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Papers by Christian Klingenberg
SIAM Journal on Scientific Computing, 2015
Nonlinear Hyperbolic Equations — Theory, Computation Methods, and Applications, 1989
Nonlinear Hyperbolic Problems: Theoretical, Applied, and Computational Aspects, 1993
ABSTRACT For the one-dimensional scalar nonconvex conservation law u t +f(u) x =0 let f '... more ABSTRACT For the one-dimensional scalar nonconvex conservation law u t +f(u) x =0 let f ''' (u) have finitely many changes of sign. We show that if the initial data consists of finitely many constant states, the solution will be piecewise smooth with finitely many shock curves. Hence the same holds true for two-dimensional Riemann problems for the scalar equation u t +f(u) x +f(u) y =0.
The IMA Volumes in Mathematics and Its Applications, 1991
Oberwolfach Reports, 2000
The Mini-Workshop is concerned with the large-scale description of microscopic many-particle syst... more The Mini-Workshop is concerned with the large-scale description of microscopic many-particle systems with two or more conservation laws. This is topic of common interest for statistical mechanics, probability theory and PDE theory. The main difficulty lies in the proof of the hydrodynamic limit in terms of a system of (generically hyperbolic) PDE's which includes a proper treatment of shock and boundary discontinuities that result from the microscopic dynamics. Moreover, fundamental properties of current-carrying stationary states of such systems (which are not Gibbs states) are studied in terms of fluctuations of macroscopic quantities. Many powerful tools developed for particle systems (or PDE's respectively) with one conservation law have no obvious generalization to systems with two or more conservation laws and hence new mathematical ideas need to be developed. : 35L65, 60K35, 82C22.
Astronomische Nachrichten, 2007
ABSTRACT E119 3D Simulations of Weakly Magnetized Accretion DisksE147 The MRI in stratified accre... more ABSTRACT E119 3D Simulations of Weakly Magnetized Accretion DisksE147 The MRI in stratified accretion discsE212 Comparison between observed and simulated globular clustersE219 Presentation of simulation results of our 3D PIC CodeE244 MAGMA: A 3D Lagrangian hydrodynamics codeE254 FEARLESS – A new modelling approach for turbulent astrophysical flowsE256 Cosmic ray transport in MHD turbulence: Numerical calculation of Dμμ(μ) and Dμμ(p)E261 FEARLESS modeling of turbulent flows applied to numerical simulations of galaxy clustersE264 FEARLESS – Subgrid Scale Turbulence modeling and Applications to Star Formation
Acta Mathematica Scientia, 2009
Based on the framework introduced in [4] or [5], the singular limits of stiff relaxation and domi... more Based on the framework introduced in [4] or [5], the singular limits of stiff relaxation and dominant diffusion for the Cauchy problem of inhomogeneous equations of elasticity is studied. We are able to reach equilibrium even though the nonlinear stress term is not strictly increasing.
ABSTRACT This document provides a general idea of what edge-detection is and how it works e.g. fo... more ABSTRACT This document provides a general idea of what edge-detection is and how it works e.g. for computer vision etc., edge detectors are often operated with arbitrary parameters such as thresholds. Determining the significant values for these parameters on a trial and error basis may be a problem. It is therefore beneficial to try to understand edge-detection in terms of established quantitative methods. Here we show how the idea of an Hypothesis test can be used for significance testing and that provided there is the same null hypothesis distribution everywhere in an image, applying Hypothesis testing is the same as thresholding. We show how the method of error propagation can be used to find out if we have uniform noise on a feature enhancement. We apply this analysis to the Canny algorithm for detection of step edges. We explain that for other than step edges this algorithm needs modification and how this can be done while staying within the overall framework for the detection of connected features via non-maximal suppression and hysteresis thresholding. The DoG is a linear filter which has the required properties for algorithmic stability, and can be used for the detection of ridge structures. The orientation of the ridge is defined for this process as the direction of maximum second derivative. This ridge detector is then evaluated for the task of fly wing analysis, by looking at the specific characteristics of noise and scale stability.
Systematic Biology, Dec 1, 1991
Abstract.Multivariate methods for "size correction," such as shearing or multi... more Abstract.Multivariate methods for "size correction," such as shearing or multiple-group principal component analysis, assume that the groups under consideration share a common allometric growth pattern. However, this assumption has rarely been tested empirically. A variety of ...
Genetics, Feb 1, 2001
This study introduces a new multivariate approach for analyzing the effects of quantitative trait... more This study introduces a new multivariate approach for analyzing the effects of quantitative trait loci (QTL) on shape and demonstrates this method for the mouse mandible. We quantified size and shape with the methods of geometric morphometrics, based on Procrustes superimposition of five morphological landmarks recorded on each mandible. Interval mapping for F 2 mice originating from an intercross of the LG/J and SM/J inbred strains revealed 12 QTL for size, 25 QTL for shape, and 5 QTL for left-right asymmetry. Multivariate ordination of QTL effects by principal component analysis identified two recurrent features of shape variation, which involved the positions of the coronoid and angular processes relative to each other and to the rest of the mandible. These patterns are reminiscent of the knockout phenotypes of a number of genes involved in mandible development, although only a few of these are possible candidates for QTL in our study. The variation of shape effects among the QTL showed no evidence of clustering into distinct groups, as would be expected from theories of morphological integration. Further, for most QTL, additive and dominance effects on shape were markedly different, implying overdominance for specific features of shape. We conclude that geometric morphometrics offers a promising new approach to address problems at the interface of evolutionary and developmental genetics.
Mathematics of Computation, 2015
Journal of evolutionary biology, 2014
The evolution of acoustic behaviour and that of the morphological traits mediating its production... more The evolution of acoustic behaviour and that of the morphological traits mediating its production are often coupled. Lack of variation in the underlying morphology of signalling traits has the potential to constrain signal evolution. This relationship is particularly likely in field crickets, where males produce acoustic advertisement signals to attract females by stridulating with specialized structures on their forewings. In this study, we characterize the size and geometric shape of the forewings of males from six allopatric populations of the black field cricket (Teleogryllus commodus) known to have divergent advertisement calls. We sample from each of these populations using both wild-caught and common-garden-reared cohorts, allowing us to test for multivariate relationships between wing morphology and call structure. We show that the allometry of shape has diverged across populations. However, there was a surprisingly small amount of covariation between wing shape and call str...
Genetics, 2001
This study introduces a new multivariate approach for analyzing the effects of quantitative trait... more This study introduces a new multivariate approach for analyzing the effects of quantitative trait loci (QTL) on shape and demonstrates this method for the mouse mandible. We quantified size and shape with the methods of geometric morphometrics, based on Procrustes superimposition of five morphological landmarks recorded on each mandible. Interval mapping for F(2) mice originating from an intercross of the LG/J and SM/J inbred strains revealed 12 QTL for size, 25 QTL for shape, and 5 QTL for left-right asymmetry. Multivariate ordination of QTL effects by principal component analysis identified two recurrent features of shape variation, which involved the positions of the coronoid and angular processes relative to each other and to the rest of the mandible. These patterns are reminiscent of the knockout phenotypes of a number of genes involved in mandible development, although only a few of these are possible candidates for QTL in our study. The variation of shape effects among the QT...
SIAM Journal on Scientific Computing, 2015
Nonlinear Hyperbolic Equations — Theory, Computation Methods, and Applications, 1989
Nonlinear Hyperbolic Problems: Theoretical, Applied, and Computational Aspects, 1993
ABSTRACT For the one-dimensional scalar nonconvex conservation law u t +f(u) x =0 let f '... more ABSTRACT For the one-dimensional scalar nonconvex conservation law u t +f(u) x =0 let f ''' (u) have finitely many changes of sign. We show that if the initial data consists of finitely many constant states, the solution will be piecewise smooth with finitely many shock curves. Hence the same holds true for two-dimensional Riemann problems for the scalar equation u t +f(u) x +f(u) y =0.
The IMA Volumes in Mathematics and Its Applications, 1991
Oberwolfach Reports, 2000
The Mini-Workshop is concerned with the large-scale description of microscopic many-particle syst... more The Mini-Workshop is concerned with the large-scale description of microscopic many-particle systems with two or more conservation laws. This is topic of common interest for statistical mechanics, probability theory and PDE theory. The main difficulty lies in the proof of the hydrodynamic limit in terms of a system of (generically hyperbolic) PDE's which includes a proper treatment of shock and boundary discontinuities that result from the microscopic dynamics. Moreover, fundamental properties of current-carrying stationary states of such systems (which are not Gibbs states) are studied in terms of fluctuations of macroscopic quantities. Many powerful tools developed for particle systems (or PDE's respectively) with one conservation law have no obvious generalization to systems with two or more conservation laws and hence new mathematical ideas need to be developed. : 35L65, 60K35, 82C22.
Astronomische Nachrichten, 2007
ABSTRACT E119 3D Simulations of Weakly Magnetized Accretion DisksE147 The MRI in stratified accre... more ABSTRACT E119 3D Simulations of Weakly Magnetized Accretion DisksE147 The MRI in stratified accretion discsE212 Comparison between observed and simulated globular clustersE219 Presentation of simulation results of our 3D PIC CodeE244 MAGMA: A 3D Lagrangian hydrodynamics codeE254 FEARLESS – A new modelling approach for turbulent astrophysical flowsE256 Cosmic ray transport in MHD turbulence: Numerical calculation of Dμμ(μ) and Dμμ(p)E261 FEARLESS modeling of turbulent flows applied to numerical simulations of galaxy clustersE264 FEARLESS – Subgrid Scale Turbulence modeling and Applications to Star Formation
Acta Mathematica Scientia, 2009
Based on the framework introduced in [4] or [5], the singular limits of stiff relaxation and domi... more Based on the framework introduced in [4] or [5], the singular limits of stiff relaxation and dominant diffusion for the Cauchy problem of inhomogeneous equations of elasticity is studied. We are able to reach equilibrium even though the nonlinear stress term is not strictly increasing.
ABSTRACT This document provides a general idea of what edge-detection is and how it works e.g. fo... more ABSTRACT This document provides a general idea of what edge-detection is and how it works e.g. for computer vision etc., edge detectors are often operated with arbitrary parameters such as thresholds. Determining the significant values for these parameters on a trial and error basis may be a problem. It is therefore beneficial to try to understand edge-detection in terms of established quantitative methods. Here we show how the idea of an Hypothesis test can be used for significance testing and that provided there is the same null hypothesis distribution everywhere in an image, applying Hypothesis testing is the same as thresholding. We show how the method of error propagation can be used to find out if we have uniform noise on a feature enhancement. We apply this analysis to the Canny algorithm for detection of step edges. We explain that for other than step edges this algorithm needs modification and how this can be done while staying within the overall framework for the detection of connected features via non-maximal suppression and hysteresis thresholding. The DoG is a linear filter which has the required properties for algorithmic stability, and can be used for the detection of ridge structures. The orientation of the ridge is defined for this process as the direction of maximum second derivative. This ridge detector is then evaluated for the task of fly wing analysis, by looking at the specific characteristics of noise and scale stability.
Systematic Biology, Dec 1, 1991
Abstract.Multivariate methods for "size correction," such as shearing or multi... more Abstract.Multivariate methods for "size correction," such as shearing or multiple-group principal component analysis, assume that the groups under consideration share a common allometric growth pattern. However, this assumption has rarely been tested empirically. A variety of ...
Genetics, Feb 1, 2001
This study introduces a new multivariate approach for analyzing the effects of quantitative trait... more This study introduces a new multivariate approach for analyzing the effects of quantitative trait loci (QTL) on shape and demonstrates this method for the mouse mandible. We quantified size and shape with the methods of geometric morphometrics, based on Procrustes superimposition of five morphological landmarks recorded on each mandible. Interval mapping for F 2 mice originating from an intercross of the LG/J and SM/J inbred strains revealed 12 QTL for size, 25 QTL for shape, and 5 QTL for left-right asymmetry. Multivariate ordination of QTL effects by principal component analysis identified two recurrent features of shape variation, which involved the positions of the coronoid and angular processes relative to each other and to the rest of the mandible. These patterns are reminiscent of the knockout phenotypes of a number of genes involved in mandible development, although only a few of these are possible candidates for QTL in our study. The variation of shape effects among the QTL showed no evidence of clustering into distinct groups, as would be expected from theories of morphological integration. Further, for most QTL, additive and dominance effects on shape were markedly different, implying overdominance for specific features of shape. We conclude that geometric morphometrics offers a promising new approach to address problems at the interface of evolutionary and developmental genetics.
Mathematics of Computation, 2015
Journal of evolutionary biology, 2014
The evolution of acoustic behaviour and that of the morphological traits mediating its production... more The evolution of acoustic behaviour and that of the morphological traits mediating its production are often coupled. Lack of variation in the underlying morphology of signalling traits has the potential to constrain signal evolution. This relationship is particularly likely in field crickets, where males produce acoustic advertisement signals to attract females by stridulating with specialized structures on their forewings. In this study, we characterize the size and geometric shape of the forewings of males from six allopatric populations of the black field cricket (Teleogryllus commodus) known to have divergent advertisement calls. We sample from each of these populations using both wild-caught and common-garden-reared cohorts, allowing us to test for multivariate relationships between wing morphology and call structure. We show that the allometry of shape has diverged across populations. However, there was a surprisingly small amount of covariation between wing shape and call str...
Genetics, 2001
This study introduces a new multivariate approach for analyzing the effects of quantitative trait... more This study introduces a new multivariate approach for analyzing the effects of quantitative trait loci (QTL) on shape and demonstrates this method for the mouse mandible. We quantified size and shape with the methods of geometric morphometrics, based on Procrustes superimposition of five morphological landmarks recorded on each mandible. Interval mapping for F(2) mice originating from an intercross of the LG/J and SM/J inbred strains revealed 12 QTL for size, 25 QTL for shape, and 5 QTL for left-right asymmetry. Multivariate ordination of QTL effects by principal component analysis identified two recurrent features of shape variation, which involved the positions of the coronoid and angular processes relative to each other and to the rest of the mandible. These patterns are reminiscent of the knockout phenotypes of a number of genes involved in mandible development, although only a few of these are possible candidates for QTL in our study. The variation of shape effects among the QT...