Machine learning advances chemistry and materials science by enabling large-scale exploration of chemical space based on quantum chemical calculations. While these models supply fast and accurate ...predictions of atomistic chemical properties, they do not explicitly capture the electronic degrees of freedom of a molecule, which limits their applicability for reactive chemistry and chemical analysis. Here we present a deep learning framework for the prediction of the quantum mechanical wavefunction in a local basis of atomic orbitals from which all other ground-state properties can be derived. This approach retains full access to the electronic structure via the wavefunction at force-field-like efficiency and captures quantum mechanics in an analytically differentiable representation. On several examples, we demonstrate that this opens promising avenues to perform inverse design of molecular structures for targeting electronic property optimisation and a clear path towards increased synergy of machine learning and quantum chemistry.
In this book some 50 papers published by K A Müller as author or co-author over several decades, amplified by more recent work mainly by T W Kool with collaborators, are reproduced. The main subject ...is Electron Paramagnetic Resonance (EPR) applied to the study of perovskites and other oxides with related subjects. This wealth of papers is organized into eleven chapters, each with an introductory text written in the light of current understanding. The contributions of the first editor on structural phase transitions have been immense, and because K A Müller and J C Fayet have published a review paper on the subject, the latter is reproduced in chapter VII. Not related to EPR is a part of chapter VIII on the dipolar and quantum paraelectric behavior with dielectric studies. In chapter X two papers proving the existence of Fermi glasses are reproduced.
•Three frequency estimation measures called instantaneous frequency, local frequency and peak frequency are explained and compared.•We also present three novel multivariate methods for the extraction ...of frequency shifts. They are based on frequency changes detected by instantaneous frequency, local frequency or peak frequency.•The proposed decomposition methods extract brain sources whose frequency estimate of interest is maximally correlated to the external/internal variable of interest.•All methods were thoroughly validated in realistic simulations and with real EEG data of 24 participants who performed a steady-state visual evoked paradigm in a BCI experiment.
Instantaneous and peak frequency changes in neural oscillations have been linked to many perceptual, motor, and cognitive processes. Yet, the majority of such studies have been performed in sensor space and only occasionally in source space. Furthermore, both terms have been used interchangeably in the literature, although they do not reflect the same aspect of neural oscillations. In this paper, we discuss the relation between instantaneous frequency, peak frequency, and local frequency, the latter also known as spectral centroid. Furthermore, we propose and validate three different methods to extract source signals from multichannel data whose (instantaneous, local, or peak) frequency estimate is maximally correlated to an experimental variable of interest. Results show that the local frequency might be a better estimate of frequency variability than instantaneous frequency under conditions with low signal-to-noise ratio. Additionally, the source separation methods based on local and peak frequency estimates, called LFD and PFD respectively, provide more stable estimates than the decomposition based on instantaneous frequency. In particular, LFD and PFD are able to recover the sources of interest in simulations performed with a realistic head model, providing higher correlations with an experimental variable than multiple linear regression. Finally, we also tested all decomposition methods on real EEG data from a steady-state visual evoked potential paradigm and show that the recovered sources are located in areas similar to those previously reported in other studies, thus providing further validation of the proposed methods.
This paper considers nonstandard hypothesis testing problems that involve a nuisance parameter. We establish an upper bound on the weighted average power of all valid tests, and develop a numerical ...algorithm that determines a feasible test with power close to the bound. The approach is illustrated in six applications: inference about a linear regression coefficient when the sign of a control coefficient is known; small sample inference about the difference in means from two independent Gaussian samples from populations with potentially different variances; inference about the break date in structural break models with moderate break magnitude; predictability tests when the regressor is highly persistent; inference about an interval identified parameter; and inference about a linear regression coefficient when the necessity of a control is in doubt.
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