the interaction of dppa which is an important component in cellular membrane with molecules of water asmedia, cause some changes in geometry of dppa .in this study we focused our attention on comparing thismolecule with related hydrated complexes employing different basis sets at hartree-fock levels of theory. thetheoretical nmr shielding tensor of some imported atoms were also reported.

Low-rank tensor learning has many applications in machine learning. A series of batch learning algorithms have achieved great successes. However, in many emerging applications, such as climate data analysis, we are confronted with largescale tensor streams, which pose significant challenges to existing solutions. In this paper, we propose an accelerated online low-rank tensor learning algorithm...

In this paper we introduce and develop the notion of minimal subspaces in the framework of algebraic and topological tensor product spaces. This mathematical structure arises in a natural way in the study of tensor representations. We use minimal subspaces to prove the existence of a best approximation, for any element in a Banach tensor space, by means a tensor given in a typical representatio...

BACKGROUND Tensor tympani contraction may have a "signature" audiogram. This study demonstrates audiometric findings during voluntary tensor tympani contraction. METHODS Five volunteers possessing the ability to voluntarily contract their tensor tympani muscles were identified and enrolled. Tensor tympani contraction was confirmed with characteristic tympanometry findings. Study subjects unde...

Nonnegative tensor factorization has applications in statistics, computer vision, exploratory multiway data analysis and blind source separation. A symmetric nonnegative tensor, which has an exact symmetric nonnegative factorization, is called a completely positive tensor. This concept extends the concept of completely positive matrices. A classical result in the theory of completely positive m...

We establish several mathematical and computational properties of the nuclear norm for higher-order tensors. We show that like tensor rank, tensor nuclear norm is dependent on the choice of base field — the value of the nuclear norm of a real 3-tensor depends on whether we regard it as a real 3-tensor or a complex 3-tensor with real entries. We show that every tensor has a nuclear norm attainin...

While tensor factorizations have become increasingly popular for learning on various forms of structured data, only very few theoretical results exist on the generalization abilities of these methods. Here, we discuss the tensor product as a principled way to represent structured data in vector spaces for machine learning tasks. To derive generalization error bounds for tensor factorizations, w...

In this paper, we study the statistical performance of robust tensor decomposition with gross corruption. The observations are noisy realization of the superposition of a low-rank tensorW∗ and an entrywise sparse corruption tensor V∗. Unlike conventional noise with bounded variance in previous convex tensor decomposition analysis, the magnitude of the gross corruption can be arbitrary large. We...

The structure tensor has been used mainly for representation of local orientation in spaces of arbitrary dimensions, where the eigenvectors represent the orientation and the corresponding eigenvalues indicate the type of structure which is represented. Apart from being local, the structure tensor may be referred to as “object centered” since it describes the corresponding structure relative to ...

This paper develops and investigates iterative tensor methods for solving large-scale systems of nonlinear equations. Direct tensor methods for nonlinear equations have performed especially well on small, dense problems where the Jacobian matrix at the solution is singular or ill-conditioned, which may occur when approaching turning points, for example. This research extends direct tensor metho...