maintenance model for systems with phase-type distributed times to failure

Magdeburg, Univ., Fak. für Mathematik, Diss., 2010

Interpolatory methods for model reduction of large-scale dynamical systems

Magdeburg, Univ., Fak. für Mathematik, Diss., 2013

Statistical model identification : dynamical processes and large-scale networks in systems biology

Magdeburg, Univ., Fak. für Verfahrens- und Systemtechnik, Diss., 2014

Statistical model identification : dynamical processes and large-scale networks in systems biology

Magdeburg, Univ., Fak. für Verfahrens- und Systemtechnik, Diss., 2014

Computational methods for model reduction of large-scale sparse structured descriptor systems

Magdeburg, Univ., Fak. für Mathematik, Diss., 2015

Bilinear H 2-optimal Model Order-Reduction with applications to thermal parametric systems

Magdeburg, Univ., Fak. für Mathematik, Diss., 2015

Line-fitting method of model order reduction for elastic multibody systems

Magdeburg, Univ., Fak. für Maschinenbau, Diss., 2015

A hierarchical approach to model parameter optimization for developmental systems.

In the context of Systems Biology, computer simulations of gene regulatory networks provide a powerful tool to validate hypotheses and to explore possible system behaviors. Nevertheless, modeling a system poses some challenges of its own: especially the step of model calibration is often difficult due to insufficient data. For example when considering developmental systems, mostly qualitative data describing the developmental trajectory is available while common calibration techniques rely on high-resolution quantitative data. Focusing on the calibration of differential equation models for developmental systems, this study investigates different approaches to utilize the available data to overcome these difficulties. More specifically, the fact that developmental processes are hierarchically organized is exploited to increase convergence rates of the calibration process as well as to save computation time. Using a gene regulatory network model for stem cell homeostasis in Arabidopsis thaliana the performance of the different investigated approaches is evaluated, documenting considerable gains provided by the proposed hierarchical approach.

Estimation of electronic coupling in π -stacked donor-bridge-acceptor systems: correction of the two-state model

Comparison of donor-acceptor electronic couplings calculated within two-state and three-state models suggests that the two-state treatment can provide unreliable estimates of Vda because of neglecting the multistate effects. We show that in most cases accurate values of the electronic coupling in a π stack, where donor and acceptor are separated by a bridging unit, can be obtained as Ṽ da = (E2 - E1) μ12 Rda + (2 E3 - E1 - E2) 2 μ13 μ23 Rda2, where E1, E2, and E3 are adiabatic energies of the ground, charge-transfer, and bridge states, respectively, μij is the transition dipole moments between the states i and j, and Rda is the distance between the planes of donor and acceptor. In this expression based on the generalized Mulliken-Hush approach, the first term corresponds to the coupling derived within a two-state model, whereas the second term is the superexchange correction accounting for the bridge effect. The formula is extended to bridges consisting of several subunits. The influence of the donor-acceptor energy mismatch on the excess charge distribution, adiabatic dipole and transition moments, and electronic couplings is examined. A diagnostic is developed to determine whether the two-state approach can be applied. Based on numerical results, we showed that the superexchange correction considerably improves estimates of the donor-acceptor coupling derived within a two-state approach. In most cases when the two-state scheme fails, the formula gives reliable results which are in good agreement (within 5%) with the data of the three-state generalized Mulliken-Hush model

Comparison of the polynomial model against explicit measurements of noise components for different mammography systems.

Given the adverse impact of image noise on the perception of important clinical details in digital mammography, routine quality control measurements should include an evaluation of noise. The European Guidelines, for example, employ a second-order polynomial fit of pixel variance as a function of detector air kerma (DAK) to decompose noise into quantum, electronic and fixed pattern (FP) components and assess the DAK range where quantum noise dominates. This work examines the robustness of the polynomial method against an explicit noise decomposition method. The two methods were applied to variance and noise power spectrum (NPS) data from six digital mammography units. Twenty homogeneously exposed images were acquired with PMMA blocks for target DAKs ranging from 6.25 to 1600 µGy. Both methods were explored for the effects of data weighting and squared fit coefficients during the curve fitting, the influence of the additional filter material (2 mm Al versus 40 mm PMMA) and noise de-trending. Finally, spatial stationarity of noise was assessed.Data weighting improved noise model fitting over large DAK ranges, especially at low detector exposures. The polynomial and explicit decompositions generally agreed for quantum and electronic noise but FP noise fraction was consistently underestimated by the polynomial method. Noise decomposition as a function of position in the image showed limited noise stationarity, especially for FP noise; thus the position of the region of interest (ROI) used for noise decomposition may influence fractional noise composition. The ROI area and position used in the Guidelines offer an acceptable estimation of noise components. While there are limitations to the polynomial model, when used with care and with appropriate data weighting, the method offers a simple and robust means of examining the detector noise components as a function of detector exposure.

Influence of the driving mechanism on the response of systems with athermal dynamics: The example of the random-field Ising model

We investigate the influence of the driving mechanism on the hysteretic response of systems with athermal dynamics. In the framework of local mean-field theory at finite temperature (but neglecting thermally activated processes), we compare the rate-independent hysteresis loops obtained in the random field Ising model when controlling either the external magnetic field H or the extensive magnetization M. Two distinct behaviors are observed, depending on disorder strength. At large disorder, the H-driven and M-driven protocols yield identical hysteresis loops in the thermodynamic limit. At low disorder, when the H-driven magnetization curve is discontinuous (due to the presence of a macroscopic avalanche), the M-driven loop is reentrant while the induced field exhibits strong intermittent fluctuations and is only weakly self-averaging. The relevance of these results to the experimental observations in ferromagnetic materials, shape memory alloys, and other disordered systems is discussed.

Mean field model for spatially extended systems in the presence of multiplicative noise

We present a mean field model that describes the effect of multiplicative noise in spatially extended systems. The model can be solved analytically. For the case of the phi4 potential it predicts that the phase transition is shifted. This conclusion is supported by numerical simulations of this model in two dimensions.

Exact lower bounds to the ground-state energy of spin systems: The two-dimensional S=1/2 antiferromagnetic Heisenberg model

We present a very simple but fairly unknown method to obtain exact lower bounds to the ground-state energy of any Hamiltonian that can be partitioned into a sum of sub-Hamiltonians. The technique is applied, in particular, to the two-dimensional spin-1/2 antiferromagnetic Heisenberg model. Reasonably good results are easily obtained and the extension of the method to other systems is straightforward.

Magnetic relaxation of a one-dimensional model for small particle systems with dipolar interactions: Monte Carlo simulation

Atribution as a function of the time are analyzed and this study leads to a deeper knowledge of the microscopic processes involved in the magnetic relaxation