Comparison of the performance and reliability between improved sampling strategies for polynomial chaos expansion

As uncertainty and sensitivity analysis of complex models grows ever more important, the difficulty of their timely realizations highlights a need for more efficient numerical operations. Non-intrusive Polynomial Chaos methods are highly efficient and accurate methods of mapping input-output relationships to investigate complex models. There is substantial potential to increase the efficacy of the method regarding the selected sampling scheme. We examine state-of-the-art sampling schemes categorized in space-filling-optimal designs such as Latin Hypercube sampling and L1-optimal sampling and compare their empirical performance against standard random sampling. The analysis was performed in the context of L1 minimization using the least-angle regression algorithm to fit the GPCE regression models. Due to the random nature of the sampling schemes, we compared different sampling approaches using statistical stability measures and evaluated the success rates to construct a surrogate model with relative errors of < 0.1 %, < 1 %, and < 10 %, respectively. The sampling schemes are thoroughly investigated by evaluating the y of surrogate models constructed for various distinct test cases, which represent different problem classes covering low, medium and high dimensional problems. Finally, the sampling schemes are tested on an application example to estimate the sensitivity of the self-impedance of a probe that is used to measure the impedance of biological tissues at different frequencies. We observed strong differences in the convergence properties of the methods between the analyzed test functions

In situ impedance measurements on postmortem porcine brain

The paper presents an experimental study where the distinctness of grey and white matter of an in situ postmortem porcine brain by impedance measurements is investigated. Experimental conditions that would allow to conduct the same experiment on in vivo human brain tissue are replicated

A principled approach to conductivity uncertainty analysis in electric field calculations

Uncertainty surrounding ohmic tissue conductivity impedes accurate calculation of the electric fields generated by non-invasive brain stimulation. We present an efficient and generic technique for uncertainty and sensitivity analyses, which quantifies the reliability of field estimates and identifies the most influential parameters. For this purpose, we employ a non-intrusive generalized polynomial chaos expansion to compactly approximate the multidimensional dependency of the field on the conductivities. We demonstrate that the proposed pipeline yields detailed insight into the uncertainty of field estimates for transcranial magnetic stimulation (TMS) and transcranial direct current stimulation (tDCS), identifies the most relevant tissue conductivities, and highlights characteristic differences between stimulation methods. Specifically, we test the influence of conductivity variations on (i) the magnitude of the electric field generated at each gray matter location, (ii) its normal component relative to the cortical sheet, (iii) its overall magnitude (indexed by the 98th percentile), and (iv) its overall spatial distribution. We show that TMS fields are generally less affected by conductivity variations than tDCS fields. For both TMS and tDCS, conductivity uncertainty causes much higher uncertainty in the magnitude as compared to the direction and overall spatial distribution of the electric field. Whereas the TMS fields were predominantly influenced by gray and white matter conductivity, the tDCS fields were additionally dependent on skull and scalp conductivities. Comprehensive uncertainty analyses of complex systems achieved by the proposed technique are not possible with classical methods, such as Monte Carlo sampling, without extreme computational effort. In addition, our method has the advantages of directly yielding interpretable and intuitive output metrics and of being easily adaptable to new problems

1 Subversive Game Design for Recursive Learning

How are players &apos; expectations challenged through subverting common design patterns in digital games? The following paper outlines a game design experiment that combines state of the art learning research with game design. The goal of the game project is to explore how subversive design patterns can be created that force the players to rethink their expectations and interpretations. In the developed game Afterland various paradigm shifts subvert common gameplay patterns in order to encourage players to modify their anticipations. This is designed to provoke a corresponding paradigm shift in the players, forcing them to reassess certain expectations and to adopt new mental models, strategies, and goals other than those commonly found in games of this genre. The paper introduces recursive learning as a theoretical foundation for the game design process and offers constructive insight derived from this particular research-based game design project conducted at the Singapore-MIT GAMBIT Game Lab

Uncertainty quantification in transcranial magnetic stimulation with correlation between tissue conductivities

The uncertainty quantification problem in Transcranial Magnetic Stimulation is solved by means of a realistic head model and considering the statistical correlation between grey matter and white matter electrical conductivities. The fast model order reduction approach, introduced by the authors, is extended here to the general case of correlated random parameters. Numerical results prove that correlations between tissue conductivities must be taken into account since their impact on the probability density function of the induced electric field is relevant