Abstract. In this paper we define the best rank-one approximation ratio of a tensor space. It turns out that in the finite dimensional case this provides an upper bound for the quotient of the residual of the best rankone approximation of any tensor in that tensor space and the norm of that tensor. This upper bound is strictly less than one, and it gives a convergence rate for the greedy rank-o...

for two normal edge-transitive cayley graphs on groups h and k which have no common direct factor and gcd(jh=h ′j; jz(k)j) = 1 = gcd(jk=k ′j; jz(h)j), we consider four standard products of them and it is proved that only tensor product of factors can be normal edge-transitive.

A new and significant source of information on earthquake studies has been provided by space geodesy. The data which are gathered by various techniques of space geodesy, can quantify potential of seismic activity in the region of interest. To achieve this goal, the main advantage of extra-terrestrial geodetic data in comparison with the conventional data from geology and seismology is the abili...

Decompositions of higher-order tensors are becoming more and more important in signal processing, data analysis, machine learning, scientific computing, optimization and many other fields. A new trend is the study of coupled matrix/tensor decompositions (i.e., decompositions of multiple matrices and/or tensors that are linked in one or several ways). Applications can be found in various fields ...

results stereoscopic displays of the nerves were obtained in all 24 elbows by vr, mip, and fiber tractography post-processing methods. the vr/mip post-processing methods were easier to perform compared to fiber tractography. there was no significant difference among the scores of fiber tracking and vr/mip reconstruction for single direction. the imaging quality scores of fiber tractography and ...

more than half of all hydrocarbon reservoirs are naturally fractured reservoirs (nfrs), in which production forecasting is a complicated function of fluid flow in a fracture-matrix system. modelling of fluid flow in nfrs is challenging due to formation heterogeneity and anisotropy. stress sensitivity and depletion effect on already-complex reservoir permeability add to the sophistication. horiz...

we characterize function spaces of rees matrixsemigroups. then we study these spaces by using the topologicaltensor product technique.

In this paper we propose new techniques to sample arbitrary third-order tensors, with an objective of speeding up tensor algorithms that have recently gained popularity in machine learning. Our main contribution is a new way to select, in a biased random way, only O(n/ǫ) of the possible n elements while still achieving each of the three goals: (a) tensor sparsification: for a tensor that has to...

Many idealized problems in signal processing, machine learning and statistics can be reduced to the problem of finding the symmetric canonical decomposition of an underlying symmetric and orthogonally decomposable (SOD) tensor. Drawing inspiration from the matrix case, the successive rank-one approximations (SROA) scheme has been proposed and shown to yield this tensor decomposition exactly, an...

A novel approach to reconstructing the principal directions of a diffusion tensor field directly from magnetic resonance imaging (MRI) data using a tensor tomography data acquisition approach was developed. If tensor eigenvalues are assumed to be known, the reconstruction of principal directions requires fewer measurements than the reconstruction of the full tensor field. The tensor tomography ...