Testing Nelder-Mead based repulsion algorithms for multiple roots of nonlinear systems via a two-level factorial design of experiments

This paper addresses the challenging task of computing multiple roots of a system of nonlinear equations. A repulsion algorithm that invokes the Nelder-Mead (N-M) local search method and uses a penalty-type merit function based on the error function, known as 'erf', is presented. In the N-M algorithm context, different strategies are proposed to enhance the quality of the solutions and improve the overall efficiency. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm.Fundação para a Ciência e Tecnologia (FCT

Exploiting Magnetic Resonance Angiography Imaging Improves Model Estimation of BOLD Signal

The change of BOLD signal relies heavily upon the resting blood volume fraction () associated with regional vasculature. However, existing hemodynamic data assimilation studies pretermit such concern. They simply assign the value in a physiologically plausible range to get over ill-conditioning of the assimilation problem and fail to explore actual . Such performance might lead to unreliable model estimation. In this work, we present the first exploration of the influence of on fMRI data assimilation, where actual within a given cortical area was calibrated by an MR angiography experiment and then was augmented into the assimilation scheme. We have investigated the impact of on single-region data assimilation and multi-region data assimilation (dynamic cause modeling, DCM) in a classical flashing checkerboard experiment. Results show that the employment of an assumed in fMRI data assimilation is only suitable for fMRI signal reconstruction and activation detection grounded on this signal, and not suitable for estimation of unobserved states and effective connectivity study. We thereby argue that introducing physically realistic in the assimilation process may provide more reliable estimation of physiological information, which contributes to a better understanding of the underlying hemodynamic processes. Such an effort is valuable and should be well appreciated