We prove rigidity results for compact Riemannian manifolds in the spirit of Tachibana. For example, we observe that with divergence free Weyl tensors and $\lfloor \frac{n-1}{2} \rfloor$-nonnegative curvature operators are locally symmetric or conformally equivalent to a quotient sphere. The main focus paper is similar special holonomy. In particular, consider K\"ahler Bochner tensor. quaternion...

Tenenbuam and Freeman proposed bilinear classifiers as a tool to classify observations influenced by both the variable to classify (“content”) and a nuisance factor (“style”). In most real-world problem however, observations are influenced by a number of such factors. Gait identification is a typical such situation. To tackle their influence, it is natural to resort to multilinear or tensor dec...

In all physical representations of numbers constructed to date, numbers are represented by strings of numerals or by tensor product states of systems in quantum mechanics. This is the case for macroscopic systems, such as classical computers, which are in such wide use. It is also true for microscopic systems or quantum computers which are of much recent interest [1,2]. The universal use of the...

We propose an inverse iterative method for computing the Perron pair of an irreducible nonnegative third order tensor. The method involves the selection of a parameter θk in the kth iteration. For every positive starting vector, the method converges quadratically and is positivity preserving in the sense that the vectors approximating the Perron vector are strictly positive in each iteration. I...

In this paper we study multivariate polynomial functions in complex variables and the corresponding associated symmetric tensor representations. The focus is on finding conditions under which such complex polynomials/tensors always take real values. We introduce the notion of symmetric conjugate forms and general conjugate forms, and present characteristic conditions for such complex polynomial...

In this work we apply non-negative matrix factorizations (NMF) to some imaging and inverse problems. We propose a sparse low-rank approximation of big data and images in terms of tensor products, and investigate its effectiveness in terms of the number of tensor products to be used in the approximation. A multi-resolution analysis (MRA) framework is presented using a sparse low-rank approximati...

Spectro-temporal modulations of speech encode speech structures and speaker characteristics. An algorithm which distinguishes speech from non-speech based on spectro-temporal modulation energies is proposed and evaluated in robust text-independent closed-set speaker identification simulations using the TIMIT and GRID corpora. Simulation results show the proposed method produces much higher spea...