Initial value constraints with tensor matter

Approximating Initial-Value Problems with Two-Point Boundary-Value Problems: BBM-Equation

On the solution of the initial value constraints for general relativity coupled to matter in terms of Ashtekar’s variables

The method of solution of the initial value constraints for pure canonical gravity in terms of Ashtekar’s new canonical variables due to CDJ (see [1]) is further developed in the present paper. There are 2 new main results : 1) We extend the method of CDJ to arbitrary matter-coupling again for non-degenerate metrics : the new feature is that the ’CDJmatrix’ adopts a nontrivial antisymmetric par...

Diffusion Tensor Regularization with Constraints Preservation

This paper deals with the problem of regularizing noisy fields of diffusion tensors, considered as symmetric and semi-positive definite n n matrices (as for instance 2D structure tensors or DT-MRI medical images). We first propose a simple anisotropic PDE-based scheme that acts directly on the matrix coefficients and preserve the semipositive constraint thanks to a specific reprojection step. T...

Nonnegative Tensor Factorization with Smoothness Constraints

Nonnegative Tensor Factorization (NTF) is an emerging technique in multidimensional signal analysis and it can be used to find partsbased representations of high-dimensional data. Inmany applications such as multichannel spectrogram processing or multiarray spectra analysis, the unknown features have locally smooth temporal or spatial structure. In this paper, we incorporate to an objective fun...

Evaluation of treatment-induced cerebral white matter injury by using diffusion-tensor MR imaging: initial experience.

BACKGROUND AND PURPOSE Treatment with chemotherapy and radiation therapy for brain tumors can cause white matter (WM) injury. Conventional MR imaging, however, cannot always depict treatment-induced transient WM abnormalities. We investigated the ability of diffusion-tensor (DT) MR imaging and proton MR spectroscopy to detect the treatment-induced transient changes within normal-appearing WM. ...