Fraunhofer Chalmers Research Center for Industrial Mathematics

Göteborg, Sweden

Fraunhofer Chalmers Research Center for Industrial Mathematics

Göteborg, Sweden
SEARCH FILTERS
Time filter
Source Type

Karlsson J.,Fraunhofer Chalmers Research Center for Industrial Mathematics | Ericsson A.,Lund University | Astrom K.,Lund University
Springer Proceedings in Mathematics | Year: 2012

In Statistical Shape Modeling, a dense correspondence between the shapes in the training set must be established. Traditionally this has been done by hand, a process that commonly requires a lot of work and is difficult, especially in 3D. In recent years there has been a lot of work on automatic construction of Shape Models. In recent papers (Davies et al., Medical Image Computing and Computer-Assisted Intervention MICCAI'2001, pp. 57-65, 2001; Davies et al., IEEE Trans. Med. Imaging. 21(5):525-537 2002; Kotcheff and Taylor, Med. Image Anal. 2:303-314 1998) Minimum Description Length, (MDL), is used to locate a dense correspondence between shapes. In this paper the gradient of the description length is derived. Using the gradient, MDL is optimised using steepest descent. The optimisation is therefore faster and experiments show that the resulting models are better. To characterise shape properties that are invariant to similarity transformations, it is first necessary to normalise with respect to the similarity transformations. This is normally done using Procrustes analysis. In this paper we propose to align shapes using the MDL criterion. The MDL based algorithm is compared to Procrustes on a number of data sets. It is concluded that there is improvement in generalisation when using MDL to align the shapes. In this paper novel theory to prevent the commonly occurring problem of clustering under correspondence optimisation is also presented. The problem is solved by calculating the covariance matrix of the shapes using a scalar product that is invariant to mutual reparameterisations. An algorithm for implementing the ideas is proposed and compared to Thodberg's state of the art algorithm for automatic shape modeling. The suggested algorithm is more stable and the resulting models are of higher quality according to the generalisation measure and according to visual inspection of the specificity. © Springer-Verlag Berlin Heidelberg 2012.


Raue A.,Albert Ludwigs University of Freiburg | Raue A.,Merrimack Pharmaceutical Inc. | Karlsson J.,Fraunhofer Chalmers Research Center for Industrial Mathematics | Saccomani M.P.,University of Padua | And 2 more authors.
Bioinformatics | Year: 2014

Motivation: Modeling of dynamical systems using ordinary differential equations is a popular approach in the field of Systems Biology. The amount of experimental data that are used to build and calibrate these models is often limited. In this setting, the model parameters may not be uniquely determinable. Structural or a priori identifiability is a property of the system equations that indicates whether, in principle, the unknown model parameters can be determined from the available data. Results: We performed a case study using three current approaches for structural identifiability analysis for an application from cell biology. The approaches are conceptually different and are developed independently. The results of the three approaches are in agreement. We discuss strength and weaknesses of each of them and illustrate how they can be applied to real world problems. © The Author 2014.


Sunnaker M.,Fraunhofer Chalmers Research Center for Industrial Mathematics | Schmidt H.,Fraunhofer Chalmers Research Center for Industrial Mathematics | Jirstrand M.,Fraunhofer Chalmers Research Center for Industrial Mathematics | Cedersund G.,Fraunhofer Chalmers Research Center for Industrial Mathematics | And 3 more authors.
BMC Systems Biology | Year: 2010

Background: Systems biology models tend to become large since biological systems often consist of complex networks of interacting components, and since the models usually are developed to reflect various mechanistic assumptions of those networks. Nevertheless, not all aspects of the model are equally interesting in a given setting, and normally there are parts that can be reduced without affecting the relevant model performance. There are many methods for model reduction, but few or none of them allow for a restoration of the details of the original model after the simplified model has been simulated.Results: We present a reduction method that allows for such a back-translation from the reduced to the original model. The method is based on lumping of states, and includes a general and formal algorithm for both determining appropriate lumps, and for calculating the analytical back-translation formulas. The lumping makes use of efficient methods from graph-theory and ε{lunate}-decomposition and is derived and exemplified on two published models for fluorescence emission in photosynthesis. The bigger of these models is reduced from 26 to 6 states, with a negligible deviation from the reduced model simulations, both when comparing simulations in the states of the reduced model and when comparing back-translated simulations in the states of the original model. The method is developed in a linear setting, but we exemplify how the same concepts and approaches can be applied to non-linear problems. Importantly, the method automatically provides a reduced model with back-translations. Also, the method is implemented as a part of the systems biology toolbox for matlab, and the matlab scripts for the examples in this paper are available in the supplementary material.Conclusions: Our novel lumping methodology allows for both automatic reduction of states using lumping, and for analytical retrieval of the original states and parameters without performing a new simulation. The two models can thus be considered as two degrees of zooming of the same model. This is a conceptually new development of model reduction approaches, which we think will stimulate much further research and will prove to be very useful in future modelling projects. © 2010 Sunnåker et al; licensee BioMed Central Ltd.


Sunnaker M.,Fraunhofer Chalmers Research Center for Industrial Mathematics | Sunnaker M.,ETH Zurich | Cedersund G.,Linköping University | Cedersund G.,Albert Ludwigs University of Freiburg | And 2 more authors.
BMC Systems Biology | Year: 2011

Background: Models of biochemical systems are typically complex, which may complicate the discovery of cardinal biochemical principles. It is therefore important to single out the parts of a model that are essential for the function of the system, so that the remaining non-essential parts can be eliminated. However, each component of a mechanistic model has a clear biochemical interpretation, and it is desirable to conserve as much of this interpretability as possible in the reduction process. Furthermore, it is of great advantage if we can translate predictions from the reduced model to the original model.Results: In this paper we present a novel method for model reduction that generates reduced models with a clear biochemical interpretation. Unlike conventional methods for model reduction our method enables the mapping of predictions by the reduced model to the corresponding detailed predictions by the original model. The method is based on proper lumping of state variables interacting on short time scales and on the computation of fraction parameters, which serve as the link between the reduced model and the original model. We illustrate the advantages of the proposed method by applying it to two biochemical models. The first model is of modest size and is commonly occurring as a part of larger models. The second model describes glucose transport across the cell membrane in baker's yeast. Both models can be significantly reduced with the proposed method, at the same time as the interpretability is conserved.Conclusions: We introduce a novel method for reduction of biochemical models that is compatible with the concept of zooming. Zooming allows the modeler to work on different levels of model granularity, and enables a direct interpretation of how modifications to the model on one level affect the model on other levels in the hierarchy. The method extends the applicability of the method that was previously developed for zooming of linear biochemical models to nonlinear models. © 2011 Sunnåker et al; licensee BioMed Central Ltd.


Mark A.,Design Science | Bohlin R.,Fraunhofer Chalmers Research Center for Industrial Mathematics | Segerdahl D.,Fraunhofer Chalmers Research Center for Industrial Mathematics | Edelvik F.,Design Science | Carlson J.S.,Fraunhofer Chalmers Research Center for Industrial Mathematics
International Journal of Manufacturing Research | Year: 2014

Application of sealing materials is done in order to prevent water leakage into cavities of the car body, and to reduce noise. The complexity of the sealing spray process is characterised by multi-phase and free surface flows, multi-scale phenomena, and large moving geometries, which poses great challenges for mathematical modelling and simulation. The aim of this paper is to present a novel framework that includes detailed process simulation and automatic generation of collision free robot paths. To verify the simulations, the resulting width, thickness and shape of applied material on test plates as a function of time and spraying distance have been compared to experiments. The agreement is in general very good. The efficient implementation makes it possible to simulate application of one meter of sealing material in less than an hour on a standard computer, and it is therefore feasible to include such detailed simulations in the production preparation process and off-line programming of the sealing robots.Copyright © 2014 Inderscience Enterprises Ltd.


Jakobsson S.,Fraunhofer Chalmers Research Center for Industrial Mathematics | Patriksson M.,Chalmers University of Technology | Patriksson M.,Gothenburg University | Rudholm J.,Chalmers University of Technology | And 3 more authors.
Optimization and Engineering | Year: 2010

We propose an algorithm for the global optimization of expensive and noisy black box functions using a surrogate model based on radial basis functions (RBFs). A method for RBF-based approximation is introduced in order to handle noise. New points are selected to minimize the total model uncertainty weighted against the surrogate function value. The algorithm is extended to multiple objective functions by instead weighting against the distance to the surrogate Pareto front; it therefore constitutes the first algorithm for expensive, noisy and multiobjective problems in the literature. Numerical results on analytical test functions show promise in comparison to other (commercial) algorithms, as well as results from a simulation based optimization problem. © 2009 Springer Science+Business Media, LLC.


Mark A.,Fraunhofer Chalmers Research Center for Industrial Mathematics | Svenning E.,Fraunhofer Chalmers Research Center for Industrial Mathematics | Edelvik F.,Fraunhofer Chalmers Research Center for Industrial Mathematics
International Journal of Heat and Mass Transfer | Year: 2013

In this work, the hybrid immersed boundary method is extended with immersed boundary conditions for the temperature field. The method is used to couple the flow solver with a shell heat transfer solver. The coupling back to the shell is handled by a heat source, calculated from Fourier's law. Natural convection in a square cavity with and without a hot circular cylinder, and free air cooling of an electrically heated plate are studied. For all cases an excellent agreement with numerical and experimental data is obtained. The proposed method is very well suited for many industrial applications involving natural convection. © 2012 Elsevier Ltd. All rights reserved.


Voronov A.,Chalmers University of Technology | Akesson K.,Chalmers University of Technology | Ekstedt F.,Fraunhofer Chalmers Research Center for Industrial Mathematics
CEUR Workshop Proceedings | Year: 2011

Models of configurable products can have hundreds of variables and thousands of configuration constraints. A product engineer usually has a limited responsibility area, and thus is interested in only a small subset of the variables that are relevant to the responsibility area. It is important for the engineer to have an overview of possible products with respect to the responsibility area, with all irrelevant information omitted. Configurations with some variables omitted we will call partial configurations, and we will call a partial configuration valid if it can be extended to a complete configuration satisfying all configuration constraints. In this paper we consider exact ways to compute valid partial configurations: we present two new algorithms based on Boolean satisfiability solvers, as well as ways to use knowledge compilation methods (Binary Decision Diagrams and Decomposable Negation Normal Form) to compute valid partial configurations. We also show that the proposed methods are feasible on configuration data from two automotive companies.


Karlsson J.,Fraunhofer Chalmers Research Center for Industrial Mathematics | Anguelova M.,Imego AB | Jirstrand M.,Fraunhofer Chalmers Research Center for Industrial Mathematics
IFAC Proceedings Volumes (IFAC-PapersOnline) | Year: 2012

Ordinary differential equation models often contain a large number of parameters that must be determined from measurements by parameter estimation. For a parameter estimation procedure to be successful, there must be a unique set of parameters that can have produced the measured data. This is not the case if a model is not structurally identifiable with the given set of outputs selected as measurements. We describe the implementation of a recent probabilistic semi-numerical method for testing local structural identifiability based on computing the rank of a numerically instantiated Jacobian matrix (observability/identifiability matrix). To obtain this, matrix parameters and initial conditions are specialized to random integer numbers, inputs are specialized to truncated random integer coefficient power series, and the corresponding output of the state space system is computed in terms of a truncated power series, which then is utilized to calculate the elements of a Jacobian matrix. To reduce the memory requirements and increase the speed of the computations all operations are done modulo a large prime number. The method has been extended to handle parametrized initial conditions and is demonstrated to be capable of handling systems in the order of a hundred state variables and equally many parameters on a standard desktop computer. © 2012 IFAC.


PubMed | Fraunhofer Chalmers Research Center for Industrial Mathematics
Type: | Journal: BMC systems biology | Year: 2011

Models of biochemical systems are typically complex, which may complicate the discovery of cardinal biochemical principles. It is therefore important to single out the parts of a model that are essential for the function of the system, so that the remaining non-essential parts can be eliminated. However, each component of a mechanistic model has a clear biochemical interpretation, and it is desirable to conserve as much of this interpretability as possible in the reduction process. Furthermore, it is of great advantage if we can translate predictions from the reduced model to the original model.In this paper we present a novel method for model reduction that generates reduced models with a clear biochemical interpretation. Unlike conventional methods for model reduction our method enables the mapping of predictions by the reduced model to the corresponding detailed predictions by the original model. The method is based on proper lumping of state variables interacting on short time scales and on the computation of fraction parameters, which serve as the link between the reduced model and the original model. We illustrate the advantages of the proposed method by applying it to two biochemical models. The first model is of modest size and is commonly occurring as a part of larger models. The second model describes glucose transport across the cell membrane in bakers yeast. Both models can be significantly reduced with the proposed method, at the same time as the interpretability is conserved.We introduce a novel method for reduction of biochemical models that is compatible with the concept of zooming. Zooming allows the modeler to work on different levels of model granularity, and enables a direct interpretation of how modifications to the model on one level affect the model on other levels in the hierarchy. The method extends the applicability of the method that was previously developed for zooming of linear biochemical models to nonlinear models.

Loading Fraunhofer Chalmers Research Center for Industrial Mathematics collaborators
Loading Fraunhofer Chalmers Research Center for Industrial Mathematics collaborators