Geometric Wavelet Scattering Networks on Compact Riemannian Manifolds

The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of convolutional neural networks. Inspired by recent interest in geometric deep learning, which aims to generalize convolutional neural networks to manifold and graph-structured domains, we define a geometric scattering transform on manifolds. Similar to the Euclidean scattering transform, the geometric scattering transform is based on a cascade of wavelet filters and pointwise nonlinearities. It is invariant to local isometries and stable to certain types of diffeomorphisms. Empirical results demonstrate its utility on several geometric learning tasks. Our results generalize the deformation stability and local translation invariance of Euclidean scattering, and demonstrate the importance of linking the used filter structures to the underlying geometry of the data.Comment: 35 pages; 3 figures; 2 tables; v3: Revisions based on reviewer comment

A Search for Gamma-Ray Burst Optical Emission with the Automated Patrol Telescope

The Automated Patrol Telescope (APT) is a wide-field (5 X 5 deg.s), modified Schmidt capable of covering large gamma-ray burst (GRB) localization regions to produce a high rate of GRB optical emission measurements. Accounting for factors such as bad weather and incomplete overlap of our field and large GRB localization regions, we estimate our search will image the actual location of 20-41 BATSE GRB sources each year. Long exposures will be made for these images, repeated for several nights, to detect delayed optical transients (OTs) with light curves similar to those already discovered. The APT can also respond within about 20 sec. to GRB alerts from BATSE to search for prompt emission from GRBs. We expect to image more than 2.4 GRBs/yr. during gamma-ray emission. More than 5.1 will be imaged/yr. within about 20 sec. of emission. The APT's 50 cm aperture is much larger than other currently operating experiments used to search for prompt emission, and the APT is the only GRB dedicated telescope in the Southern Hemisphere. Given the current rate of about 25% OTs per X/gamma localization, we expect to produce a sample of about 10 OTs for detailed follow-up observations in 1-2 years of operation.Comment: 4 pages latex + 3 ps figures. Download a single tar file of ps at http://panisse.lbl.gov/public/bruce/optgrbsearch.tar.g

Gauge-noninvariance of quantum cosmology and vacuum dark energy

We address the question how to adapt cosmological constant $\Lambda$ for description of a vacuum dark energy density jumping from the big initial value to the small today value suggested by observations. We find such a possibility in the gauge-noninvariance of quantum cosmology which leads to a connection between a choice of the gauge and quantum spectrum for a certain physical quantity which can be specified in the framework of the minisuperspace model. We introduce a particular gauge in which the cosmological constant $\Lambda$ is quantized and show that making a measurement of $\Lambda$ today one can find its small value with the biggest probability, while at the beginning of the evolution, the biggest probability corresponds to its biggest value. Transitions between quantum levels of $\Lambda$ in the course of the Universe evolution, could be related to several scales for symmetry breaking.Comment: 5 pages, 1 figur