The 24 components of the relativistic spin tensor consist of 3 + 3 basic spin fields and 9 + 9 constitutive fields. Empirically only 3 basic spin fields and 9 constitutive fields are known. This empirem can be expressed by two spin axioms, one of them identifying 3 spin fields, and the other one 9 constitutive fields to each other. This identification by the spin axioms is material-independent ...

Attention is focused in this paper on: (i) definitions of alternate measures of “stress-resultants” and “stress-couples” in a finitely deformed shell (finite mid-plane stretches as well as finite rotations); (ii) mixed variational principles for shells, undergoing large mid-plane stretches and large rotations, in terms of a stress function vector and the rotation tensor. In doing so, both types...

The core of multiple-view geometry is governed by the fundamental matrix and the trilinear tensor. In this paper we unify both representations by rst deriving the fundamental matrix as a rank-2 trivalent tensor, and secondly by deriving a uniied set of operators that are transparent to the number of views. As a result, we show that the basic building block of the geometry of multiple views is a...

Scale is a widely used notion in computer vision and image understanding that evolved in the form of scale-space theory where the key idea is to represent and analyze an image at various resolutions. Recently, we introduced a notion of local morphometric scale referred to as "tensor scale" using an ellipsoidal model that yields a unified representation of structure size, orientation and anisotr...

In this paper we introduce a tensor subspace based format for the representation of a tensor in a topological tensor space. To do this we use a property of minimal subspaces which allow us to describe the tensor representation by means of a rooted tree. By using the tree structure and the dimensions of the associated minimal subspaces, we introduce the set of tensors in a tree based format with...

In this study, fast and clinically feasible model-based bootstrapping algorithms using a geometrically constrained two-tensor diffusion model are employed for estimating uncertainty in fibre-orientation. Voxels are classified based on tensor morphologies before applying single or two-tensor model-based bootstrapping algorithms. Classification of tensor morphologies allows the tensor morphology ...

We introduce a tensor category O+ (resp. O−) of certain modules of ĝl∞ with non-negative (resp. non-positive) integral central charges with the usual tensor product. We also introduce a tensor category (Of , ⊙ ) consisting of certain modules over GL(N) for all N . We show that the tensor categories O± and Of are semisimple abelian and all equivalent to each other. We give a formula to decompose...

Low-rank tensor estimation has been frequently applied in many real-world problems. Despite successful applications, existing Schatten 1-norm minimization (SNM) methods may become very slow or even not applicable for large-scale problems. To address this difficulty, we therefore propose an efficient and scalable core tensor Schatten 1-norm minimization method for simultaneous tensor decompositi...

Abstract. It is known that a high order tensor does not necessarily have an optimal low rank approximation, and that a tensor might not be orthogonally decomposable (i.e., admit a tensor SVD). We provide several sufficient conditions which lead to the failure of the tensor SVD, and characterize the existence of the tensor SVD with respect to the Higher Order SVD (HOSVD) of a tensor. In face of ...

In this paper, we provide local and global convergence guarantees for recovering CP (Candecomp/Parafac) tensor decomposition. The main step of the proposed algorithm is a simple alternating rank-1 update which is the alternating version of the tensor power iteration adapted for asymmetric tensors. Local convergence guarantees are established for third order tensors of rank k in d dimensions, wh...