Time-varying effective EEG source connectivity: the optimization of model parameters*

Adaptive estimation methods based on general Kalman filter are powerful tools to investigate brain networks dynamics given the non-stationary nature of neural signals. These methods rely on two parameters, the model order p and adaptation constant c, which determine the resolution and smoothness of the time-varying multivariate autoregressive estimates. A sub-optimal filtering may present consistent biases in the frequency domain and temporal distortions, leading to fallacious interpretations. Thus, the performance of these methods heavily depends on the accurate choice of these two parameters in the filter design. In this work, we sought to define an objective criterion for the optimal choice of these parameters. Since residual- and information-based criteria are not guaranteed to reach an absolute minimum, we propose to study the partial derivatives of these functions to guide the choice of p and c. To validate the performance of our method, we used a dataset of human visual evoked potentials during face perception where the generation and propagation of information in the brain is well understood and a set of simulated data where the ground truth is available

Optimization-based comparison of different approaches for the automatized calculation of residual stresses and fiber orientations in arteries

Residual stresses and fiber orientations in arterial walls can be approximated by means of the simulation of growth and remodeling processes. In order to enable a comparison of different approaches of combined growth and remodeling in one framework, a method based on the optimization of model parameters is developed. The minimization of a mechano-biologically motivated objective function permits to evaluate the approaches with respect to their ability of effectively reducing stress peaks and stress inhomogeneities in the arterial wall. This examination is performed for a simplified, one-layered, rotationally symmetric arterial segment in order to enable the analysis of the fundamental mechanisms included in the individual model variants. Once the most probable growth mechanism is identified, multi-layered segments can be analyzed in more detail

Model selection and efficiency testing for normalization of cDNA microarray data

In this study we present two novel normalization schemes for cDNA microarrays. They are based on iterative local regression and optimization of model parameters by generalized cross-validation. Permutation tests assessing the efficiency of normalization demonstrated that the proposed schemes have an improved ability to remove systematic errors and to reduce variability in microarray data. The analysis also reveals that without parameter optimization local regression is frequently insufficient to remove systematic errors in microarray data

Optimal model parameters for multi-objective large-eddy simulations

A methodology is proposed for the assessment of error dynamics in large-eddy simulations. It is demonstrated that the optimization of model parameters with respect to one flow property can be obtained at the expense of the accuracy with which other flow properties are predicted. Therefore, an approach is introduced which allows to assess the total errors based on various flow properties simultaneously. We show that parameter settings exist, for which all monitored errors are "near optimal," and refer to such regions as "multi-objective optimal parameter regions." We focus on multi-objective errors that are obtained from weighted spectra, emphasizing both large- as well small-scale errors. These multi-objective optimal parameter regions depend strongly on the simulation Reynolds number and the resolution. At too coarse resolutions, no multi-objective optimal regions might exist as not all error-components might simultaneously be sufficiently small. The identification of multi-objective optimal parameter regions can be adopted to effectively compare different subgrid models. A comparison between large-eddy simulations using the Lilly-Smagorinsky model, the dynamic Smagorinsky model and a new Re-consistent eddy-viscosity model is made, which illustrates this. Based on the new methodology for error assessment the latter model is found to be the most accurate and robust among the selected subgrid models, in combination with the finite volume discretization used in the present study