Improved physiological noise regression in fNIRS: a multimodal extension of the General Linear Model using temporally embedded Canonical Correlation Analysis

For the robust estimation of evoked brain activity from functional Near-Infrared Spectroscopy (fNIRS) signals, it is crucial to reduce nuisance signals from systemic physiology and motion. The current best practice incorporates short-separation (SS) fNIRS measurements as regressors in a General Linear Model (GLM). However, several challenging signal characteristics such as non-instantaneous and non-constant coupling are not yet addressed by this approach and additional auxiliary signals are not optimally exploited. We have recently introduced a new methodological framework for the unsupervised multivariate analysis of fNIRS signals using Blind Source Separation (BSS) methods. Building onto the framework, in this manuscript we show how to incorporate the advantages of regularized temporally embedded Canonical Correlation Analysis (tCCA) into the supervised GLM. This approach allows flexible integration of any number of auxiliary modalities and signals. We provide guidance for the selection of optimal parameters and auxiliary signals for the proposed GLM extension. Its performance in the recovery of evoked HRFs is then evaluated using both simulated ground truth data and real experimental data and compared with the GLM with short-separation regression. Our results show that the GLM with tCCA significantly improves upon the current best practice, yielding significantly better results across all applied metrics: Correlation (HbO max. +45%), Root Mean Squared Error (HbO max. -55%), F-Score (HbO up to 3.25-fold) and p-value as well as power spectral density of the noise floor. The proposed method can be incorporated into the GLM in an easily applicable way that flexibly combines any available auxiliary signals into optimal nuisance regressors. This work has potential significance both for conventional neuroscientific fNIRS experiments as well as for emerging applications of fNIRS in everyday environments, medicine and BCI, where high Contrast to Noise Ratio is of importance for single trial analysis.Published versio

Non-standard Hubbard models in optical lattices: a review

Originally, the Hubbard model has been derived for describing the behaviour of strongly-correlated electrons in solids. However, since over a decade now, variations of it are also routinely being implemented with ultracold atoms in optical lattices. We review some of the rich literature on this subject, with a focus on more recent non-standard forms of the Hubbard model. After an introduction to standard (fermionic and bosonic) Hubbard models, we discuss briefly common models for mixtures, as well as the so called extended Bose-Hubbard models, that include interactions between neighboring sites, next-neighboring sites, and so on. The main part of the review discusses the importance of additional terms appearing when refining the tight-binding approximation on the original physical Hamiltonian. Even when restricting the models to the lowest Bloch band is justified, the standard approach neglects the density-induced tunneling (which has the same origin as the usual on-site interaction). The importance of these contributions is discussed for both contact and dipolar interactions. For sufficiently strong interactions, also the effects related to higher Bloch bands become important even for deep optical lattices. Different approaches that aim at incorporating these effects, mainly via dressing the basis Wannier functions with interactions, leading to effective, density-dependent Hubbard-type models, are reviewed. We discuss also examples of Hubbard-like models that explicitly involve higher $p$-orbitals, as well as models that couple dynamically spin and orbital degrees of freedom. Finally, we review mean-field nonlinear-Schr\"odinger models of the Salerno type that share with the non-standard Hubbard models the nonlinear coupling between the adjacent sites. In that part, discrete solitons are the main subject of the consideration. We conclude by listing some future open problems.Comment: expanded version 47pp, accepted in Rep. Prog. Phy

Intrinsic Pinning in the High Field C-Phase of UPt_3

We report on the a.c. magnetic response of superconducting UPt_3 in a d.c. magnetic field. At low fields (H < H^*), the in-phase susceptibility shows a sharp drop at $T_c$ followed by a gradual decrease with decreasing temperature, while the out-of-phase component shows a large peak at T_c followed by an unusual broad peak. As the B-C phase line is crossed (H>H^*), however, both the in-phase and out-of-phase susceptibilities resemble the zero-field Meissner curves. We interpret these results in terms of a vortex pinning force which, while comparatively small in the A/B-phases, becomes large enough to effectively prevent vortex motion in the C-phase.Comment: Modified discussion, slight changes to figures, accepted in PRB Rapid Communications. RevTex file, 5 figure

Application of SQUIDs to low temperature and high magnetic field measurements—ultra low noise torque magnetometry

Authors thank the Max-Planck Society and Deutsche Forschungsgemeinschaft, project “Fermi-surface topology and emergence of novel electronic states in strongly correlated electron systems,” for their financial support.Torque magnetometry is a key method to measure the magnetic anisotropy and quantum oscillations in metals. In order to resolve quantum oscillations in sub-millimeter sized samples, piezo-electric micro-cantilevers were introduced. In the case of strongly correlated metals with large Fermi surfaces and high cyclotron masses, magnetic torque resolving powers in excess of 104 are required at temperatures well below 1 K and magnetic fields beyond 10 T. Here, we present a new broadband read-out scheme for piezo-electric micro-cantilevers via Wheatstone-type resistance measurements in magnetic fields up to 15 T and temperatures down to 200 mK. By using a two-stage superconducting-quantum interference device as a null detector of a cold Wheatstone bridge, we were able to achieve a magnetic moment resolution of Δm = 4 × 10−15 J/T at maximal field and 700 mK, outperforming conventional magnetometers by at least one order of magnitude in this temperature and magnetic field range. Exemplary de Haas-van Alphen measurement of a newly grown delafossite, PdRhO2, was used to show the superior performance of our setup.PostprintPeer reviewe

Using the General Linear Model to Improve Performance in fNIRS Single Trial Analysis and Classification: A Perspective

Within a decade, single trial analysis of functional Near Infrared Spectroscopy (fNIRS) signals has gained significant momentum, and fNIRS joined the set of modalities frequently used for active and passive Brain Computer Interfaces (BCI). A great variety of methods for feature extraction and classification have been explored using state-of-the-art Machine Learning methods. In contrast, signal preprocessing and cleaning pipelines for fNIRS often follow simple recipes and so far rarely incorporate the available state-of-the-art in adjacent fields. In neuroscience, where fMRI and fNIRS are established neuroimaging tools, evoked hemodynamic brain activity is typically estimated across multiple trials using a General Linear Model (GLM). With the help of the GLM, subject, channel, and task specific evoked hemodynamic responses are estimated, and the evoked brain activity is more robustly separated from systemic physiological interference using independent measures of nuisance regressors, such as short-separation fNIRS measurements. When correctly applied in single trial analysis, e.g., in BCI, this approach can significantly enhance contrast to noise ratio of the brain signal, improve feature separability and ultimately lead to better classification accuracy. In this manuscript, we provide a brief introduction into the GLM and show how to incorporate it into a typical BCI preprocessing pipeline and cross-validation. Using a resting state fNIRS data set augmented with synthetic hemodynamic responses that provide ground truth brain activity, we compare the quality of commonly used fNIRS features for BCI that are extracted from (1) conventionally preprocessed signals, and (2) signals preprocessed with the GLM and physiological nuisance regressors. We show that the GLM-based approach can provide better single trial estimates of brain activity as well as a new feature type, i.e., the weight of the individual and channel-specific hemodynamic response function (HRF) regressor. The improved estimates yield features with higher separability, that significantly enhance accuracy in a binary classification task when compared to conventional preprocessing—on average +7.4% across subjects and feature types. We propose to adapt this well-established approach from neuroscience to the domain of single-trial analysis and preprocessing wherever the classification of evoked brain activity is of concern, for instance in BCI

Bose-Einstein Condensation of Magnons in Cs2CuCl4

We report on results of specific heat measurements on single crystals of the frustrated quasi-2D spin-1/2 antiferromagnet Cs_2CuCl_4 (T_N=0.595 K) in external magnetic fields B30 mK. Decreasing B from high fields leads to the closure of the field-induced gap in the magnon spectrum at a critical field B_c = 8.51 T and a magnetic phase transition is clearly seen below B_c. In the vicinity to B_c, the phase transition boundary is well described by the power-law T_c(B)\propto (B_c-B)^{1/\phi} with the measured critical exponent \phi\simeq 1.5. These findings are interpreted as a Bose-Einstein condensation of magnons.Comment: 5 pages, 4 figures, experiment and theor

Quantum phase transition to unconventional multi-orbital superfluidity in optical lattices

Orbital physics plays a significant role for a vast number of important phenomena in complex condensed matter systems such as high-T$_c$ superconductivity and unconventional magnetism. In contrast, phenomena in superfluids -- especially in ultracold quantum gases -- are commonly well described by the lowest orbital and a real order parameter. Here, we report on the observation of a novel multi-orbital superfluid phase with a {\it complex} order parameter in binary spin mixtures. In this unconventional superfluid, the local phase angle of the complex order parameter is continuously twisted between neighboring lattice sites. The nature of this twisted superfluid quantum phase is an interaction-induced admixture of the p-orbital favored by the graphene-like band structure of the hexagonal optical lattice used in the experiment. We observe a second-order quantum phase transition between the normal superfluid (NSF) and the twisted superfluid phase (TSF) which is accompanied by a symmetry breaking in momentum space. The experimental results are consistent with calculated phase diagrams and reveal fundamentally new aspects of orbital superfluidity in quantum gas mixtures. Our studies might bridge the gap between conventional superfluidity and complex phenomena of orbital physics.Comment: 5 pages, 4 figure

Room-Temperature Solid-State Transformation of Na4 SnS4 ⋅ 14H2 O into Na4 Sn2 S6 ⋅ 5H2 O: An Unusual Epitaxial Reaction Including Bond Formation, Mass Transport, and Ionic Conductivity

A highly unusual solid-state epitaxy-induced phase transformation of Na4 SnS4  ⋅ 14H2 O (I) into Na4 Sn2 S6  ⋅ 5H2 O (II) occurs at room temperature. Ab initio molecular dynamics (AIMD) simulations indicate an internal acid-base reaction to form [SnS3 SH]3- which condensates to [Sn2 S6 ]4- . The reaction involves a complex sequence of O-H bond cleavage, S2- protonation, Sn-S bond formation and diffusion of various species while preserving the crystal morphology. In situ Raman and IR spectroscopy evidence the formation of [Sn2 S6 ]4- . DFT calculations allowed assignment of all bands appearing during the transformation. X-ray diffraction and in situ 1 H NMR demonstrate a transformation within several days and yield a reaction turnover of ≈0.38 %/h. AIMD and experimental ionic conductivity data closely follow a Vogel-Fulcher-Tammann type T dependence with D(Na)=6×10-14  m2  s-1 at T=300 K with values increasing by three orders of magnitude from -20 to +25 °C

Room‐Temperature Solid‐State Transformation of Na4_{4}SnS4_{4} ⋅ 14H2_{2}O into Na4_{4}Sn2_{2}S6_{6} ⋅ 5H2_{2}O: An Unusual Epitaxial Reaction Including Bond Formation, Mass Transport, and Ionic Conductivity

A highly unusual solid-state epitaxy-induced phase transformation of Na$_{4}$SnS$_{4}$ ⋅ 14H$_{2}$O (I) into Na$_{4}$Sn$_{2}$S$_{6}$ ⋅ 5H$_{2}$O (II) occurs at room temperature. Ab initio molecular dynamics (AIMD) simulations indicate an internal acid-base reaction to form [SnS$_{3}$SH]$^{3-}$ which condensates to [Sn$_{2}$S$_{6}$]$^{4–}$. The reaction involves a complex sequence of O−H bond cleavage, S$^{2–}$ protonation, Sn−S bond formation and diffusion of various species while preserving the crystal morphology. In situ Raman and IR spectroscopy evidence the formation of [Sn$_{2}$S$_{6}$]$^{4–}$. DFT calculations allowed assignment of all bands appearing during the transformation. X-ray diffraction and in situ $^{1}$H NMR demonstrate a transformation within several days and yield a reaction turnover of ≈0.38 %/h. AIMD and experimental ionic conductivity data closely follow a Vogel-Fulcher-Tammann type T dependence with D(Na)=6×10$^{-14}$ m$^{2}$ s$^{-1}$ at T=300 K with values increasing by three orders of magnitude from −20 to +25 °C

Hall-effect evolution across a heavy-fermion quantum critical point

A quantum critical point (QCP) develops in a material at absolute zero when a new form of order smoothly emerges in its ground state. QCPs are of great current interest because of their singular ability to influence the finite temperature properties of materials. Recently, heavy-fermion metals have played a key role in the study of antiferromagnetic QCPs. To accommodate the heavy electrons, the Fermi surface of the heavy-fermion paramagnet is larger than that of an antiferromagnet. An important unsolved question concerns whether the Fermi surface transformation at the QCP develops gradually, as expected if the magnetism is of spin density wave (SDW) type, or suddenly as expected if the heavy electrons are abruptly localized by magnetism. Here we report measurements of the low-temperature Hall coefficient ($R_H$) - a measure of the Fermi surface volume - in the heavy-fermion metal YbRh2Si2 upon field-tuning it from an antiferromagnetic to a paramagnetic state. $R_H$ undergoes an increasingly rapid change near the QCP as the temperature is lowered, extrapolating to a sudden jump in the zero temperature limit. We interpret these results in terms of a collapse of the large Fermi surface and of the heavy-fermion state itself precisely at the QCP.Comment: 20 pages, 3 figures; to appear in Natur