Energy–momentum tensor from the Yang–Mills gradient flow

The Spherical Tensor Gradient Operator

The spherical tensor gradient operator Y l (∇), which is obtained by replacing the Cartesian components of r by the Cartesian components of ∇ in the regular solid harmonic Y l (r), is an irreducible spherical tensor of rank l. Accordingly, its application to a scalar function produces an irreducible spherical tensor of rank l. Thus, it is in principle sufficient to consider only multicenter int...

Sign of the Electric Field Gradient Tensor

Escaping From Saddle Points - Online Stochastic Gradient for Tensor Decomposition

We analyze stochastic gradient descent for optimizing non-convex functions. In many cases for non-convex functions the goal is to find a reasonable local minimum, and the main concern is that gradient updates are trapped in saddle points. In this paper we identify strict saddle property for non-convex problem that allows for efficient optimization. Using this property we show that from an arbit...

Dense Optical Flow Estimation from the Monogenic Curvature Tensor

In this paper, we address the topic of estimating two-frame dense optical flow from the monogenic curvature tensor. The monogenic curvature tensor is a novel image model, from which local phases of image structures can be obtained in a multi-scale way. We adapt the combined local and global (CLG) optical flow estimation approach to our framework. In this way, the intensity constraint equation i...

Gravity Gradient Tensor Eigendecomposition for Spacecraft Positioning

Pei Chen1, Xiucong Sun2, and Chao Han3 Beihang University, Beijing, 100191, People’s Republic of China Nomenclature U = gravitational potential, m2/s2 T = gravity gradient tensor (GGT), E TECEF = GGT in ECEF, E TENU = GGT in ENU, E TEIG = GGT in the Eigen frame, E T0 = GGT in GRF, E LA→B = rotation matrix from A to B r = observation position, m x, y, z = cartesian coordinates of r r, φ, λ = sph...