Star formation near the Sun is driven by expansion of the Local Bubble.

For decades we have known that the Sun lies within the Local Bubble, a cavity of low-density, high-temperature plasma surrounded by a shell of cold, neutral gas and dust1-3. However, the precise shape and extent of this shell4,5, the impetus and timescale for its formation6,7, and its relationship to nearby star formation8 have remained uncertain, largely due to low-resolution models of the local interstellar medium. Here we report an analysis of the three-dimensional positions, shapes and motions of dense gas and young stars within 200 pc of the Sun, using new spatial9-11 and dynamical constraints12. We find that nearly all of the star-forming complexes in the solar vicinity lie on the surface of the Local Bubble and that their young stars show outward expansion mainly perpendicular to the bubble's surface. Tracebacks of these young stars' motions support a picture in which the origin of the Local Bubble was a burst of stellar birth and then death (supernovae) taking place near the bubble's centre beginning approximately 14 Myr ago. The expansion of the Local Bubble created by the supernovae swept up the ambient interstellar medium into an extended shell that has now fragmented and collapsed into the most prominent nearby molecular clouds, in turn providing robust observational support for the theory of supernova-driven star formation.

A Galactic-scale gas wave in the solar neighbourhood.

For the past 150 years, the prevailing view of the local interstellar medium has been based on a peculiarity known as the Gould Belt1-4, an expanding ring of young stars, gas and dust, tilted about 20 degrees to the Galactic plane. However, the physical relationship between local gas clouds has remained unknown because the accuracy in distance measurements to such clouds is of the same order as, or larger than, their sizes5-7. With the advent of large photometric surveys8 and the astrometric survey9, this situation has changed10. Here we reveal the three-dimensional structure of all local cloud complexes. We find a narrow and coherent 2.7-kiloparsec arrangement of dense gas in the solar neighbourhood that contains many of the clouds thought to be associated with the Gould Belt. This finding is inconsistent with the notion that these clouds are part of a ring, bringing the Gould Belt model into question. The structure comprises the majority of nearby star-forming regions, has an aspect ratio of about 1:20 and contains about three million solar masses of gas. Remarkably, this structure appears to be undulating, and its three-dimensional shape is well described by a damped sinusoidal wave on the plane of the Milky Way with an average period of about 2 kiloparsecs and a maximum amplitude of about 160 parsecs.

Equivariant Wavelets: Fast Rotation and Translation Invariant Wavelet Scattering Transforms.

Wavelet scattering networks, which are convolutional neural networks (CNNs) with fixed filters and weights, are promising tools for image analysis. Imposing symmetry on image statistics can improve human interpretability, aid in generalization, and provide dimension reduction. In this work, we introduce a fast-to-compute, translationally invariant and rotationally equivariant wavelet scattering network (EqWS) and filter bank of wavelets (triglets). We demonstrate the interpretability and quantify the invariance/equivariance of the coefficients, briefly commenting on difficulties with implementing scale equivariance. On MNIST, we show that training on a rotationally invariant reduction of the coefficients maintains rotational invariance when generalized to test data and visualize residual symmetry breaking terms. Rotation equivariance is leveraged to estimate the rotation angle of digits and reconstruct the full rotation dependence of each coefficient from a single angle. We benchmark EqWS with linear classifiers on EMNIST and CIFAR-10/100, introducing a new second-order, cross-color channel coupling for the color images. We conclude by comparing the performance of an isotropic reduction of the scattering coefficients and RWST, a previous coefficient reduction, on an isotropic classification of magnetohydrodynamic simulations with astrophysical relevance.