In this paper, we prove that a real tensor is strictly semi-positive if and only if the corresponding tensor complementarity problem has a unique solution for any nonnegative vector and a real tensor is semi-positive if and only if the corresponding tensor complementarity problem has a unique solution for any positive vector. It is showed that a real symmetric tensor is a (strictly) semi-positi...

Second-order tensors may be described in terms of shape and orientation. Shape is quantified by tensor invariants, which are fixed with respect to coordinate system changes. This chapter describes an anatomically-motivated method of detecting edges in diffusion tensor fields based on the gradients of invariants. Three particular invariants (the mean, variance, and skewness of the tensor eigenva...

This paper deals with the class of Q-tensors, that is, a Q-tensor is a real tensor A such that the tensor complementarity problem (q,A): finding x ∈ R such that x ≥ 0,q+Axm−1 ≥ 0, and x⊤(q+Axm−1) = 0, has a solution for each vector q ∈ Rn. Several subclasses of Q-tensors are given: P-tensors, R-tensors, strictly semi-positive tensors and semi-positive R0-tensors. We prove that a nonnegative ten...

neglected, untreated and delayed femur neck fractures are commonly encountered and the treatment dilemma arises especially when the patient is physiologically young and osteosynthesis is the preferred option. controversy exists in the current literature as the various head salvage surgeries like valgus subtrochanteric osteotomy, non-vascularized fibular bone grafting, muscle pedicle bone grafti...

The Bakry-Émery tensor gives an analog of the Ricci tensor for a Riemannian manifold with a smooth measure. We show that some of the topological consequences of having a positive or nonnegative Ricci tensor are also valid for the Bakry-Émery tensor. We show that the Bakry-Émery tensor is nondecreasing under a Riemannian submersion whose fiber transport preserves measures up to constants. We giv...

Human action can be naturally represented as multidimensional arrays known as tensors. In this paper, a simple and efficient algorithm based on tensor subspace learning is proposed for human action recognition. An action is represented as a 3th-order tensor first, then tensor principal component analysis is used to reduce dimensionality and extract the most useful features for action recognitio...

Numerical tensor calculus comprise basic tensor operations such as the entrywise addition and contraction of higher-order tensors. We present, TLib, flexible tensor framework with generic tensor functions and tensor classes that assists users to implement generic and flexible tensor algorithms in C++. The number of dimensions, the extents of the dimensions of the tensors and the contraction mod...