Large Memory Demands Research Articles

Computing Lagrangian means

Lagrangian averaging plays an important role in the analysis of wave–mean-flow interactions and other multiscale fluid phenomena. The numerical computation of Lagrangian means, e.g. from simulation data, is, however, challenging. Typical implementations require tracking a large number of particles to construct Lagrangian time series, which are then averaged using a low-pass filter. This has drawbacks that include large memory demands, particle clustering and complications of parallelisation. We develop a novel approach in which the Lagrangian means of various fields (including particle positions) are computed by solving partial differential equations (PDEs) that are integrated over successive averaging time intervals. We propose two strategies, distinguished by their spatial independent variables. The first, which generalises the algorithm of Kafiabad (J. Fluid Mech., vol. 940, 2022, A2), uses end-of-interval particle positions; the second uses directly the Lagrangian mean positions. The PDEs can be discretised in a variety of ways, e.g. using the same discretisation as that employed for the governing dynamical equations, and solved on-the-fly to minimise the memory footprint. We illustrate the new approach with a pseudo-spectral implementation for the rotating shallow-water model. Two applications to flows that combine vortical turbulence and Poincaré waves demonstrate the superiority of Lagrangian averaging over Eulerian averaging for wave–vortex separation.

Minian, an open-source miniscope analysis pipeline.

Miniature microscopes have gained considerable traction for in vivo calcium imaging in freely behaving animals. However, extracting calcium signals from raw videos is a computationally complex problem and remains a bottleneck for many researchers utilizing single-photon in vivo calcium imaging. Despite the existence of many powerful analysis packages designed to detect and extract calcium dynamics, most have either key parameters that are hard-coded or insufficient step-by-step guidance and validations to help the users choose the best parameters. This makes it difficult to know whether the output is reliable and meets the assumptions necessary for proper analysis. Moreover, large memory demand is often a constraint for setting up these pipelines since it limits the choice of hardware to specialized computers. Given these difficulties, there is a need for a low memory demand, user-friendly tool offering interactive visualizations of how altering parameters at each step of the analysis affects data output. Our open-source analysis pipeline, Minian (miniscope analysis), facilitates the transparency and accessibility of single-photon calcium imaging analysis, permitting users with little computational experience to extract the location of cells and their corresponding calcium traces and deconvolved neural activities. Minian contains interactive visualization tools for every step of the analysis, as well as detailed documentation and tips on parameter exploration. Furthermore, Minian has relatively small memory demands and can be run on a laptop, making it available to labs that do not have access to specialized computational hardware. Minian has been validated to reliably and robustly extract calcium events across different brain regions and from different cell types. In practice, Minian provides an open-source calcium imaging analysis pipeline with user-friendly interactive visualizations to explore parameters and validate results.

Determination of 3‐D Velocity Anomalies of the Nanbei Tectonic Zone of China Based on Local Earthquakes

Abstract: In this paper, 3‐D velocity images of the crust and upper mantle beneath the Nanbei tectonic zone of China are constructed using P‐wave travel time residuals of earthquakes, with the data supplied by China's seismic networks and the International Seismic Centre.During the model parameterization in the tomographic inversion the interpolation function of grid node velocities is used as the space function of velocity, and the velocity function is allowed to be discontinuous. The difficulties caused by large memory demand and high computing cost in solving the system of equations are avoided by utilizing the least squares QR decomposition algorithm. Thus, the stability of the algorithm is ensured. Though resolution images are not derived in the inversion process based on the resolution theory of Backus and Gilbert, a covariance resolution method is put forward by the authors. The resolution analyses have proved the reliability of the image results. 3‐D ray tracing is conducted to obtain the ray paths in a spherical coordinate system.The imaging results indicate that there is a significant lateral heterogeneity in the crust and upper mantle beneath the North‐South tectonic zone of China persisting down to 200 km in depth. The velocity images of the upper crust show features closely related to the tectonic features on the surface. A low‐velocity layer exists in a very wide range of the mid‐crust. The lowest velocity value is about 5.60 km/s. In a long narrow area between 25.0°N‐38.0°N and 100.0°E‐103.2°E, a low‐velocity anomaly of about 7.49 km/s appears at the top of the upper mantle. Almost all of the major earthquakes (ML≥6.0) took place in the transitional strips between high and low velocity zones at depths above 20 km in the crust. From the velocity images at 20+0 km and 50+0 km depth respectively, we find that the epicentres of strong earthquakes with magnitudes larger than 6.0 are almost entirely distributed in the low‐velocity zones or on their boundaries.

3-D velocity images beneath the Chinese continent and adjacent regions

In this paper, 3-D velocity images beneath the Chinese continent and adjacent regions are reconstructed using P-wave traveltime residuals of regional and distant earthquakes, supplied by Chinese seismic networks and ISC. In the tomographic inversion, an orthogonal projection operator is used to separate the velocity from the hypocentral parameters, the fast Givens transformation without square-root calculations is then used in sequential orthogonal triangularizations, and the modified singular value decomposition is also utilized. Thus the difficulties of large memory demand and high computing cost in solving the system of equations with coupled velocity and hypocentre parameters are avoided. At the same time the stability of the algorithm is ensured. Resolution images are also obtained in the inversion process, based on the resolution theory of Backus & Gilbert modified for discrete models. In model parametrization, the interpolation function of grid node velocities is used as the space function of velocity. To meet the practical needs, the velocity function is allowed to be discontinuous. The consequent complications of the forward problem have been dealt with in the paper. The main results are summarized as follows. (1) The velocity images given in this paper indicate lateral heterogeneity of the crust and upper mantle beneath the Chinese continent and adjacent regions, which persist down to a depth of at least 1100 km. The correlation between the velocity image and the known surface geological features can be traced down to a depth of 110 km. Below 220 km this correlation is hardly obvious. (2) The images at 45−0 km (immediately above the Moho) and 45+0 km (below the Moho) show clearly that the crust of the Chinese continent can be approximately divided into two parts by the 102.5°E longitude. The crust to the east is thinner than that to the west. (3) The images at 400 and 600 km also display differences between the eastern and western part. This means that tectonic differences between eastern and western China may exist in the whole upper mantle.