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  • 1.
    Dress, A.
    et al.
    FSPM-Strukturbildungsprozesse, University of Bielefeld, D-33501 Bielefeld, Germany.
    Huber, Katharina T
    Institute of Fundamental Sciences, Massey University, Private Bag 11 222, Palmerston North, New Zealand.
    Koolen, J. H.
    FSPM-Strukturbildungsprozesse, University of Bielefeld, D-33501 Bielefeld, Germany.
    Moulton, Vincent
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Six points suffice: How to check for metric consistency2001In: European journal of combinatorics (Print), ISSN 0195-6698, E-ISSN 1095-9971, Vol. 22, no 4, p. 465-474Article in journal (Refereed)
    Abstract [en]

    In many areas of data analysis, it is desirable to have tools at hand for analyzing the structure of distance tables-or, in more mathematical terms, of finite metric spaces. One such tool, known as split decomposition theory has proven particularly useful in this respect. Tbe class of so-called totally decomposable metrics forms a cornerstone for this theory, and much work has been devoted to their study. Recently, it has become apparent that a particular subclass of these metrics, the consistent metrics, are also of fundamental importance. In this paper, we give a six-point characterization of consistent metrics amongst the totally decomposable ones.

  • 2.
    Edström, Per
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
    Gustafsson Coppel, Ludovic
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
    Open PaperOpt – A Monte Carlo Simulation Tool for Simulating Light Scattering in Paper and Print2010Report (Other academic)
    Abstract [en]

    The Kubelka-Munk model and extensions thereof are extensively used in product development, thanks to their simplicity and the fact that they are invertible. However, their explanative power is limited to distinguishing processes that affect scattering properties from those that affect absorption properties, an example being the frequently observed decrease of the scattering coefficient with calendering. Better understanding of how internal structural changes affect the optical properties requires modelling the composite structure of a paper layer. We propose a modular object-oriented Open Source Monte Carlo simulation platform, Open PaperOpt, which allows different geometrical representations of the inner paper structure. The proposed file formats open for a standardisation that facilitates data exchange between different simulation tools and measuring instruments, and supports a broad dissemination of the simulation software.

  • 3.
    Edvardsson, Sverker
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences.
    Neuman, Magnus
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences.
    Edström, Per
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences.
    Olin, Håkan
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences.
    Solving equations through particle dynamics2015In: Computer Physics Communications, ISSN 0010-4655, E-ISSN 1879-2944, Vol. 197, p. 169-181Article in journal (Refereed)
    Abstract [en]

    The present work evaluates a recently developed particle method (DFPM). The basic idea behind this method is to utilize a Newtonian system of interacting particles that through dissipation solves mathematical problems. We find that this second order dynamical system results in an algorithm that is among the best methods known. The present work studies large systems of linear equations. Of special interest is the wide eigenvalue spectrum. This case is common as the discretization of the continuous problem becomes dense. The convergence rate of DFPM is shown to be in parity with that of the conjugate gradient method, both analytically and through numerical examples. However, an advantage with DFPM is that it is cheaper per iteration. Another advantage is that it is not restricted to symmetric matrices only, as is the case for the conjugate gradient method. The convergence properties of DFPM are shown to be superior to the closely related approach utilizing only a first order dynamical system, and also to several other iterative methods in numerical linear algebra. The performance properties are understood and optimized by taking advantage of critically damped oscillators in classical mechanics. Just as in the case of the conjugate gradient method, a limitation is that all eigenvalues (spring constants) are required to be of the same sign. DFPM has no other limitation such as matrix structure or a spectral radius as is common among iterative methods. Examples are provided to test the particle algorithm’s merits and also various performance comparisons with existent numerical algorithms are provided.

  • 4.
    Feng, Tao
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
    Gulliksson, Mårten
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
    Liu, Wenbin
    Adaptive finite element methods for parameter estimation problems in linear elasticity2009In: International Journal of Numerical Analysis & Modeling, ISSN 1705-5105, Vol. 6, no 1, p. 17-32Article in journal (Refereed)
    Abstract [en]

    In this paper, the Lame coefficients in the linear elasticity problem are estimated by using the measurements of displacement. Some a posteriori error estimators for the approximation error of the parameters are derived, and then adaptive finite element schemes are developed for the discretization of the parameter estimation problem, based on the error estimators. The Gauss-Newton method is employed to solve the discretized nonlinear least-squares problem. Some numerical results are presented.

  • 5.
    Flodén, Liselott
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering and Sustainable Development.
    Holmbom, Anders
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering and Sustainable Development.
    Olsson, Marianne
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering and Sustainable Development.
    Persson, Jens
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering and Sustainable Development.
    A myriad shades of green2009In: Proceedings of Bridges 2009, Banff, Alberta, Canada, 2009Conference paper (Refereed)
    Abstract [en]

    We discuss the possible application of techniques inspired by the theories of G-convergence and homogenization to understand mixtures of colors and how they appear as observed by the human eye.  The ideas are illustrated by pictures describing the equivalent of a convergence process     for different kinds of mixtures of colors.

  • 6.
    Gulliksson, Mårten
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
    Carlsson, Nils
    Department of Mathematics, Luleå University, Sweden.
    Surface Fitting with NURBS - a Gauss Newton with Trust Region Approach: 13th WSEAS International Conference on APPLIED MATHEMATICS Puerto de la Cruz, SPAIN, DEC 15-17, 20082008In: APPLIED AND COMPUTATIONAL MATHEMATICS, 2ND EDITION, AG LOANNOU THEOLOGOU 17-23, 15773 ZOGRAPHOU, ATHENS, GREECE: World Scientific and Engineering Academy and Society, 2008, p. 169-174Conference paper (Refereed)
    Abstract [en]

    This paper shows a new approach for non-linear least squares fitting with NURBS as curves and surfaces to measured data by the Gauss-Newton method. A Trust Region algorithm is used to reach global convergence as well as variable substitution and simple bounds.

  • 7.
    Gulliksson, Mårten
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of applied science and design.
    Edvardsson, Sverker
    Mid Sweden University, Faculty of Science, Technology and Media, Department of applied science and design.
    Lind, Andreas
    Mid Sweden University, Faculty of Science, Technology and Media, Department of applied science and design.
    The dynamical functional method2012Other (Other academic)
  • 8.
    Hallberg, Daniel
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Information and Communication systems.
    Gustavsson, Klas
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Information and Communication systems.
    Beslutsstöd för lagerhantering: Matematisk optimeringsmodell för godsplanering och simulering2013Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    An increasingly common part in third party logistics is that customers rent an area for storage. For the party that leases out the area, in this case Delta Terminal, the area is the limiting factor for the amount of how much can be let out to lease. Today Delta Terminal uses decision sup-port in the form of premises area and experience where goods should be placed and have no means to calculate where and how much goods that can be allocated to use as small space as possible. The purpose of this study was therefore to develop a data based tool that can be used as support in the decision process. To achieve the objective a mathematical model was developed to optimize how freight can be placed at different locations to use as small an area as possible and also be able to simulate changes. The model was tested by comparing the maximum amount of cargo during 2012 against optimization model solution based on the same freight and local data. The most common goods handled at Delta Terminal were bulk, big bags and EUR-pallets and were used in the optimization model. For those goods an approximation of the expected area and volume was made that gave the decision maker an expected volume capacity for each local and goods. The result showed with the optimized solution that one of the goods could be moved to another storage place which would release approximate 25 percent reduction in area compared to where the goods are placed today and also three of the local spaces were released. The result from simulation of the volume capacity of each goods and local can help in a decision situation if a given volume of goods will fit in the local space and thus help to adapt the local capacity against the goods volume. Theoretically the model works and could be implemented as a useful tool for decision-makers on issues related to optimization or simulation of surfaces. However, when implementing the optimization model it is important to validate and compare the model’s result against actual outcomes.

  • 9.
    Holmberg, Joakim
    et al.
    Linköpings Universitet.
    Lund, Marie
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering and Sustainable Development.
    A Musculoskeletal Full‐body Simulation of Cross‐Country Skiing2008In: Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology, ISSN 1754-3371, Vol. 222, no P1, p. 11-22Article in journal (Refereed)
    Abstract [en]

    This paper presents a measurement-driven, musculoskeletal, full-body simulation model for biomechanical analysis of the double-poling (DP) technique in cross-country skiing. DP is a fast and powerful full-body movement; therefore, it is interesting to examine whether inverse dynamics using static optimization is working for a musculoskeletal full-body model with high accelerations, a large range of motion, and realistic loads. An experiment was carried out to measure motion and pole force of a skier on a double-poling ergometer. Using the measurement data, a simulation model was implemented in the AnyBody Modeling System (AnyBody Technology A/S, Denmark). Experimental results of motion and pole force from the DP ergometer, and also simulation results of relative muscle force profiles, are presented. These results agree with results found in literature when the kinematics and external kinetics are similar. Consequently, it should be possible to use computer simulations of this type for cross-country skiing simulations. With a simulation model, it is possible to perform optimization studies and to ask and answer ‘what if’ questions. Solutions to such problems are not easy to obtain by traditional testing alone.

  • 10.
    Holmberg, Joakim
    et al.
    Linköpings Universitet.
    Lund, Marie
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Using Double‐Poling Simulations to Study the Load Distribution between Teres Major and Latissimus Dorsi2007In: Science and Nordic Skiing, Oxford: Meyer & Meyer Sport, 2007, p. 81-89Conference paper (Refereed)
  • 11.
    Johansson, Amandus
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Information Systems and Technology.
    Axelsson, Manfred
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Information Systems and Technology.
    Gustavsson, Klas
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Information Systems and Technology.
    Heuristic Approach of Exact Bin-Packing Model2017In: The IEEE International Conference on Industrial Engineering and Engineering Management (IEEM), IEEE, 2017, p. 1042-1046Conference paper (Refereed)
    Abstract [en]

    Bin packing problem has gained a wide interest in academia and in practice since the problems quickly becomes intractable as the problem grows. In this paper two models are compared: one model that generates exact solutions for bin packing problem and one that uses the same fundamental approach on the problem but extended with a heuristic combination of next-fit and a combinational best-fit. The results proves that the heuristic approach has competitive features of linearity as the problem grows, but still with satisfying optimums in the evaluated instances.

  • 12.
    Karbalaie, Abdolamir
    et al.
    KTH, Systemsäkerhet och organisation.
    Hamid Muhammed, Hamed
    KTH, Systemsäkerhet och organisation.
    Erlandsson, Björn-Erik
    KTH, Systemsäkerhet och organisation.
    Using Homo-Separation of Variables for Solving Systems of Nonlinear Fractional Partial Differential Equations2013In: International journal of mathematics and mathematical sciences, ISSN 0161-1712, E-ISSN 1687-0425, Vol. 2013, p. 8-Article in journal (Refereed)
    Abstract [en]

    A new method proposed and coined by the authors as the homo-separation of variables method is utilized to solve systems oflinear and nonlinear fractional partial differential equations (FPDEs). The new method is a combination of two well-establishedmathematical methods, namely, the homotopy perturbation method (HPM) and the separation of variables method. Whencompared to existing analytical and numerical methods, the method resulting from our approach shows that it is capable ofsimplifying the target problem at hand and reducing the computational load that is required to solve it, considerably.The efficiencyand usefulness of this new general-purposemethod is verified by several examples, where different systems of linear and nonlinearFPDEs are solved.

  • 13.
    Koolen, J H
    et al.
    Univ Bielefeld.
    Moulton, Vincent
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Maximal energy graphs2001In: Advances in Applied Mathematics, ISSN 0196-8858, E-ISSN 1090-2074, Vol. 26, no 1, p. 47-52Article in journal (Refereed)
    Abstract [en]

    Given a graph G, its energy E(G) is defined as the sum of the absolute values of the eigenvalues of G. The concept of the energy of a graph was introduced in the subject of chemistry by I. Gutman. due to its relevance to the total pi -elrctron energy of certain molecules. In this paper, we show that if G is a graph on n vertices, then E(G) less than or equal to (n/2)(1 + rootn) must hold, and we give an infinite family of graphs for which this bound is sharp.

  • 14.
    Lund, Marie
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering and Sustainable Development.
    Holmberg, Joakim
    Linköpings Universitet.
    Which are the Antagonists to the Pectoralis MajorMuscle in 4th Gear, Free‐style Technique, Cross‐Country Skiing?2008In: Science and Nordic Skiing, Oxford: Meyer & Meyer Sport, 2008, p. 110-118Conference paper (Refereed)
  • 15.
    Lund, Marie
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering and Sustainable Development.
    Ståhl, Fredrik
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering and Sustainable Development.
    Gulliksson, Mårten
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
    Regularity Aspects in Inverse Musculoskeletal Biomechanics2008In: NUMERICAL ANALYSIS AND APPLIED MATHEMATICS / [ed] Simos, TE; Psihoyios, G; Tsitouras, C, American Institute of Physics (AIP), 2008, p. 368-371Conference paper (Refereed)
    Abstract [en]

    Inverse simulations of musculoskeletal models computes the internal forces such as muscle and joint reaction forces, which are hard to measure, using the more easily measured motion and external forces as input data. Because of the difficulties of measuring muscle forces and joint reactions, simulations are hard to validate. One way of reducing errors for the simulations is to ensure that the mathematical problem is well-posed. This paper presents a study of regularity aspects for an inverse simulation method, often called forward dynamics or dynamical optimization, that takes into account both measurement errors and muscle dynamics. Regularity is examined for a test problem around the optimum using the approximated quadratic problem. The results shows improved rank by including a regularization term in the objective that handles the mechanical over-determinancy. Using the 3-element Hill muscle model the chosen regularization term is the norm of the activation. To make the problem full-rank only the excitation bounds should be included in the constraints. However, this results in small negative values of the activation which indicates that muscles are pushing and not pulling, which is unrealistic but the error maybe small enough to be accepted for specific applications. These results are a start to ensure better results of inverse musculoskeletal simulations from a numerical point of view.

  • 16.
    Lund Ohlsson, Marie
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
    New methods for movement technique development in cross-country skiing using mathematical models and simulation2009Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    This Licentiate Thesis is devoted to the presentation and discussion of some new contributions in applied mathematics directed towards scientific computing in sports engineering. It considers inverse problems of biomechanical simulations with rigid body musculoskeletal systems especially in cross-country skiing. This is a contrast to the main research on cross-country skiing biomechanics, which is based mainly on experimental testing alone. The thesis consists of an introduction and five papers. The introduction motivates the context of the papers and puts them into a more general framework. Two papers (D and E) consider studies of real questions in cross-country skiing, which are modelled and simulated. The results give some interesting indications, concerning these challenging questions, which can be used as a basis for further research. However, the measurements are not accurate enough to give the final answers. Paper C is a simulation study which is more extensive than paper D and E, and is compared to electromyography measurements in the literature. Validation in biomechanical simulations is difficult and reducing mathematical errors is one way of reaching closer to more realistic results. Paper A examines well-posedness for forward dynamics with full muscle dynamics. Moreover, paper B is a technical report which describes the problem formulation and mathematical models and simulation from paper A in more detail. Our new modelling together with the simulations enable new possibilities. This is similar to simulations of applications in other engineering fields, and need in the same way be handled with care in order to achieve reliable results. The results in this thesis indicate that it can be very useful to use mathematical modelling and numerical simulations when describing cross-country skiing biomechanics. Hence, this thesis contributes to the possibility of beginning to use and develop such modelling and simulation techniques also in this context.

  • 17.
    Lund Ohlsson, Marie
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering and Sustainable Development.
    Gulliksson, Mårten
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
    Least Squares Approach to Inverse Problems in Musculoskeletal Biomechanics2009Report (Other academic)
    Abstract [en]

    Inverse simulations of musculoskeletal models computes the internal forces such as muscle and joint reaction forces, which are hard to measure, using the more easily measured motion and external forces as input data. Because of the difficulties of measuring muscle forces and joint reactions, simulations are hard to validate. One way of reducing errors for the simulations is to ensure that the mathematical problem is well-posed. This paper presents a study of regularity aspects for an inverse simulation method, often called forward dynamics or dynamical optimization, that takes into account both measurement errors and muscle dynamics. The simulation method is explained in detail. Regularity is examined for a test problem around the optimum using the approximated quadratic problem. The results shows improved rank by including a regularization term in the objective that handles the mechanical over-determinancy. Using the 3-element Hill muscle model the chosen regularization term is the norm of the activation. To make the problem full-rank only the excitation bounds should be included in the constraints. However, this results in small negative values of the activation which indicates that muscles are pushing and not pulling. Despite this unrealistic behavior the error maybe small enough to be accepted for specific applications. These results is a starting point start for achieving better results of inverse musculoskeletal simulations from a numerical point of view.

  • 18.
    Neuman, Magnus
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
    Coppel, Ludovic
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
    Edström, Per
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
    Point spreading in turbid media with anisotropic single scattering2011In: Optics Express, ISSN 1094-4087, E-ISSN 1094-4087, Vol. 19, no 3, p. 1915-1920Article in journal (Refereed)
    Abstract [en]

    Point spreading is investigated using general radiative transfer theory. We find that the single scattering anisotropy plays a significant role for point spreading together with the medium mean free path, single scattering albedo and thickness. When forward scattering dominates, the light will on average undergo more scattering events to give a specific optical response in reflectance measurements. This will significantly increase point spreading if the medium is low absorbing with large mean free path. Any fundamental and generic model of point spreading must capture the dependence on all of these medium characteristics.

  • 19.
    Neuman, Magnus
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences.
    Edvardsson, Sverker
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences.
    Edström, Per
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences.
    Solving the radiative transfer equation with a mathematical particle method2015In: Optics Letters, ISSN 0146-9592, E-ISSN 1539-4794, Vol. 40, no 18, p. 4325-4328Article in journal (Refereed)
    Abstract [en]

    We solve the radiative transfer equation (RTE) using a recently proposed mathematical particle method, originally developed for solving general functional equations. We show that, in the case of the RTE, it gives several advantages, such as handling arbitrary boundary conditions and phase functions and avoiding numerical instability in strongly forward-scattering media. We also solve the RTE, including fluorescence, and an example is shown with a fluorescence cascade where light is absorbed and emitted in several steps. We show that the evaluated particle method is straightforward to implement, which is in contrast with many traditional RTE solvers, but a potential drawback is the tuning of the method parameters.

  • 20.
    Strimmer, K
    et al.
    Department of Zoology, University of Oxford, Oxford, United Kingdom.
    Wiuf, C
    Department of Statistics, University of Oxford, Oxford, United Kingdom.
    Moulton, Vincent
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Recombination analysis using directed graphical models2001In: Molecular biology and evolution, ISSN 0737-4038, E-ISSN 1537-1719, Vol. 18, no 1, p. 97-99Article in journal (Other academic)
1 - 20 of 20
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