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Whole-body PET imaging is often hindered by respiratory motion during acquisition, causing significant degradation in the quality of reconstructed activity images. An additional challenge in PET/CT imaging arises from the respiratory phase mismatch between CT-based attenuation correction and PET acquisition, leading to attenuation artifacts. To address these issues, we propose two new, purely data-driven methods for the joint estimation of activity, attenuation, and motion in respiratory self-gated TOF PET. These methods enable the reconstruction of a single activity image free from motion and attenuation artifacts. The proposed methods were evaluated using data from the anthropomorphic Wilhelm phantom acquired on a Siemens mCT PET/CT system, as well as 3 clinical FDG PET/CT datasets acquired on a GE DMI PET/CT system. Image quality was assessed visually to identify motion and attenuation artifacts. Lesion uptake values were quantitatively compared across reconstructions without motion modeling, with motion modeling but static attenuation correction, and with our proposed methods. For the Wilhelm phantom, the proposed methods delivered image quality closely matching the reference reconstruction from a static acquisition. The lesion-to-background contrast for a liver dome lesion improved from 2.0 (no motion correction) to 5.2 (proposed methods), matching the contrast from the static acquisition (5.2). In contrast, motion modeling with static attenuation correction yielded a lower contrast of 3.5. In patient datasets, the proposed methods successfully reduced motion artifacts in lung and liver lesions and mitigated attenuation artifacts, demonstrating superior lesion to background separation. Our proposed methods enable the reconstruction of a single, high-quality activity image that is motion-corrected and free from attenuation artifacts, without the need for external hardware., Comment: 18 pages, 7 figures, 2 tables

We present and distribute a parallel finite-element toolbox written in the free software FreeFem for computing the Bogoliubov-de Gennes (BdG) spectrum of stationary solutions to one- and two-component Gross-Pitaevskii (GP) equations, in two or three spatial dimensions. The parallelization of the toolbox relies exclusively upon the recent interfacing of FreeFem with the PETSc library. The latter contains itself a wide palette of state-of-the-art linear algebra libraries, graph partitioners, mesh generation and domain decomposition tools, as well as a suite of eigenvalue solvers that are embodied in the SLEPc library. Within the present toolbox, stationary states of the GP equations are computed by a Newton method. Branches of solutions are constructed using an adaptive step-size continuation algorithm. The combination of mesh adaptivity tools from FreeFem with the parallelization features from PETSc makes the toolbox efficient and reliable for the computation of stationary states. Their BdG spectrum is computed using the SLEPc eigenvalue solver. We perform extensive tests and validate our programs by comparing the toolbox's results with known theoretical and numerical findings that have been reported in the literature., Comment: arXiv admin note: text overlap with arXiv:2303.05350

The northern Chile region of the Nazca subduction zone ruptured in an Mw$\sim$8.5--9.0 earthquake in 1877, which induced a tsunami. The various magnitude estimates of this event are based on the evaluation of historical records, seismic intensities, and/or tide gauge information; however, its actual along-strike extent is debated. Based on geodetic data, the previous studies have suggested that this region has the potential for an Mw8.2--8.8 event. We re-evaluate the seismic potential of the region, accounting for the buildup rate of moment deficit along the megathrust, the earthquake magnitude--frequency distribution, and the physics of earthquakes. We combine an improved probabilistic estimate of moment deficit rate with results from dynamic models of the earthquake cycle, testing, in particular, the influence of a potential aseismic barrier near the city of Iquique, which may influence the extent and magnitude of large events in this region. We find that Mw8.8 is the most probable maximum magnitude earthquake in the region, and that the potential barrier likely has a limited impact considering uncertainties. We discuss the effect of the moment deficit rate on the fault, the b-value, and the importance of postseismic processes on our results.

This paper introduces a fully algebraic two-level additive Schwarz preconditioner for general sparse large-scale matrices. The preconditioner is analyzed for symmetric positive definite (SPD) matrices. For those matrices, the coarse space is constructed based on approximating two local subspaces in each subdomain. These subspaces are obtained by approximating a number of eigenvectors corresponding to dominant eigenvalues of two judiciously posed generalized eigenvalue problems. The number of eigenvectors can be chosen to control the condition number. For general sparse matrices, the coarse space is constructed by approximating the image of a local operator that can be defined from information in the coefficient matrix. The connection between the coarse spaces for SPD and general matrices is also discussed. Numerical experiments show the great effectiveness of the proposed preconditioners on matrices arising from a wide range of applications. The set of matrices includes SPD, symmetric indefinite, nonsymmetric, and saddle-point matrices. In addition, we compare the proposed preconditioners to the state-of-the-art domain decomposition preconditioners.

Accurate land use maps, describing the territory from an anthropic utilisation point of view, are useful tools for land management and planning. To produce them, the use of optical images alone remains limited. It is therefore necessary to make use of several heterogeneous sources, each carrying complementary or contradictory information due to their imperfections or their different specifications. This study compares two different approaches i.e. a pre-classification and a post-classification fusion approach for combining several sources of spatial data in the context of land use classification. The approaches are applied on authoritative land use data located in the Gers department in the southwest of France. Pre-classification fusion, while not explicitly modeling imperfections, has the best final results, reaching an overall accuracy of 97% and a macro-mean F1 score of 88%.

This article discusses the uncertainty quantification (UQ) for time-independent linear and nonlinear partial differential equation (PDE)-based systems with random model parameters carried out using sampling-free intrusive stochastic Galerkin method leveraging multilevel scalable solvers constructed combining two-grid Schwarz method and AMG. High-resolution spatial meshes along with a large number of stochastic expansion terms increase the system size leading to significant memory consumption and computational costs. Domain decomposition (DD)-based parallel scalable solvers are developed to this end for linear and nonlinear stochastic PDEs. A generalized minimum residual (GMRES) iterative solver equipped with a multilevel preconditioner consisting of restricted additive Schwarz (RAS) for the fine grid and algebraic multigrid (AMG) for the coarse grid is constructed to improve scalability. Numerical experiments illustrate the scalabilities of the proposed solver for stochastic linear and nonlinear Poisson problems.

Frequency-domain Full Waveform Inversion (FWI) is potentially amenable to efficient processing of full-azimuth long-offset stationary-recording seabed acquisition carried out with sparse layout of ocean bottom nodes (OBNs) and broadband sources because the inversion can be performed with a few discrete frequencies. However, computing efficiently the solution of the forward (boundary-value) problem in the frequency domain with linear algebra solvers remains a challenge for large computational domains involving tens to hundreds of millions of parameters. We illustrate the feasibility of 3D frequency-domain FWI with the 2015/16 Gorgon OBN case study in the NorthWestern shelf, Australia. We solve the forward problem with the massively-parallel multifrontal direct solver MUMPS, which includes four key features to reach high computational efficiency: An efficient parallelism combining message-passing interface and multithreading, block low-rank compression, mixed precision arithmetic and efficient processing of sparse sources. The Gorgon subdataset involves 650 OBNs that are processed as reciprocal sources and 400,000 sources. Mono-parameter FWI for vertical wavespeed is performed in the visco-acoustic VTI approximation with a classical frequency continuation approach proceeding from a starting frequency of 1.7 Hz to a final frequency of 13 Hz. The target covers an area ranging from 260 km2 (frequency > 8.5 Hz) to 705 km2 (frequency < 8.5 Hz) for a maximum depth of 8 km. Compared to the starting model, FWI dramatically improves the reconstruction of the bounding faults of the Gorgon horst at reservoir depths as well as several intra-horst faults and several horizons of the Mungaroo formation down to a depth of 7 km.

Photovoltaic (PV) energy generation plays a crucial role in the energy transition. Small-scale PV installations are deployed at an unprecedented pace, and their integration into the grid can be challenging since public authorities often lack quality data about them. Overhead imagery is increasingly used to improve the knowledge of residential PV installations with machine learning models capable of automatically mapping these installations. However, these models cannot be easily transferred from one region or data source to another due to differences in image acquisition. To address this issue known as domain shift and foster the development of PV array mapping pipelines, we propose a dataset containing aerial images, annotations, and segmentation masks. We provide installation metadata for more than 28,000 installations. We provide ground truth segmentation masks for 13,000 installations, including 7,000 with annotations for two different image providers. Finally, we provide installation metadata that matches the annotation for more than 8,000 installations. Dataset applications include end-to-end PV registry construction, robust PV installations mapping, and analysis of crowdsourced datasets., Comment: 12 pages, 3 figures, 7 tables, revised preprint resubmitted to Scientific Data

A nonlinear partial differential equation (PDE) based compartmental model of COVID-19 provides a continuous trace of infection over space and time. Finer resolutions in the spatial discretization, the inclusion of additional model compartments and model stratifications based on clinically relevant categories contribute to an increase in the number of unknowns to the order of millions. We adopt a parallel scalable solver allowing faster solutions for these high fidelity models. The solver combines domain decomposition and algebraic multigrid preconditioners at multiple levels to achieve the desired strong and weak scalability. As a numerical illustration of this general methodology, a five-compartment susceptible-exposed-infected-recovered-deceased (SEIRD) model of COVID-19 is used to demonstrate the scalability and effectiveness of the proposed solver for a large geographical domain (Southern Ontario). It is possible to predict the infections up to three months for a system size of 92 million (using 1780 processes) within 7 hours saving months of computational effort needed for the conventional solvers.

Domain decomposition methods are among the most efficient for solving sparse linear systems of equations. Their effectiveness relies on a judiciously chosen coarse space. Originally introduced and theoretically proved to be efficient for self-adjoint operators, spectral coarse spaces have been proposed in the past few years for indefinite and non-self-adjoint operators. This paper presents a new spectral coarse space that can be constructed in a fully-algebraic way unlike most existing spectral coarse spaces. We present theoretical convergence result for Hermitian positive definite diagonally dominant matrices. Numerical experiments and comparisons against state-of-the-art preconditioners in the multigrid community show that the resulting two-level Schwarz preconditioner is efficient especially for non-self-adjoint operators. Furthermore, in this case, our proposed preconditioner outperforms state-of-the-art preconditioners.

Dual Energy Cone Beam Computed Tomography (DE-CBCT) is a promising technique for several medical applications, including dynamic angiography. Recently, a dynamical two-step method has been proposed : first, the water and iodine projections are computed from the multi-energy sinograms, then, a dynamic image of the iodine contrast is reconstructed using 4D Total-Variation (TV) constrained reconstruction from the iodine projections. In contrast to the 2-step methods, one-step methods use a model relating directly the multi-material images to the multi-energy sinograms. This kind of methods are well-known to reduce the noise correlation between the material images by avoiding the intermediate decomposition step, but request to solve an non-convex large scale optimization problem which can be challenging. In this work we use the Non-Linear Primal-Dual Hybrid Gradient Method (NL-PDHGM) optimization framework to propose two versions of a one-step method which is based on an empirical model : the first one is a version which considers the multi-material images as static object whereas the second version is developped for a specific application with a static water image and a dynamic iodine image consisting of a series of 3D iodine images associated to different time points. This last version is developped to obtain the evolution of the iodine concentration in the blood vessels during a single CBCT scan. To evaluate the proposed one-step methods we used simulations which consider a CBCT system with dual layer spectral detector and a brain phantom with a static and a dynamic vascular tree. The proposed one-step methods are compared with 2-step methods.

Efficient frequency-domain Full Waveform Inversion (FWI) of long-offset node data can be designed with a few discrete frequencies hence allowing for compact volume of data to be managed. Moreover, attenuation effects can be straightforwardly implemented in the forward problem without computational overhead. However, 3D frequency-domain seismic modeling is challenging since it requires solving a large and sparse linear indefinite system per frequency with multiple right-hand sides. This linear system can be solved by direct or iterative methods. The former are very efficient to process multiple right-hand sides but may suffer from limited scalability for very large problems. Iterative methods equipped with a domain decomposition preconditioner provide a suitable alternative to process large computational domains for sparse node acquisition. The domain decomposition preconditioner relies on an optimized restricted additive Schwarz (ORAS) method, where a Robin or Perfectly-Matched Layer (PML) condition is implemented at the boundaries between the subdomains. The preconditioned system is solved by a Krylov subspace method, while a block low-rank Lower-Upper (LU) decomposition of the local matrices is performed at a preprocessing stage. Multiple sources are processed in group with a pseudo-block method. The accuracy, the computational cost and the scalability of the ORAS solver are assessed against several realistic benchmarks. For the considered benchmarks, a compact wavelength-adaptive 27-point finite-difference stencil on regular Cartesian grid shows better accuracy and computational efficiency than a P3 finite-element method on h-adaptive tetrahedral mesh, which remains however beneficial to comply with known boundaries such as bathymetry.

Domain decomposition (DD) methods are widely used as preconditioner techniques. Their effectiveness relies on the choice of a locally constructed coarse space. Thus far, this construction was mostly achieved using non-assembled matrices from discretized partial differential equations (PDEs). Therefore, DD methods were mainly successful when solving systems stemming from PDEs. In this paper, we present a fully algebraic multilevel DD method where the coarse space can be constructed locally and efficiently without any information besides the coefficient matrix. The condition number of the preconditioned matrix can be bounded by a user-prescribed number. Numerical experiments illustrate the effectiveness of the preconditioner on a range of problems arising from different applications.

Solving the normal equations corresponding to large sparse linear least-squares problems is an important and challenging problem. For very large problems, an iterative solver is needed and, in general, a preconditioner is required to achieve good convergence. In recent years, a number of preconditioners have been proposed. These are largely serial and reported results demonstrate that none of the commonly used preconditioners for the normal equations matrix is capable of solving all sparse least-squares problems. Our interest is thus in designing new preconditioners for the normal equations that are efficient, robust, and can be implemented in parallel. Our proposed preconditioners can be constructed efficiently and algebraically without any knowledge of the problem and without any assumption on the least-squares matrix except that it is sparse. We exploit the structure of the symmetric positive definite normal equations matrix and use the concept of algebraic local symmetric positive semi-definite splittings to introduce two-level Schwarz preconditioners for least-squares problems. The condition number of the preconditioned normal equations is shown to be theoretically bounded independently of the number of subdomains in the splitting. This upper bound can be adjusted using a single parameter $\tau$ that the user can specify. We discuss how the new preconditioners can be implemented on top of the PETSc library using only 150 lines of Fortran, C, or Python code. Problems arising from practical applications are used to compare the performance of the proposed new preconditioner with that of other preconditioners.

Recently there has been an increased interest to apply the sensitive $\beta$-decay asymmetry detected nuclear magnetic resonance ($\beta$-NMR) technique to biological studies. A liquid-sample $\beta$-NMR setup was build at ISOLDE to allow such investigations and to use the resolution gain of liquid-state NMR in nuclear physics. As part of this setup a magnetic field locking system, a set of printed circuit board shimming coils, a sample exchange system, a set of compact $\beta$-detectors and a custom experimental vacuum chamber were developed. The main magnetic field was stabilized down to the ppm level by the locking system while allowing the direct determination of the absolute magnetic field. The homogeneity of the magnetic field was improved to $\leq$~5~ppm over the sample volume by the shimming coils. Time spent on changing samples was reduced by a factor of five by the liquid sample exchange system. During experiments it was possible to continuously observe the liquid sample thanks to the custom chamber and compact $\beta$-detectors. The absolute field determination allows for a novel way to reference $\beta$-NMR measurements, removing the need for time consuming reference measurements. The improved accuracy and resolution resulting from these innovations allows the study of the distribution of nuclear magnetization and (bio)chemicals using high-accuracy liquid-sample $\beta$-NMR.

We examine the use of a two-level deflation preconditioner combined with GMRES to locally solve the subdomain systems arising from applying domain decomposition methods to Helmholtz problems. Our results show that the direct solution method can be replaced with an iterative approach. This will be particularly important when solving large 3D high-frequency problems as subdomain problems can be too large for direct inversion or otherwise become inefficient. We additionally show that, even with a relatively low tolerance, inexact solution of the subdomain systems does not lead to a drastic increase in the number of outer iterations. As a result, it is promising that a combination of a two-level domain decomposition preconditioner with inexact subdomain solves could provide more economical and memory efficient numerical solutions to large-scale Helmholtz problems., Comment: 26th International Domain Decomposition Conference (DD26) proceedings

The emergence of long-offset sparse stationary-recording surveys carried out with ocean bottom nodes (OBN) makes frequency-domain full waveform inversion (FWI) attractive to manage compact volume of data and perform attenuation imaging. One challenge of frequency-domain FWI is the forward problem, which requires the solution of large and sparse linear systems with multiple right-hand sides. While direct methods are suitable for dense acquisitions and problems involving less than 100 million unknowns, iterative solver are more suitable for large computational domains covered by sparse OBN surveys. Here, we solve these linear systems with a Krylov subspace method preconditioned with the two-level Optimized Restricted Additive Schwarz (ORAS) domain decomposition preconditioner, the prefix optimized referring to the use of absorbing conditions at the subdomain interfaces. We implement this method with finite differences on uniform grid and finite elements on unstructured tetrahedral meshes. A simulation in a model where the velocity linearly increases with depth allows us to validate the accuracy of the two schemes against an analytical solution while highlighting how their relative cost varies with the band of propagated wavelengths. A simulation in the overthrust model involving up to 2 billions of parameters allows us to tune the method and highlights its scalability., Comment: arXiv admin note: substantial text overlap with arXiv:2004.07930, arXiv:2004.06309

Information measures are often used to assess the efficacy of neural networks, and learning rules can be derived through optimization procedures on such measures. In biological neural networks, computation is restricted by the amount of available resources. Considering energy restrictions, it is thus reasonable to balance information processing efficacy with energy consumption. Here, we studied networks of non-linear Hawkes neurons and assessed the information flow through these networks using mutual information. We then applied gradient descent for a combination of mutual information and energetic costs to obtain a learning rule. Through this procedure, we obtained a rule containing a sliding threshold, similar to the Bienenstock-Cooper-Munro rule. The rule contains terms local in time and in space plus one global variable common to the whole network. The rule thus belongs to so-called three-factor rules and the global variable could be related to a number of biological processes. In neural networks using this learning rule, frequent inputs get mapped onto low energy orbits of the network while rare inputs aren't learned.

Wave propagation problems are notoriously difficult to solve. Time-harmonic problems are especially challenging in mid and high frequency regimes. The main reason is the oscillatory nature of solutions, meaning that the number of degrees of freedom after discretisation increases drastically with the wave number, giving rise to large complex-valued problems to solve. Additional difficulties occur when the problem is defined in a highly heterogeneous medium, as is often the case in realistic physical applications. For time-discretised problems of Maxwell type, the main challenge remains the significant kernel in curl-conforming spaces, an issue that impacts on the design of robust preconditioners. This has already been addressed theoretically for a homogeneous medium but not yet in the presence of heterogeneities. In this review we provide a big-picture view of the main difficulties encountered when solving wave propagation problems, from the first step of their discretisation through to their parallel solution using two-level methods, by showing their limitations on a few realistic examples. We also propose a new preconditioner inspired by the idea of subspace decomposition, but based on spectral coarse spaces, for curl-conforming discretisations of Maxwell's equations in heterogeneous media.

Systematic characterization of slip behaviours on active faults is key to unraveling the physics of tectonic faulting and the interplay between slow and fast earthquakes. Interferometric Synthetic Aperture Radar (InSAR), by enabling measurement of ground deformation at a global scale every few days, may hold the key to those interactions. However, atmospheric propagation delays often exceed ground deformation of interest despite state-of-the art processing, and thus InSAR analysis requires expert interpretation and a priori knowledge of fault systems, precluding global investigations of deformation dynamics. Here we show that a deep auto-encoder architecture tailored to untangle ground deformation from noise in InSAR time series autonomously extracts deformation signals, without prior knowledge of a fault's location or slip behaviour. Applied to InSAR data over the North Anatolian Fault, our method reaches 2 mm detection, revealing a slow earthquake twice as extensive as previously recognized. We further explore the generalization of our approach to inflation/deflation-induced deformation, applying the same methodology to the geothermal field of Coso, California.

Active faults release tectonic stress imposed by plate motion through a spectrum of slip modes, from slow, aseismic slip, to dynamic, seismic events. Slow earthquakes are often associated with tectonic tremor, non-impulsive signals that can easily be buried in seismic noise and go undetected. We present a new methodology aimed at improving the detection and location of tremors hidden within seismic noise. After identifying tremors with a classic convolutional neural network, we rely on neural network attribution to extract core tremor signatures and denoise input waveforms. We then use these cleaned waveforms to locate tremors with standard array-based techniques. We apply this method to the Cascadia subduction zone, where we identify tremor patches consistent with existing catalogs. In particular, we show that the cleaned signals resulting from the neural network attribution analysis correspond to a waveform traveling in the Earth's crust and mantle at wavespeeds consistent with local estimates. This approach allows us to extract small signals hidden within the noise, and therefore to locate more tremors than in existing catalogs., Comment: 7 pages, 6 figures

Solving time-harmonic wave propagation problems in the frequency domain and within heterogeneous media brings many mathematical and computational challenges, especially in the high frequency regime. We will focus here on computational challenges and try to identify the best algorithm and numerical strategy for a few well-known benchmark cases arising in applications. The aim is to cover, through numerical experimentation and consideration of the best implementation strategies, the main two-level domain decomposition methods developed in recent years for the Helmholtz equation. The theory for these methods is either out of reach with standard mathematical tools or does not cover all cases of practical interest. More precisely, we will focus on the comparison of three coarse spaces that yield two-level methods: the grid coarse space, DtN coarse space, and GenEO coarse space. We will show that they display different pros and cons, and properties depending on the problem and particular numerical setting.

We present $L$'-band imaging of the PDS 70 planetary system with Keck/NIRC2 using the new infrared pyramid wavefront sensor. We detected both PDS 70 b and c in our images, as well as the front rim of the circumstellar disk. After subtracting off a model of the disk, we measured the astrometry and photometry of both planets. Placing priors based on the dynamics of the system, we estimated PDS 70 b to have a semi-major axis of $20^{+3}_{-4}$~au and PDS 70 c to have a semi-major axis of $34^{+12}_{-6}$~au (95\% credible interval). We fit the spectral energy distribution (SED) of both planets. For PDS 70 b, we were able to place better constraints on the red half of its SED than previous studies and inferred the radius of the photosphere to be 2-3~$R_{Jup}$. The SED of PDS 70 c is less well constrained, with a range of total luminosities spanning an order of magnitude. With our inferred radii and luminosities, we used evolutionary models of accreting protoplanets to derive a mass of PDS 70 b between 2 and 4 $M_{\textrm{Jup}}$ and a mean mass accretion rate between $3 \times 10^{-7}$ and $8 \times 10^{-7}~M_{\textrm{Jup}}/\textrm{yr}$. For PDS 70 c, we computed a mass between 1 and 3 $M_{\textrm{Jup}}$ and mean mass accretion rate between $1 \times 10^{-7}$ and $5 \times~10^{-7} M_{\textrm{Jup}}/\textrm{yr}$. The mass accretion rates imply dust accretion timescales short enough to hide strong molecular absorption features in both planets' SEDs., Comment: 20 pages, 5 figures, Accepted to AJ. Updated author list from original version. Fixed equation typo

Frequency-domain full-waveform inversion (FWI) is suitable for long-offset stationary-recording acquisition, since reliable subsurface models can be reconstructed with a few frequencies and attenuation is easily implemented without computational overhead. In the frequency domain, wave modeling is a Helmholtz-type boundary-value problem which requires to solve a large and sparse system of linear equations per frequency with multiple right-hand sides (sources). This system can be solved with direct or iterative methods. While the former are suitable for FWI application on 3D dense OBC acquisitions covering spatial domains of moderate size, the later should be the approach of choice for sparse node acquisitions covering large domains (more than 50 millions of unknowns). Fast convergence of iterative solvers for Helmholtz problems remains however challenging in high frequency regime due to the non definiteness of the Helmholtz operator, on one side and on the discretization constraints in order to minimize the dispersion error for a given frequency, on the other side, hence requiring efficient preconditioners. In this study, we use the Krylov subspace GMRES iterative solver combined with a two-level domain-decomposition preconditioner. Discretization relies on continuous Lagrange finite elements of order 3 on unstructured tetrahedral meshes to comply with complex geometries and adapt the size of the elements to the local wavelength ($h$-adaptivity). We assess the accuracy, the convergence and the scalability of our method with the acoustic 3D SEG/EAGE Overthrust model up to a frequency of 20~Hz., Comment: arXiv admin note: substantial text overlap with arXiv:2004.06309

Frequency-domain full-waveform inversion (FWI) is suitable for long-offset stationary-recording acquisition, since reliable subsurface models can be reconstructed with a few frequencies and attenuation is easily implemented without computational overhead. In the frequency domain, wave modelling is a Helmholtz-type boundary-value problem which requires to solve a large and sparse system of linear equations per frequency with multiple right-hand sides (sources). This system can be solved with direct or iterative methods. While the former are suitable for FWI application on 3D dense OBC acquisitions covering spatial domains of moderate size, the later should be the approach of choice for sparse node acquisitions covering large domains (more than 50 millions of unknowns). Fast convergence of iterative solvers for Helmholtz problems remains however challenging due to the non definiteness of the Helmholtz operator, hence requiring efficient preconditioners. In this study, we use the Krylov subspace GMRES iterative solver combined with a multi-level domain-decomposition preconditioner. Discretization relies on continuous finite elements on unstructured tetrahedral meshes to comply with complex geometries and adapt the size of the elements to the local wavelength ($h$-adaptivity). We assess the convergence and the scalability of our method with the acoustic 3D SEG/EAGE Overthrust model up to a frequency of 20~Hz and discuss its efficiency for multi right-hand side processing.

We determine for the first time the magnetic dipole moment of a short-lived nucleus with part-per-million (ppm) accuracy. To achieve this two orders of magnitude improvement over previous studies, we implement a number of innovations into our $\beta$-detected Nuclear Magnetic Resonance ($\beta$-NMR) setup at ISOLDE/CERN. Using liquid samples as hosts we obtain narrow, sub-kHz linewidth, resonances, while a simultaneous in-situ $^1$H NMR measurement allows us to calibrate and stabilize the magnetic field to ppm precision, thus eliminating the need for additional $\beta$-NMR reference measurements. Furthermore, we use ab initio calculations of NMR shielding constants to improve the accuracy of the reference magnetic moment, thus removing a large systematic error. We demonstrate the potential of this combined approach with the 1.1 s half-life radioactive nucleus $^{26}$Na, which is relevant for biochemical studies. Our technique can be readily extended to other isotopic chains, providing accurate magnetic moments for many short-lived nuclei. Furthermore, we discuss how our approach can open the path towards a wide range of applications of the ultra-sensitive $\beta$-NMR in physics, chemistry, and biology., Comment: re-submitted

In recent years, the field of neuroscience has gone through rapid experimental advances and a significant increase in the use of quantitative and computational methods. This growth has created a need for clearer analyses of the theory and modeling approaches used in the field. This issue is particularly complex in neuroscience because the field studies phenomena across a wide range of scales and often requires consideration of these phenomena at varying degrees of abstraction, from precise biophysical interactions to the computations they implement. We argue that a pragmatic perspective of science, in which descriptive, mechanistic, and normative approaches each play a distinct role in defining and bridging levels of abstraction will facilitate neuroscientific practice. This analysis leads to methodological suggestions, including selecting a level of abstraction that is appropriate for a given problem, identifying transfer functions to connect models and data, and the use of models themselves as a form of experiment.

Most earthquake ruptures propagate at speeds below the shear wave velocity within the crust, but in some rare cases, ruptures reach supershear speeds. The physics underlying the transition of natural subshear earthquakes to supershear ones is currently not fully understood. Most observational studies of supershear earthquakes have focused on determining which fault segments sustain fully-grown supershear ruptures. Experimentally cross-validated numerical models have identified some of the key ingredients required to trigger a transition to supershear speed. However, the conditions for such a transition in nature are still unclear, including the precise location of this transition. In this work, we provide theoretical and numerical insights to identify the precise location of such a transition in nature. We use fracture mechanics arguments with multiple numerical models to identify the signature of supershear transition in coseismic off-fault damage. We then cross-validate this signature with high-resolution observations of fault zone width and early aftershock distributions. We confirm that the location of the transition from subshear to supershear speed is characterized by a decrease in the width of the coseismic off-fault damage zone. We thus help refine the precise location of such a transition for natural supershear earthquakes.