In [12], Hillar and Lim famously demonstrated that “multilinear (tensor) analogues of many efficiently computable problems in numerical linear algebra are NP-hard”. Despite many recent advancements, the state-of-the-art methods for computing such ‘tensor analogues’ still suffer severely from the curse of dimensionality. In this paper we show that the Tucker core of a tensor however, retains man...

Supervised dimensionality reduction with tensor representation has attracted great interest in recent years. It has been successfully applied to problems with tensor data, such as image and video recognition tasks. However, in the tensor based methods, how to select the suitable dimensions is a very important problem. Since the number of possible dimension combinations exponentially increases w...

A molecular dynamics simulation of the demixing process of a binary complex plasma is analyzed and the role of distinct interaction potentials is discussed by using morphological Minkowski tensor analysis of the minority phase domain growth in a demixing simulated binary complex plasma. These Minkowski tensor methods are compared with previous results that utilized a power spectrum method based...

The dynamics of magnetization under the applied spin current is modeled by the generalized Landau-Lifshitz-Gilbert equation with a spin transfer torque term. Using matched asymptotic expansion with the domain wall thickness ǫ as the small parameter, we derive analytically the dynamic law for the domain wall motion induced by the spin current. We show that the domain wall driven by adiabatic cur...

Using the 3-dimensional structure tensor, dense displacement vector fields (DVF) can be computed with subpixel accuracy. The approach is based on the detection of linear symmetries and the corresponding orientation angle within a local spatio–temporal neighborhood. The proposed technique is well suited to be applied within a multiresolution framework in order to avoid corresponence problem erro...

A simple theoretical analysis and direct numerical simulations on 512(3) grid points suggest that the velocity correlation spectrum tensor in the inertial subrange of homogeneous turbulent shear flow at high Reynolds number is given by a simple form that is an anisotropic function of the wave vector. The tensor is determined by the rate of the strain tensor of the mean flow, the rate of energy ...

INTRODUCTION –Short-Axis Propeller EPI (SAP-EPI) has been shown to be very effective in obtaining highresolution, artifact-free DTI data [2]. One challenge with SAP-EPI is that in the presence of head rotation each blade of SAP-EPI data is potentially encoded with a different diffusionencoding direction (i.e. b-matrix) (Fig. 1). Since the diffusion-encoding is ‘imprinted’ on the magnetization, ...

We determine the algebraic degree of minimal problems for the calibrated trifocal variety in computer vision. We rely on numerical algebraic geometry and the homotopy continuation software Bertini.

Simple models and algorithms based on restrictive assumptions are often used in the field of neuroimaging for studies involving functional magnetic resonance imaging, voxel based morphometry, and diffusion tensor imaging. Nonparametric statistical methods or flexible Bayesian models can be applied rather easily to yield more trustworthy results. The spatial normalization step required for multi...

By including the full pressure tensor dynamics in a fluid plasma model, we show that a sheared velocity field can provide an effective mechanism that makes the initial isotropic pressure nongyrotropic. This is distinct from the usual gyrotropic anisotropy related to the fluid compressibility and usually accounted for in double-adiabatic models. We determine the time evolution of the pressure ag...