The non-abelian tensor product of groups which has its origins in algebraic K-theory as well as inhomotopy theory, was introduced by Brown and Loday in 1987. Group theoretical aspects of non-abelian tensor products have been studied extensively. In particular, some studies focused on the relationship between the exponent of a group and exponent of its tensor square. On the other hand, com...

Canonical correlation analysis (CCA) is a useful technique for measuring relationship between two sets of vector data. For paired tensor data sets, we propose a multilinear CCA (MCCA) method. Unlike existing multilinear variations of CCA, MCCA extracts uncorrelated features under two architectures while maximizing paired correlations. Through a pair of tensor-to-vector projections, one architec...

Following trauma, imaging of brain stem lesions is often inconclusive. In a man who suffered a lethal accident, postmortem MR diffusion tensor (DT) imaging of the brain and neuropathologic examination were performed. DT imaging showed a disorganization of fibers in the brain stem that was not found in 2 controls and corresponded to changes on neuropathologic correlation. Diffusion tensor imagin...

We synthesize colloidal particles with various anisotropic shapes and track their orientationally resolved Brownian trajectories using confocal microscopy. An analysis of appropriate short-time correlation functions provides direct access to the hydrodynamic friction tensor of the particles revealing nontrivial couplings between the translational and rotational degrees of freedom. The results a...

With the help of scaling methods. a general relation is established between the thermodynamic pressure and the mechanical pressure tensor of an equilibrium one-component plasma in a magnetic field. The mechanical pressure tensor is shown lo be anisotropic. A general proof of the compressibility sum rule for a magnetized quantum plasma is presented. Finally, fourth-order wavenumber inequalities ...

In this article, the notions of non-abelian tensor and exterior products of two normal crossed submodules of a given crossed module of groups are introduced and some of their basic properties are established. In particular, we investigate some common properties between normal crossed modules and their tensor products, and present some bounds on the nilpotency class and solvability length of the...

We present Deep Tensor Canonical Correlation Analysis (DTCCA), a method to learn complex nonlinear transformations of multiple views (more than two) data such that the resulting representations are linearly correlated in high order. The high-order correlation given is modeled by covariance tensor, which different from most CCA formulations relying solely on pairwise correlations. Parameters eac...

We present a unitary correlation operator that explicitly induces into shell model type many-body states short ranged two-body correlations caused by the strong repulsive core and the pronounced tensor part of the nucleon-nucleon interaction. Alternatively an effective Hamiltonian can be defined by applying this unitary correlator to the realistic nucleon-nucleon interaction. The momentum space...