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Available online 25 May 2023, 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 occasion- ally 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 pro- pose 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 fre- quency 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.

Synchronization between oscillatory signals is considered to be one of the main mechanisms through which neuronal populations interact with each other. It is conventionally studied with mass-bivariate measures utilizing either sensor-to-sensor or voxel-to-voxel signals. However, none of these approaches aims at maximizing synchronization, especially when two multichannel datasets are present. Examples include cortico-muscular coherence (CMC), cortico-subcortical interactions or hyperscanning (where electroencephalographic EEG/magnetoencephalographic MEG activity is recorded simultaneously from two or more subjects). For all of these cases, a method which could find two spatial projections maximizing the strength of synchronization would be desirable. Here we present such method for the maximization of coherence between two sets of EEG/MEG/EMG (electromyographic)/LFP (local field potential) recordings. We refer to it as canonical Coherence (caCOH). caCOH maximizes the absolute value of the coherence between the two multivariate spaces in the frequency domain. This allows very fast optimization for many frequency bins. Apart from presenting details of the caCOH algorithm, we test its efficacy with simulations using realistic head modelling and focus on the application of caCOH to the detection of cortico-muscular coherence. For this, we used diverse multichannel EEG and EMG recordings and demonstrate the ability of caCOH to extract complex patterns of CMC distributed across spatial and frequency domains. Finally, we indicate other scenarios where caCOH can be used for the extraction of neuronal interactions.

Synchronization between oscillatory signals is considered to be one of the main mechanisms through which neuronal populations interact with each other. It is conventionally studied with mass-bivariate measures utilizing either sensor-to-sensor or voxel-to-voxel signals. However, none of these approaches aims at maximizing synchronization, especially when two multichannel datasets are present. Examples include cortico-muscular coherence (CMC), cortico-subcortical interactions or hyperscanning (where electroencephalographic EEG/magnetoencephalographic MEG activity is recorded simultaneously from two or more subjects). For all of these cases, a method which could find two spatial projections maximizing the strength of synchronization would be desirable. Here we present such method for the maximization of coherence between two sets of EEG/MEG/EMG (electromyographic)/LFP (local field potential) recordings. We refer to it as canonical Coherence (caCOH). caCOH maximizes the absolute value of the coherence between the two multivariate spaces in the frequency domain. This allows very fast optimization for many frequency bins. Apart from presenting details of the caCOH algorithm, we test its efficacy with simulations using realistic head modelling and focus on the application of caCOH to the detection of cortico-muscular coherence. For this, we used diverse multichannel EEG and EMG recordings and demonstrate the ability of caCOH to extract complex patterns of CMC distributed across spatial and frequency domains. Finally, we indicate other scenarios where caCOH can be used for the extraction of neuronal interactions.

Objective: Using traditional approaches, a Brain-Computer Interface (BCI) requires the collection of calibration data for new subjects prior to online use. Calibration time can be reduced or eliminated e.g.~by transfer of a pre-trained classifier or unsupervised adaptive classification methods which learn from scratch and adapt over time. While such heuristics work well in practice, none of them can provide theoretical guarantees. Our objective is to modify an event-related potential (ERP) paradigm to work in unison with the machine learning decoder to achieve a reliable calibration-less decoding with a guarantee to recover the true class means. Method: We introduce learning from label proportions (LLP) to the BCI community as a new unsupervised, and easy-to-implement classification approach for ERP-based BCIs. The LLP estimates the mean target and non-target responses based on known proportions of these two classes in different groups of the data. We modified a visual ERP speller to meet the requirements of the LLP. For evaluation, we ran simulations on artificially created data sets and conducted an online BCI study with N=13 subjects performing a copy-spelling task. Results: Theoretical considerations show that LLP is guaranteed to minimize the loss function similarly to a corresponding supervised classifier. It performed well in simulations and in the online application, where 84.5% of characters were spelled correctly on average without prior calibration. Significance: The continuously adapting LLP classifier is the first unsupervised decoder for ERP BCIs guaranteed to find the true class means. This makes it an ideal solution to avoid a tedious calibration and to tackle non-stationarities in the data. Additionally, LLP works on complementary principles compared to existing unsupervised methods, allowing for their further enhancement when combined with LLP., Comment: The EEG data of 13 subjects is freely available online at: http://doi.org/10.5281/zenodo.192684

Simultaneously accurate and efficient prediction of molecular properties throughout chemical compound space is a critical ingredient toward rational compound design in chemical and pharmaceutical industries. Aiming toward this goal, we develop and apply a systematic hierarchy of efficient empirical methods to estimate atomization and total energies of molecules. These methods range from a simple sum over atoms, to addition of bond energies, to pairwise interatomic force fields, reaching to the more sophisticated machine learning approaches that are capable of describing collective interactions between many atoms or bonds. In the case of equilibrium molecular geometries, even simple pairwise force fields demonstrate prediction accuracy comparable to benchmark energies calculated using density functional theory with hybrid exchange-correlation functionals; however, accounting for the collective many-body interactions proves to be essential for approaching the "holy grail" of chemical accuracy of 1 kcal/mol for both equilibrium and out-of-equilibrium geometries. This remarkable accuracy is achieved by a vectorized representation of molecules (so-called Bag of Bonds model) that exhibits strong nonlocality in chemical space. In addition, the same representation allows us to predict accurate electronic properties of molecules, such as their polarizability and molecular frontier orbital energies. © 2015 American Chemical Society.

Simultaneously accurate and efficient prediction of molecular properties throughout chemical compound space is a critical ingredient toward rational compound design in chemical and pharmaceutical industries. Aiming toward this goal, we develop and apply a systematic hierarchy of efficient empirical methods to estimate atomization and total energies of molecules. These methods range from a simple sum over atoms, to addition of bond energies, to pairwise interatomic force fields, reaching to the more sophisticated machine learning approaches that are capable of describing collective interactions between many atoms or bonds. In the case of equilibrium molecular geometries, even simple pairwise force fields demonstrate prediction accuracy comparable to benchmark energies calculated using density functional theory with hybrid exchange-correlation functionals; however, accounting for the collective many-body interactions proves to be essential for approaching the "holy grail" of chemical accuracy of 1 kcal/mol for both equilibrium and out-of-equilibrium geometries. This remarkable accuracy is achieved by a vectorized representation of molecules (so-called Bag of Bonds model) that exhibits strong nonlocality in chemical space. In addition, the same representation allows us to predict accurate electronic properties of molecules, such as their polarizability and molecular frontier orbital energies. © 2015 American Chemical Society.

[No abstract available]

[No abstract available]

Radial velocities and central velocity dispersions are derived for 238 E/S0 galaxies from medium-resolution spectroscopy. New spectroscopic data have been obtained as part of a study of the Fundamental Plane distances and peculiar motions of early-type galaxies in three selected directions of the South Equatorial Strip, undertaken in order to investigate the reality of large-scale streaming motion; results of this study have been reported in M\"uller $et$ $al.$ (1998). The new APM South Equatorial Strip Catalog ($-17^{\circ}.5 < \delta < +2^{\circ}.5$) was used to select the sample of field galaxies in three directions: (1) 15h10 - 16h10; (2) 20h30 - 21h50; (3) 00h10 - 01h30. The spectra obtained have a median S/N per ${\AA}$ of 23, an instrumental resolution (FWHM) of $\sim$ 4 ${\AA}$, and the spectrograph resolution (dispersion) is $\sim$ 100 km~s$^{-1}$. The Fourier cross-correlation method was used to derive the radial velocities and velocity dispersions. The velocity dispersions have been corrected for the size of the aperture and for the galaxy effective radius. Comparisons of the derived radial velocities with data from the literature show that our values are accurate to 40 km~s$^{-1}$. A comparison with results from J$\o$rgensen et al. (1995) shows that the derived central velocity dispersion have an rms scatter of 0.036 in $\log \sigma$. There is no offset relative to the velocity dispersions of Davies et al. (1987)., Comment: accepted for publication in Astronomy & Astrophysics Supplement Series

Radial velocities and central velocity dispersions are derived for 238 E/S0 galaxies from medium-resolution spectroscopy. New spectroscopic data have been obtained as part of a study of the Fundamental Plane distances and peculiar motions of early-type galaxies in three selected directions of the South Equatorial Strip, undertaken in order to investigate the reality of large-scale streaming motion; results of this study have been reported in M\"uller $et$ $al.$ (1998). The new APM South Equatorial Strip Catalog ($-17^{\circ}.5 < \delta < +2^{\circ}.5$) was used to select the sample of field galaxies in three directions: (1) 15h10 - 16h10; (2) 20h30 - 21h50; (3) 00h10 - 01h30. The spectra obtained have a median S/N per ${\AA}$ of 23, an instrumental resolution (FWHM) of $\sim$ 4 ${\AA}$, and the spectrograph resolution (dispersion) is $\sim$ 100 km~s$^{-1}$. The Fourier cross-correlation method was used to derive the radial velocities and velocity dispersions. The velocity dispersions have been corrected for the size of the aperture and for the galaxy effective radius. Comparisons of the derived radial velocities with data from the literature show that our values are accurate to 40 km~s$^{-1}$. A comparison with results from J$\o$rgensen et al. (1995) shows that the derived central velocity dispersion have an rms scatter of 0.036 in $\log \sigma$. There is no offset relative to the velocity dispersions of Davies et al. (1987)., Comment: accepted for publication in Astronomy & Astrophysics Supplement Series

We investigate the reality of large-scale streaming on scales of up to 150 Mpc using the peculiar motions of galaxies in three directions. New R-band CCD photometry and spectroscopy for elliptical galaxies is used. The Fundamental Plane distance indicator is calibrated using the Coma cluster and an inhomogeneous Malmquist bias correction is applied. A linear bulk-flow model is fitted to the peculiar velocities in the sample regions and the results do not reflect the bulk flow observed by Lauer and Postman (LP). Accounting for the difference in geometry between the galaxy distribution in the three regions and the LP clustersconfirms the disagreement; assuming a low-density CDM power spectrum, we find that the observed bulk flow of the galaxies in our sample excludes the LP bulk flow at the 99.8% confidence level., Comment: 16 pages, 1 figure

We investigate the reality of large-scale streaming on scales of up to 150 Mpc using the peculiar motions of galaxies in three directions. New R-band CCD photometry and spectroscopy for elliptical galaxies is used. The Fundamental Plane distance indicator is calibrated using the Coma cluster and an inhomogeneous Malmquist bias correction is applied. A linear bulk-flow model is fitted to the peculiar velocities in the sample regions and the results do not reflect the bulk flow observed by Lauer and Postman (LP). Accounting for the difference in geometry between the galaxy distribution in the three regions and the LP clustersconfirms the disagreement; assuming a low-density CDM power spectrum, we find that the observed bulk flow of the galaxies in our sample excludes the LP bulk flow at the 99.8% confidence level., Comment: 16 pages, 1 figure