skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Title: Fast ℓ1 -regularized EEG source localization using variable projection
Abstract Electroencephalograms (EEG) are invaluable for treating neurological disorders, however, mapping EEG electrode readings to brain activity requires solving a challenging inverse problem. For time series data, the use of 1 regularization quickly becomes intractable for many solvers, and, despite the reconstruction advantages of 1 regularization, 2 -based approaches such as standardized low-resolution brain electromagnetic tomographysLORETAare used in practice. In this work, we formulate EEG source localization as a graphical generalized elastic net inverse problem and present avariable projectedaugmented Lagrangian algorithm (VPAL) suitable for fast EEG source localization. We prove convergence of this solver for a broad class of separable convex, potentially non-smooth functions subject to linear constraints. Leveraging the efficiency of the proposedVPALalgorithm, we introduce a windowed variation,VPAL W , that computes time dynamics in sequence suitable for real-time reconstruction. Our proposed methods are compared to state-of-the-art approaches includingsLORETAand other methods for 1 -regularized inverse problems.  more » « less
Award ID(s):
2152704 2152661
PAR ID:
10599286
Author(s) / Creator(s):
; ;
Publisher / Repository:
IOP Publishing
Date Published:
Journal Name:
Inverse Problems
Volume:
41
Issue:
6
ISSN:
0266-5611
Format(s):
Medium: X Size: Article No. 065014
Size(s):
Article No. 065014
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract We investigate the stellar mass–black hole mass ( * BH ) relation with type 1 active galactic nuclei (AGNs) down to BH = 10 7 M , corresponding to a ≃ −21 absolute magnitude in rest-frame ultraviolet, atz= 2–2.5. Exploiting the deep and large-area spectroscopic survey of the Hobby–Eberly Telescope Dark Energy Experiment (HETDEX), we identify 66 type 1 AGNs with BH ranging from 107–1010Mthat are measured with single-epoch virial method using Civemission lines detected in the HETDEX spectra. * of the host galaxies are estimated from optical to near-infrared photometric data taken with Spitzer, the Wide-field Infrared Survey Explorer, and ground-based 4–8 m class telescopes byCIGALEspectral energy distribution (SED) fitting. We further assess the validity of SED fitting in two cases by host-nuclear decomposition performed through surface brightness profile fitting on spatially resolved host galaxies with the James Webb Space Telescope/NIRCam CEERS data. We obtain the * BH relation covering the unexplored low-mass ranges of BH 10 7 10 8 M , and conduct forward modeling to fully account for the selection biases and observational uncertainties. The intrinsic * BH relation atz∼ 2 has a moderate positive offset of 0.52 ± 0.14 dex from the local relation, suggestive of more efficient black hole growth at higher redshift even in the low-mass regime of BH 10 7 10 8 M . Our * BH relation is inconsistent with the BH suppression at the low- * regime predicted by recent hydrodynamic simulations at a 98% confidence level, suggesting that feedback in the low-mass systems may be weaker than those produced in hydrodynamic simulations. 
    more » « less
  2. Abstract We analyze an optical atomic clock using two-photon 5 S 1 / 2 4 D J transitions in rubidium. Four one- and two-color excitation schemes to probe the 4 D 3 / 2 and 4 D 5 / 2 fine-structure states are considered in detail. We compare key characteristics of Rb 4 D J and 5 D 5 / 2 two-photon clocks. The 4 D J clock features a high signal-to-noise ratio due to two-photon decay at favorable wavelengths, low dc electric and magnetic susceptibilities, and minimal black-body shifts. Ac Stark shifts from the clock interrogation lasers are compensated by two-color Rabi-frequency matching. We identify a ‘magic’ wavelength near 1060 nm, which allows for in-trap, Doppler-free clock-transition interrogation with lattice-trapped cold atoms. From our analysis of clock statistics and systematics, we project a quantum-noise-limited relative clock stability at the 10 13 / τ ( s ) -level, with integration timeτin seconds, and a relative accuracy of 10 13 . We describe a potential architecture for implementing the proposed clock using a single telecom clock laser at 1550 nm, which is conducive to optical communication and long-distance clock comparisons. Our work could be of interest in efforts to realize small and portable Rb clocks and in high-precision measurements of atomic properties of Rb 4 D J -states. 
    more » « less
  3. Abstract Fe 3 + δ GeTe 2 (FGT) has proved to be an interesting van der Waals (vdW) ferromagnetic compound with a tunable Curie temperature ( T C ). However, the underlying mechanism for varying T C remains elusive. Here, we systematically investigate and compare low-temperature magnetic properties of single crystalline FGT samples that exhibit T C s ranging from 160 K to 205 K. Spin stiffness (D) and spin excitation gap (Δ) are extracted using Bloch’s theory for crystals with varying Fe content. Compared to Cr-based vdW ferromagnets, FGT compounds have higher spin stiffness values but lower spin wave excitation gaps. We discuss the implication of these relationships in Fe–Fe ion magnetic interactions in FGT unit cells. The itinerancy of magnetic electrons is measured and discussed under the Rhodes–Wohlfarth ratio (RWR) and the Takahashi theory. 
    more » « less
  4. Abstract We investigate the differential geometry of the moduli space of instantons on S 3 × S 1 . Extending previous results, we show that a sigma-model with this target space can be expected to possess a large N = 4 superconformal symmetry, supporting speculations that this sigma-model may be dual to Type IIB superstring theory on AdS 3 × S 3 × S 3 × S 1 . The sigma-model is parametrized by three integers—the rank of the gauge group, the instanton number, and a ‘level’ (the integer coefficient of a topologically nontrivialB-field, analogous to a WZW level). These integers are expected to correspond to two five-brane charges and a one-brane charge. The sigma-model is weakly coupled when the level, conjecturally corresponding to one of the five-brane changes, becomes very large, keeping the other parameters fixed. The central charges of the large N = 4 algebra agree, at least semiclassically, with expectations from the duality. 
    more » « less
  5. Abstract A measurement of off-shell Higgs boson production in the H Z Z 4 decay channel is presented. The measurement uses 140 fb−1of proton–proton collisions at s = 13 TeV collected by the ATLAS detector at the Large Hadron Collider and supersedes the previous result in this decay channel using the same dataset. The data analysis is performed using a neural simulation-based inference method, which builds per-event likelihood ratios using neural networks. The observed (expected) off-shell Higgs boson production signal strength in the Z Z 4 decay channel at 68% CL is 0.87 0.54 + 0.75 ( 1.00 0.95 + 1.04 ). The evidence for off-shell Higgs boson production using the Z Z 4 decay channel has an observed (expected) significance of 2.5σ(1.3σ). The expected result represents a significant improvement relative to that of the previous analysis of the same dataset, which obtained an expected significance of 0.5σ. When combined with the most recent ATLAS measurement in the Z Z 2 2 ν decay channel, the evidence for off-shell Higgs boson production has an observed (expected) significance of 3.7σ(2.4σ). The off-shell measurements are combined with the measurement of on-shell Higgs boson production to obtain constraints on the Higgs boson total width. The observed (expected) value of the Higgs boson width at 68% CL is 4.3 1.9 + 2.7 ( 4.1 3.4 + 3.5 ) MeV. 
    more » « less