a suit quickly in most cases.

    We also establish certain general facts about the game, for instance the nontrivial fact that a higher card is always at least as good as a smaller card in the same suit.

  • 2455.
    Wästlund, Johan
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Two-person symmetric whist2005Ingår i: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 12, nr 1, s. R44-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We introduce a two-person perfect information model of trick taking games. A set of cards is distributed between two players, and play proceeds in tricks with the obligation to follow suit, as in many real-world card games.

    We assume that in each suit, the two players have the same number of cards. Under this assumption, we show how to assign a value from a  certain semigroup to each single-suit card distribution in such a way that the outcome of a multi-suit deal under optimal play is determined by the sum of the values of the individual suits.

  • 2456.
    Yang, Xiangfeng
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    Asymptotic expansions for Laplace transforms of Markov processes2018Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 457, nr 1, s. 694-721Artikel i tidskrift (Refereegranskat)
    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.

  • 2457.
    Yang, Xiangfeng
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    Exact upper tail probabilities of random series2015Ingår i: Statistics and Probability Letters, ISSN 0167-7152, E-ISSN 1879-2103, Vol. 99, s. 13-19Artikel i tidskrift (Refereegranskat)
    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.

  • 2458.
    Yang, Xiangfeng
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan.
    Large deviations for Markov bridges with jumps2014Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 416, nr 1, s. 1-12Artikel i tidskrift (Refereegranskat)
    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.

  • 2459.
    Yang, Xiangfeng
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    On the large deviation principle of generalized Brownian bridges2015Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 430, nr 2, s. 845-856Artikel i tidskrift (Refereegranskat)
    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.

  • 2460.
    Ying, Daniel
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Cyclic Trigonal Riemann Surfaces of Genus 42004Licentiatavhandling, monografi (Övrigt vetenskapligt)
    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.

  • 2461.
    Ying, Daniel
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Klassificering av automorfigrupper på trigonala Riemannytor2003Ingår i: Unga matematiker Svenska matematikersamfundets höstmöte,2003, 2003Konferensbidrag (Övrigt vetenskapligt)
  • 2462.
    Ying, Daniel
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Kubiska riemannytor2004Ingår i: Workshop i tillämpad matematik,2004, 2004Konferensbidrag (Övrigt vetenskapligt)
  • 2463.
    Ying, Daniel
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    On the Moduli Space of Cyclic Trigonal Riemann Surfaces of Genus 42006Doktorsavhandling, monografi (Övrigt vetenskapligt)
    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.

  • 2464.
    Zhao, Hongmei
    et al.
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Lei, Lei
    Linköpings universitet, Institutionen för teknik och naturvetenskap, Kommunikations- och transportsystem. Linköpings universitet, Tekniska högskolan.
    Yuan, Di
    Linköpings universitet, Institutionen för teknik och naturvetenskap, Kommunikations- och transportsystem. Linköpings universitet, Tekniska högskolan.
    Larsson, Torbjörn
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Rönnberg, Elina
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Power efficient uplink scheduling in SC-FDMA: Bounding global optimality by column generation2013Ingår i: 2013 IEEE 18th International Workshop on Computer Aided Modeling and Design of Communication Links and Networks (CAMAD, IEEE , 2013, s. 119-123Konferensbidrag (Refereegranskat)
    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.

  • 2465.
    Zhao, Yixin
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    On the Integration of Heuristics with Column-Oriented Models for Discrete Optimization2016Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    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.

    Delarbeten
    1. Power efficient uplink scheduling in SC-FDMA: benchmarking by column generation
    Öppna denna publikation i ny flik eller fönster >>Power efficient uplink scheduling in SC-FDMA: benchmarking by column generation
    Visa övriga...
    2016 (Engelska)Ingår i: Optimization and Engineering, ISSN 1389-4420, E-ISSN 1573-2924, Vol. 17, nr 4, s. 695-725Artikel i tidskrift (Refereegranskat) 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.

    Ort, förlag, år, upplaga, sidor
    Springer-Verlag New York, 2016
    Nyckelord
    Localized SC-FDMA, Stabilized column generation, Power minimization, Integer linear programming, Uplink scheduling, Matheuristic
    Nationell ämneskategori
    Matematik
    Identifikatorer
    urn:nbn:se:liu:diva-127355 (URN)10.1007/s11081-015-9304-z (DOI)000387857500004 ()
    Anmärkning

    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

    Tillgänglig från: 2016-04-22 Skapad: 2016-04-22 Senast uppdaterad: 2019-08-06Bibliografiskt granskad
    2. Power efficient uplink scheduling in SC-FDMA: Bounding global optimality by column generation
    Öppna denna publikation i ny flik eller fönster >>Power efficient uplink scheduling in SC-FDMA: Bounding global optimality by column generation
    Visa övriga...
    2013 (Engelska)Ingår i: 2013 IEEE 18th International Workshop on Computer Aided Modeling and Design of Communication Links and Networks (CAMAD, IEEE , 2013, s. 119-123Konferensbidrag, Publicerat paper (Refereegranskat)
    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.

    Ort, förlag, år, upplaga, sidor
    IEEE, 2013
    Serie
    International Workshop on Computer Aided Modeling and Design of Communication Links and Networks (CAMAD), ISSN 2378-4865 ; 2013
    Nationell ämneskategori
    Matematik
    Identifikatorer
    urn:nbn:se:liu:diva-106237 (URN)10.1109/CAMAD.2013.6708101 (DOI)
    Konferens
    2013 IEEE 18th International Workshop on Computer Aided Modeling and Design of Communication Links and Networks (CAMAD)
    Tillgänglig från: 2014-04-29 Skapad: 2014-04-29 Senast uppdaterad: 2018-06-25
  • 2466.
    Zhao, Yixin
    et al.
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Larsson, Torbjörn
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Rönnberg, Elina
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    A Large Neighbourhood Search Principle for Column-Oriented Models: Theoretical Derivation and Example Applications2016Ingår i: Matheuristics 2016: Proceedings of the Sixth International Workshop on Model-based Metaheuristics / [ed] V. Maniezzo and T. Stutzle, Bruxelles, Belgium: IRIDIA , 2016Konferensbidrag (Refereegranskat)
  • 2467.
    Zhao, Yixin
    et al.
    Nanjing University of Science and Technology, School of Automation.
    Larsson, Torbjörn
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Rönnberg, Elina
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    An integer programming column generation principlefor heuristic search methods2019Ingår i: International Transactions in Operational Research, ISSN 0969-6016, E-ISSN 1475-3995, Vol. 27, nr 1, s. 665-695Artikel i tidskrift (Refereegranskat)
    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.

  • 2468.
    Zhao, Yixin
    et al.
    Nanjing University of Science and Technology, School of Automation.
    Larsson, Torbjörn
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Rönnberg, Elina
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    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 generation2018Ingår i: Journal of Global Optimization, ISSN 0925-5001, E-ISSN 1573-2916, Vol. 72, nr 3, s. 517-538Artikel i tidskrift (Refereegranskat)
    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.

  • 2469.
    Zhao, Yixin
    et al.
    Nanjing Univ Sci and Technol, Peoples R China.
    Larsson, Torbjörn
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Yuan, Di
    Linköpings universitet, Institutionen för teknik och naturvetenskap, Kommunikations- och transportsystem. Linköpings universitet, Tekniska fakulteten.
    Rönnberg, Elina
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Lei, Lei
    Linköpings universitet, Institutionen för teknik och naturvetenskap. Linköpings universitet, Tekniska fakulteten.
    Correction: Power efficient uplink scheduling in SC-FDMA: benchmarking by column generation (vol 17, pg 695, 2016)2019Ingår i: Optimization and Engineering, ISSN 1389-4420, E-ISSN 1573-2924, Vol. 20, nr 3, s. 959-959Artikel i tidskrift (Övrigt vetenskapligt)
    Abstract [en]

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

  • 2470.
    Zhao, Yixin
    et al.
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Larsson, Torbjörn
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Yuan, Di
    Linköpings universitet, Institutionen för teknik och naturvetenskap, Kommunikations- och transportsystem. Linköpings universitet, Tekniska fakulteten.
    Rönnberg, Elina
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Lei, Lei
    Linköpings universitet, Institutionen för teknik och naturvetenskap, Kommunikations- och transportsystem. Linköpings universitet, Tekniska fakulteten.
    Power efficient uplink scheduling in SC-FDMA: benchmarking by column generation2016Ingår i: Optimization and Engineering, ISSN 1389-4420, E-ISSN 1573-2924, Vol. 17, nr 4, s. 695-725Artikel i tidskrift (Refereegranskat)
    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.

  • 2471.
    Zhu, Yurong
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    Large Deviations on Longest Runs2016Studentarbete övrigt, 10 poäng / 15 hpStudentuppsats (Examensarbete)
    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.

  • 2472.
    Zikrin, Spartak
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Large-Scale Optimization Methods with Application to Design of Filter Networks2014Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    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.

    Delarbeten
    1. On Efficiently Combining Limited Memory and Trust-Region Techniques
    Öppna denna publikation i ny flik eller fönster >>On Efficiently Combining Limited Memory and Trust-Region Techniques
    2013 (Engelska)Rapport (Övrigt vetenskapligt)
    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.

    Ort, förlag, år, upplaga, sidor
    Linköping: Linköping University Electronic Press, 2013. s. 33
    Serie
    LiTH-MAT-R, ISSN 0348-2960 ; 2013:13
    Nyckelord
    Unconstrained Optimization; Large-scale Problems; Limited Memory Methods;
    Nationell ämneskategori
    Beräkningsmatematik
    Identifikatorer
    urn:nbn:se:liu:diva-102005 (URN)LiTH-MAT-R--2013/13--SE (ISRN)
    Tillgänglig från: 2013-11-26 Skapad: 2013-11-26 Senast uppdaterad: 2016-01-12Bibliografiskt granskad
    2. Global search strategies for solving multilinear least-squares problems
    Öppna denna publikation i ny flik eller fönster >>Global search strategies for solving multilinear least-squares problems
    2012 (Engelska)Ingår i: Sultan Qaboos University Journal for Science, ISSN 1027-524X, Vol. 17, nr 1, s. 12-21Artikel i tidskrift (Refereegranskat) 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.

    Ort, förlag, år, upplaga, sidor
    Sultan Qaboos University, 2012
    Nyckelord
    Global optimization; Global search strategies; Multilinear least-squares; Filter
    Nationell ämneskategori
    Beräkningsmatematik Medicinsk bildbehandling
    Identifikatorer
    urn:nbn:se:liu:diva-78918 (URN)
    Tillgänglig från: 2012-08-28 Skapad: 2012-06-25 Senast uppdaterad: 2015-09-03Bibliografiskt granskad
    3. Sparsity Optimization in Design of Multidimensional Filter Networks
    Öppna denna publikation i ny flik eller fönster >>Sparsity Optimization in Design of Multidimensional Filter Networks
    2013 (Engelska)Rapport (Övrigt vetenskapligt)
    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.

    Ort, förlag, år, upplaga, sidor
    Linköping: Linköping University Electronic Press, 2013. s. 21
    Serie
    LiTH-MAT-R, ISSN 0348-2960 ; 2013:16
    Nyckelord
    Sparse optimization; Cardinality Constraint; Multicriteria Optimization; Multilinear Least-Squares Problem; Filter networks; Medical imaging
    Nationell ämneskategori
    Beräkningsmatematik Medicinsk bildbehandling Signalbehandling
    Identifikatorer
    urn:nbn:se:liu:diva-103915 (URN)LiTH-MAT-R-2013/16-SE (ISRN)
    Tillgänglig från: 2014-02-03 Skapad: 2014-02-03 Senast uppdaterad: 2016-11-24Bibliografiskt granskad
  • 2473.
    Äng, Oscar
    et al.
    Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska fakulteten.
    Trygg, Alexander
    Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska fakulteten.
    Planering av stränggjutningsproduktion: En heruistisk metod2017Självständigt arbete på grundnivå (kandidatexamen), 10,5 poäng / 16 hpStudentuppsats (Examensarbete)
    Abstract [sv]

    Detta arbete syftar till att undersöka om det är möjligt att med en heuristisk metod skapa giltiga lösningar till ett problem vid planering av stränggjutningsproduktion på SSAB. Planeringsproblemet uppstår när stål av olika sorter ska gjutas under samma dag. Beroende på i vilken ordning olika kundordrar av stål gjuts uppstår spill av olika storlek. Detta spill ska minimeras och tidigare arbete har genomförts på detta problem och resulterat i en matematisk modell för att skapa lösningar till problemet. Det tar i praktiken lång tid att hitta bra lösningar med modellen och frågeställningen är om det går att göra detta med en heuristisk metod för att kunna generera bra lösningar snabbare.

    Med inspiration från Variable Neighbourhood Search, Simulated Annealing och tabusökning har heuristiker skapats, implementerats och utvärderats mot den matematiska modellen. En av heuristikerna presterar bättre än den matematiska modellen gör på 10 minuter. Matematiska modellens resultat efter 60 minuter körtid är bättre än den utvecklade heuristiken, men resultaten är nära varandra. Körtiden för heuristiken tar signifikant mindre tid än 10 minuter.

  • 2474.
    Åberg, Johnny
    Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska fakulteten.
    Programmering i Ma1c: ett specialanpassat utbildningsmaterial för lösning av sannolikhetsproblem2019Självständigt arbete på grundnivå (yrkesexamen), 10 poäng / 15 hpStudentuppsats (Examensarbete)
    Abstract [sv]

    Från den 1 juli 2018 ingår matematisk problemlösning med programmering i ämnet matematik på gymnasieskolans teknik- och naturvetenskapsprogram. Den här studien utgår från den nya kursplanen för Matematik 1c (Ma1c), försöker göra en rimlig tolkning av Skolverkets skrivningar, presenterar ett specialanpassat utbildningsmaterial avsett för kursens programmeringsdel och beskriver hur materialet har utarbetats. Materialet består av en projektorpresentation och ett elevhäfte med övningsuppgifter, fokuserar på sannolikhetsproblemen i Ma1c, är provat i tre mindre och osystematiska pilotförsök, är inte helt utprovat och behöver förbättras ytterligare. Givet studiens tolkning, och 9 timmar undervisning i programmering, finns det goda skäl att misstänka att eleverna inte kommer att hinna lära sig matematisk problemlösning med programmering i Ma1c.

  • 2475.
    Ålund, Oskar
    et al.
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    A provably stable, non-iterative domain decomposition technique for the advection-diffusion equation2016Rapport (Övrigt vetenskapligt)
    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.

  • 2476.
    Ålund, Oskar
    et al.
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    A Stable Domain Decomposition Technique for Advection–Diffusion Problems2018Ingår i: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 77, nr 2, s. 755-774Artikel i tidskrift (Refereegranskat)
    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.

  • 2477.
    Ålund, Oskar
    et al.
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    A stable, high order accurate and efficient hybrid method for flow calculations in complex geometries2018Ingår i: 2018 AIAA Aerospace Sciences Meeting, AIAA SciTech Forum, (AIAA 2018-1096), American Institute of Aeronautics and Astronautics, 2018, nr 210059, s. 1-9Konferensbidrag (Refereegranskat)
    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.

  • 2478.
    Ålund, Oskar
    et al.
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Encapsulated high order difference operators on curvilinear non-conforming grids2019Ingår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 385, s. 209-224Artikel i tidskrift (Refereegranskat)
    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.

    Publikationen är tillgänglig i fulltext från 2021-02-26 12:23
  • 2479.
    Åslund, Jan
    Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska högskolan.
    Asymptotic analysis of junctions in multi-structures2002Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    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.

  • 2480.
    Österberg, Sofia
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Motiverad för matematik?: En litteraturstudie om yttre och inre faktorers påverkan på gymnasieelevers motivation i skolmatematik2014Självständigt arbete på avancerad nivå (masterexamen), 10 poäng / 15 hpStudentuppsats (Examensarbete)
    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.

  • 2481.
    Österholm, Magnus
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    A metacognitive perspective on reading mathe-matical texts: Students’ beliefs and criteria for comprehension2006Manuskript (preprint) (Övrigt vetenskapligt)
  • 2482.
    Österholm, Magnus
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    A reading comprehension perspective on problem solving2006Ingår i: 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, s. 136-145Konferensbidrag (Refereegranskat)
    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.

  • 2483.
    Österholm, Magnus
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Characterizing reading comprehension of mathematical texts2006Ingår i: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 63, nr 3, s. 325-346Artikel i tidskrift (Refereegranskat)
    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.

  • 2484.
    Österholm, Magnus
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Epistemological beliefs and communication in mathematics education at upper secondary and university levels2009Ingår i: 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, s. 132-134Konferensbidrag (Övrigt vetenskapligt)
  • 2485.
    Österholm, Magnus
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Kognitiva och metakognitiva perspektiv på läsförståelse inom matematik2006Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [sv]

    Det verkar finnas en allmän uppfattning om att matematiska texter är så speciella att man måste få lära sig en särskild typ av läsförmåga för att förstå sådana texter. Denna uppfattning verkar dock inte vara baserad på forskningsresultat eftersom det visar sig inte finnas mycket forskning genomförd som behandlar läsförståelse inom matematik.

    Huvudsyftet med denna avhandling är att undersöka om det krävs speciella kunskaper eller förmågor för att läsa matematiska texter. Fokus ligger på studerandes läsning av olika typer av texter som behandlar matematik från grundläggande universitetsnivå. Detta studeras utifrån två olika perspektiv, dels ett kognitivt, där läsförmågor och ämneskunskaper studeras i relation till läsförståelse, och dels ett metakognitivt, vilket innefattar uppfattningar och hur man som läsare avgör om man förstått en text.

    I avhandlingen ingår tre empiriska studier samt teoretiska diskussioner som bland annat utgår från två litteraturstudier, den ena om egenskaper hos matematiska texter och den andra om läsning i relation till problemlösning. I de empiriska studierna jämförs dels läsning av matematiska texter med läsning av texter med annat ämnesinnehåll och dels läsning av olika typer av matematiska texter, där speciellt symbolanvändningen och om innehållet berör begrepp eller procedurer studeras. Dessutom undersöks hur studerande uppfattar sin egen läsförståelse samt läsning och texter i allmänhet inom matematik, och huruvida variationer i dessa uppfattningar kan kopplas till läsförståelsen.

    Resultat från studierna i denna avhandling visar att de studerande verkar använda en speciell sorts läsförmåga för matematiska texter; att fokusera på symboler i en text. För matematiska texter utan symboler utnyttjas en mer generell läsförmåga, det vill säga en läsförmåga som används också för texter med annat ämnesinnehåll. Men när symboler finns i texten läses alltså texten på ett särskilt sätt, vilket påverkar läsförståelsen på olika sätt för olika typer av texter (avseende om de berör begrepp eller procedurer). Jämfört med när den generella läsförmågan utnyttjas, skapas sämre läsförståelse när den speciella läsförmågan används.

    Det verkar finnas ett behov av att fokusera på läsning och läsförståelse inom matematikutbildning eftersom resultat visar att kurser på gymnasiet (kurs E) och på universitetet (inom algebra och analys) inte påverkar den speciella läsförmågan. De nämnda resultaten påvisar dock att det primärt inte nödvändigtvis handlar om att lära sig att läsa matematiska texter på något särskilt sätt utan att utnyttja en befintlig generell läsförmåga också för matematiska texter.

    Resultat från det metakognitiva perspektivet påvisar en skillnad mellan medvetna aspekter, såsom avseende uppfattningar och reflektion kring förståelse, samt omedvetna aspekter, såsom de mer automatiska processer som gör att man förstår en text när den läses, där också metakognitiva processer finns aktiva. Speciellt visar det sig att uppfattningar, som undersökts med hjälp av en enkät, inte har någon tydlig och oberoende effekt på läsförståelse.

    Utifrån de texter som använts och de studerande som deltagit verkar det som helhet inte finnas någon anledning att betrakta läsning av matematiska texter som en speciell sorts process som kräver särskilda läsförmågor. Studerandes utveckling av speciella läsförmågor kan istället handla om att de inte upplevt något behov av (eller krav på) att läsa olika typer av matematiska texter där likheter med läsning i allmänhet kan uppmärksammas och utnyttjas.

    Delarbeten
    1. A reading comprehension perspective on problem solving
    Öppna denna publikation i ny flik eller fönster >>A reading comprehension perspective on problem solving
    2006 (Engelska)Ingår i: 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, s. 136-145Konferensbidrag, Publicerat paper (Refereegranskat)
    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.

    Ort, förlag, år, upplaga, sidor
    Linköping: Svensk förening för matematikdidaktisk forskning (SMDF), 2006
    Serie
    Skrifter från Svensk förening för matematikdidaktisk forskning, ISSN 1651-3274 ; 5
    Nationell ämneskategori
    Annan matematik Didaktik
    Identifikatorer
    urn:nbn:se:liu:diva-14116 (URN)91-973934-4-4 (ISBN)
    Konferens
    MADIF 5, the 5th Swedish mathematics education research seminar, January 24-25, Malmö, Sweden
    Tillgänglig från: 2012-04-18 Skapad: 2006-11-10 Senast uppdaterad: 2012-04-18Bibliografiskt granskad
    2. Characterizing reading comprehension of mathematical texts
    Öppna denna publikation i ny flik eller fönster >>Characterizing reading comprehension of mathematical texts
    2006 (Engelska)Ingår i: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 63, nr 3, s. 325-346Artikel i tidskrift (Refereegranskat) 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.

    Nyckelord
    literacy, mathematical texts, mental representation, reading comprehension, symbols, university, upper secondary level
    Nationell ämneskategori
    Annan matematik Didaktik
    Identifikatorer
    urn:nbn:se:liu:diva-14117 (URN)10.1007/s10649-005-9016-y (DOI)
    Tillgänglig från: 2006-11-10 Skapad: 2006-11-10 Senast uppdaterad: 2017-12-13
    3. Metacognition and reading - criteria for comprehension of mathematics texts
    Öppna denna publikation i ny flik eller fönster >>Metacognition and reading - criteria for comprehension of mathematics texts
    2006 (Engelska)Ingår i: 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, s. 289-296Konferensbidrag, Publicerat paper (Övrigt vetenskapligt)
    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.

    Ort, förlag, år, upplaga, sidor
    Prague: The International Group for the Psychology of Mathematics Education, 2006
    Serie
    PME Conference Proceedings, ISSN 0771-100X
    Nationell ämneskategori
    Annan matematik Didaktik
    Identifikatorer
    urn:nbn:se:liu:diva-14118 (URN)000281571400037 ()
    Konferens
    Conference of the International Group for the Psychology of Mathematics Education, 16 – 21 July, Prague, Czech Republic
    Tillgänglig från: 2010-02-16 Skapad: 2009-03-18 Senast uppdaterad: 2012-08-16Bibliografiskt granskad
    4. A metacognitive perspective on reading mathe-matical texts: Students’ beliefs and criteria for comprehension
    Öppna denna publikation i ny flik eller fönster >>A metacognitive perspective on reading mathe-matical texts: Students’ beliefs and criteria for comprehension
    2006 (Engelska)Manuskript (preprint) (Övrigt vetenskapligt)
    Nationell ämneskategori
    Didaktik Annan matematik
    Identifikatorer
    urn:nbn:se:liu:diva-52953 (URN)
    Tillgänglig från: 2010-01-14 Skapad: 2010-01-14 Senast uppdaterad: 2010-02-24
  • 2486.
    Österholm, Magnus
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Learning mathematics by reading - a study of students interacting with a text2003Rapport (Övrigt vetenskapligt)
    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.

  • 2487.
    Österholm, Magnus
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Learning mathematics by reading - a study of students interacting with a text2003Ingår i: Nordic pre-conference to ICME 10, 2003Konferensbidrag (Övrigt vetenskapligt)
  • 2488.
    Österholm, Magnus
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Läsa matematiska texter: Förståelse och lärande i läsprocessen2004Licentiatavhandling, monografi (Övrigt vetenskapligt)
    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.

  • 2489.
    Österholm, Magnus
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Metacognition and reading - criteria for comprehension of mathematics texts2006Ingår i: 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, s. 289-296Konferensbidrag (Övrigt vetenskapligt)
    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.

  • 2490.
    Österholm, Magnus
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Reading mathematical texts: cognitive processes and mental representations2004Konferensbidrag (Refereegranskat)
  • 2491.
    Özarslan, Evren
    et al.
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten.
    Yolcu, Cem
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten.
    Herberthson, Magnus
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Knutsson, Hans
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV.
    Westin, Carl-Fredrik
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten. 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 Signal2018Ingår i: Frontiers in Physics, E-ISSN 2296-424X, Vol. 6, s. 1-10, artikel-id 17Artikel i tidskrift (Refereegranskat)
    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.

  • 2492.
    Özarslan, Evren
    et al.
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten.
    Yolcu, Cem
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten.
    Herberthson, Magnus
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Westin, Carl-Fredrik
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten. Laboratory for Mathematics in Imaging, Department of Radiology, Harvard Medical School, Brigham and Women's Hospital, Boston, MA, United States.
    Knutsson, Hans
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten.
    Effective Potential for Magnetic Resonance Measurements of Restricted Diffusion2017Ingår i: Frontiers in Physics, E-ISSN 2296-424X, Vol. 5, artikel-id 68Artikel i tidskrift (Refereegranskat)
    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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