Testing protostellar disk formation models with ALMA observations

Abridged: Recent simulations have explored different ways to form accretion disks around low-mass stars. We aim to present observables to differentiate a rotationally supported disk from an infalling rotating envelope toward deeply embedded young stellar objects and infer their masses and sizes. Two 3D magnetohydrodynamics (MHD) formation simulations and 2D semi-analytical model are studied. The dust temperature structure is determined through continuum radiative transfer RADMC3D modelling. A simple temperature dependent CO abundance structure is adopted and synthetic spectrally resolved submm rotational molecular lines up to $J_{\rm u} = 10$ are simulated. All models predict similar compact components in continuum if observed at the spatial resolutions of 0.5-1$"$ (70-140 AU) typical of the observations to date. A spatial resolution of $\sim$14 AU and high dynamic range ($> 1000$) are required to differentiate between RSD and pseudo-disk in the continuum. The peak-position velocity diagrams indicate that the pseudo-disk shows a flatter velocity profile with radius than an RSD. On larger-scales, the CO isotopolog single-dish line profiles are similar and are narrower than the observed line widths of low-$J$ lines, indicating significant turbulence in the large-scale envelopes. However a forming RSD can provide the observed line widths of high-$J$ lines. Thus, either RSDs are common or a higher level of turbulence ($b \sim 0.8 \ {\rm km \ s^{-1}}$ ) is required in the inner envelope compared with the outer part. Multiple spatially and spectrally resolved molecular line observations are needed. The continuum data give a better estimate on disk masses whereas the disk sizes can be estimated from the spatially resolved molecular lines observations. The general observable trends are similar between the 2D semi-analytical models and 3D MHD RSD simulations.Comment: 16 pages, 14 figures, accepted for publication, A&

A Bayesian approach to single-particle electron cryo-tomography in RELION-4.0

We present a new approach for macromolecular structure determination from multiple particles in electron cryo-tomography (cryo-ET) data sets. Whereas existing subtomogram averaging approaches are based on 3D data models, we propose to optimise a regularised likelihood target that approximates a function of the 2D experimental images. In addition, analogous to Bayesian polishing and contrast transfer function (CTF) refinement in single-particle analysis, we describe the approaches that exploit the increased signal-to-noise ratio in the averaged structure to optimise tilt-series alignments, beam-induced motions of the particles throughout the tilt-series acquisition, defoci of the individual particles, as well as higher-order optical aberrations of the microscope. Implementation of our approaches in the open-source software package RELION aims to facilitate their general use, particularly for those researchers who are already familiar with its single-particle analysis tools. We illustrate for three applications that our approaches allow structure determination from cryo-ET data to resolutions sufficient for de novo atomic modelling.This work was funded by the UK Research and Innovation (UKRI) Medical Research Council (MC_UP_A025_1013 to SHWS; and MC_UP_1201/16 to JAGB), the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (ERC-CoG-2014, grant 648432, MEMBRANEFUSION to JAGB and ERC StG-2019, grant 852915 CRYTOCOP to GZ); the Swiss National Science Foundation (grant 205321_179041/1 to DC-D), the Max Planck Society (to JAGB) and the UKRI Biotechnology and Biological Sciences Research Council (grant BB/T002670/1 to GZ). TAMB is a recipient of a Sir Henry Dale Fellowship, jointly funded by the Wellcome Trust and the Royal Society (202231/Z/16/Z). JZ was partially funded by the European Union’s Horizon 2020 research and innovation program (ERC-ADG-2015, grant 692726, GlobalBioIm to Michael Unser)

Geometric deep learning: going beyond Euclidean data

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions), and are natural targets for machine learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of these structures are built into networks used to model them. Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds. The purpose of this paper is to overview different examples of geometric deep learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field

3D Fractal Flame Wisps

This thesis presents a method for integrating two algorithms, fractal flames and wisps, to create visually rich and interesting patterns with 3D volumetric structure. Twenty-one single 3D flame variations are described and specified. These patterns were used to produce an aesthetically designed animation, inspired by both Hubble Telescope photographs and data from a simulation of a predicted collision between the Milky Way and Sagittarius galaxies. The thesis also describes Python tools and a Houdini pre-visualization pipeline that were developed to facilitate the animation design and production

Mapping Topographic Structure in White Matter Pathways with Level Set Trees

Fiber tractography on diffusion imaging data offers rich potential for describing white matter pathways in the human brain, but characterizing the spatial organization in these large and complex data sets remains a challenge. We show that level set trees---which provide a concise representation of the hierarchical mode structure of probability density functions---offer a statistically-principled framework for visualizing and analyzing topography in fiber streamlines. Using diffusion spectrum imaging data collected on neurologically healthy controls (N=30), we mapped white matter pathways from the cortex into the striatum using a deterministic tractography algorithm that estimates fiber bundles as dimensionless streamlines. Level set trees were used for interactive exploration of patterns in the endpoint distributions of the mapped fiber tracks and an efficient segmentation of the tracks that has empirical accuracy comparable to standard nonparametric clustering methods. We show that level set trees can also be generalized to model pseudo-density functions in order to analyze a broader array of data types, including entire fiber streamlines. Finally, resampling methods show the reliability of the level set tree as a descriptive measure of topographic structure, illustrating its potential as a statistical descriptor in brain imaging analysis. These results highlight the broad applicability of level set trees for visualizing and analyzing high-dimensional data like fiber tractography output