Inverse transformed encoding models - A solution to the problem of correlated trial-by-trial parameter estimates in fMRI decoding

Techniques of multivariate pattern analysis (MVPA) can be used to decode the discrete experimental condition or a continuous modulator variable from measured brain activity during a particular trial. In functional magnetic resonance imaging (fMRI), trial-wise response amplitudes are sometimes estimated from the measured signal using a general linear model (GLM) with one onset regressor for each trial. When using rapid event-related designs with trials closely spaced in time, those estimates are highly variable and serially correlated due to the temporally extended shape of the hemodynamic response function (HRF). Here, we describe inverse transformed encoding modelling (ITEM), a principled approach of accounting for those serial correlations and decoding from the resulting estimates, at low computational cost and with no loss in statistical power. We use simulated data to show that ITEM outperforms the current standard approach in terms of decoding accuracy and analyze empirical data to demonstrate that ITEM is capable of visual reconstruction from fMRI signals

Generating Equidistributed Meshes in 2D via Domain Decomposition

In this paper we consider Schwarz domain decomposition applied to the generation of 2D spatial meshes by a local equidistribution principle. We briefly review the derivation of the local equidistribution principle and the appropriate choice of boundary conditions. We then introduce classical and optimized Schwarz domain decomposition methods to solve the resulting system of nonlinear equations. The implementation of these iterations are discussed, and we conclude with numerical examples to illustrate the performance of the approach

A Schwarz Method for the Magnetotelluric Approximation of Maxwell's equations

The magnetotelluric approximation of the Maxwell's equations is used to model the propagation of low frequency electro-magnetic waves in the Earth's subsurface, with the purpose of reconstructing the presence of mineral or oil deposits. We propose a classical Schwarz method for solving this magnetotelluric approximation of the Maxwell equations, and prove its convergence using maximum principle techniques. This is not trivial, since solutions are complex valued, and we need a new result that the magnetotelluric approximations satisfy a maximum modulus principle for our proof. We illustrate our analysis with numerical experiments.Comment: 9 pages, 3 figure

Experimental determination of the state-dependent enhancement of the electron-positron momentum density in solids

The state-dependence of the enhancement of the electron-positron momentum density is investigated for some transition and simple metals (Cr, V, Ag and Al). Quantitative comparison with linearized muffin-tin orbital calculations of the corresponding quantity in the first Brillouin zone is shown to yield a measurement of the enhancement of the s, p and d states, independent of any parameterizations in terms of the electron density local to the positron. An empirical correction that can be applied to a first-principles state-dependent model is proposed that reproduces the measured state-dependence very well, yielding a general, predictive model for the enhancement of the momentum distribution of positron annihilation measurements, including those of angular correlation and coincidence Doppler broadening techniques

How to avoid mismodelling in GLM-based fMRI data analysis: cross-validated Bayesian model selection

Voxel-wise general linear models (GLMs) are a standard approach for analyzing functional magnetic resonance imaging (fMRI) data. An advantage of GLMs is that they are flexible and can be adapted to the requirements of many different data sets. However, the specification of first-level GLMs leaves the researcher with many degrees of freedom which is problematic given recent efforts to ensure robust and reproducible fMRI data analysis. Formal model comparisons that allow a systematic assessment of GLMs are only rarely performed. On the one hand, too simple models may underfit data and leave real effects undiscovered. On the other hand, too complex models might overfit data and also reduce statistical power. Here we present a systematic approach termed cross-validated Bayesian model selection (cvBMS) that allows to decide which GLM best describes a given fMRI data set. Importantly, our approach allows for non-nested model comparison, i.e. comparing more than two models that do not just differ by adding one or more regressors. It also allows for spatially heterogeneous modelling, i.e. using different models for different parts of the brain. We validate our method using simulated data and demonstrate potential applications to empirical data. The increased use of model comparison and model selection should increase the reliability of GLM results and reproducibility of fMRI studies

Rotorcraft contingency power study

Twin helicopter engines are often sized by the power requirement of a safe mission completion after the failure of one of the two engines. This study was undertaken for NASA Lewis by General Electric Co. to evaluate the merits of special design features to provide a 2-1/2 Contingency Power rating, permitting an engine size reduction. The merits of water injection, turbine cooling airflow modulation, throttle push, and a propellant auxiliary power plant were evaluated using military Life Cycle Cost (LCC) and commercial helicopter Direct Operating Cost (DOC) merit factors in a rubber engine and a rubber aircraft scenario

How to improve parameter estimates in GLM-based fMRI data analysis: cross-validated Bayesian model averaging

In functional magnetic resonance imaging (fMRI), model quality of general linear models (GLMs) for first-level analysis is rarely assessed. In recent work (Soch et al., 2016: “How to avoid mismodelling in GLM-based fMRI data analysis: cross-validated Bayesian model selection”, NeuroImage, vol. 141, pp. 469–489; http://dx.doi.org/10.1016/j.neuroimage.2016.07.047), we have introduced cross-validated Bayesian model selection (cvBMS) to infer the best model for a group of subjects and use it to guide second-level analysis. While this is the optimal approach given that the same GLM has to be used for all subjects, there is a much more efficient procedure when model selection only addresses nuisance variables and regressors of interest are included in all candidate models. In this work, we propose cross-validated Bayesian model averaging (cvBMA) to improve parameter estimates for these regressors of interest by combining information from all models using their posterior probabilities. This is particularly useful as different models can lead to different conclusions regarding experimental effects and the most complex model is not necessarily the best choice. We find that cvBMS can prevent not detecting established effects and that cvBMA can be more sensitive to experimental effects than just using even the best model in each subject or the model which is best in a group of subjects

Electrostatic considerations affecting the calculated HOMO-LUMO gap in protein molecules.

A detailed study of energy differences between the highest occupied and lowest unoccupied molecular orbitals (HOMO-LUMO gaps) in protein systems and water clusters is presented. Recent work questioning the applicability of Kohn-Sham density-functional theory to proteins and large water clusters (E. Rudberg, J. Phys.: Condens. Mat. 2012, 24, 072202) has demonstrated vanishing HOMO-LUMO gaps for these systems, which is generally attributed to the treatment of exchange in the functional used. The present work shows that the vanishing gap is, in fact, an electrostatic artefact of the method used to prepare the system. Practical solutions for ensuring the gap is maintained when the system size is increased are demonstrated. This work has important implications for the use of large-scale density-functional theory in biomolecular systems, particularly in the simulation of photoemission, optical absorption and electronic transport, all of which depend critically on differences between energies of molecular orbitals.Comment: 13 pages, 4 figure