New currents with Killing–Yano tensors

A New Sampling Technique for Tensors

In this paper we propose new techniques to sample arbitrary third-order tensors, with an objective of speeding up tensor algorithms that have recently gained popularity in machine learning. Our main contribution is a new way to select, in a biased random way, only O(n/ǫ) of the possible n elements while still achieving each of the three goals: (a) tensor sparsification: for a tensor that has to...

New Topological Invariants Expressible as Tensors.

On New Classes of Nonnegative Symmetric Tensors

In this paper we introduce three new classes of nonnegative forms (or equivalently, symmetric tensors) and their extensions. The newly identified nonnegative symmetric tensors constitute distinctive convex cones in the space of general symmetric tensors (order 6 or above). For the special case of quartic forms, they collapse into the set of convex quartic homogeneous polynomial functions. We di...

Killing Tensors and a New Geometric Duality

We present a theorem describing a dual relation between the local geometry of a space admitting a symmetric second-rank Killing tensor, and the local geometry of a space with a metric specified by this Killing tensor. The relation can be generalized to spinning spaces, but only at the expense of introducing torsion. This introduces new supersymmetries in their geometry. Interesting examples in ...

Seiberg-Witten-type Maps for Currents and Energy-Momentum Tensors in Noncommutative Gauge Theories

We derive maps relating the currents and energy-momentum tensors in noncommutative (NC) gauge theories with their commutative equivalents. Some uses of these maps are discussed. Especially, in NC electrodynamics, we obtain a generalization of the Lorentz force law. Also, the same map for anomalous currents relates the Adler-BellJackiw type NC covariant anomaly with the standard commutative-theo...