相关论文: Orthogonal invariant sets of the diffusion tensor …

The statistical analysis of covariance matrix data is considered and, in particular, methodology is discussed which takes into account the non-Euclidean nature of the space of positive semi-definite symmetric matrices. The main motivation…

Biaxial anisotropy, arising from distinct optical responses along three principal directions, underlies the complex structure of many crystalline, polymeric, and biological materials. However, existing techniques such as X-ray diffraction…

The statistical analysis of covariance matrices occurs in many important applications, e.g. in diffusion tensor imaging and longitudinal data analysis. We consider the situation where it is of interest to estimate an average covariance…

Measurements of the resistivity anisotropy can provide crucial information about the electronic structure and scattering processes in anisotropic and low-dimensional materials, but quantitative measurements by conventional means often…

Heterogeneous anisotropic diffusion problems arise in the various areas of science and engineering including plasma physics, petroleum engineering, and image processing. Standard numerical methods can produce spurious oscillations when they…

We propose bending energies for isotropic elastic plates and shells. For a plate, we define and employ a surface tensor that symmetrically couples stretch and curvature such that any elastic energy density constructed from its invariants is…

We theoretically analyze diffusion trajectories of an anisotropic object moving on a two dimensional space in the absence of an external field. In determining diffusion parameters associated with the shape anisotropy, we devise a measure…

An inhomogeneous fractal set is one which exhibits different scaling behaviour at different points. The Assouad dimension of a set is a quantity which finds the `most difficult location and scale' at which to cover the set and its…

We measure all nonzero elements of the three-dimensional (3D) diffusion tensor D for clusters of colloidal spheres to a precision of 1% or better using digital holographic microscopy. We study both dimers and triangular trimers of spheres,…

Statistical analysis of Diffusion Tensor Imaging (DTI) data requires a computational framework that is both numerically tractable (to account for the high dimensional nature of the data) and geometric (to account for the nonlinear nature of…

We aim at estimating in a non-parametric way the density $\pi$ of the stationary distribution of a $d$-dimensional stochastic differential equation $(X_t)_{t \in [0, T]}$, for $d \ge 2$, from the discrete observations of a finite sample…

Methods for anomaly detection of new physics processes are often limited to low-dimensional spaces due to the difficulty of learning high-dimensional probability densities. Particularly at the constituent level, incorporating desirable…

The analysis of data sets arising from multiple sensors has drawn significant research attention over the years. Traditional methods, including kernel-based methods, are typically incapable of capturing nonlinear geometric structures. We…

We present a straightforward analytical-numerical methodology for determining polynomially complete and irreducible scalar-valued invariant sets for anisotropic hyperelasticity. By applying the proposed technique, we obtain irreducible…

The analysis of contours of scalar fields plays an important role in visualization. For example the contour tree and contour statistics can be used as a means for interaction and filtering or as signatures. In the context of tensor field…

In a series of papers Tsirelson constructed from measure types of random sets and generalised random processes a new range of examples for continuous tensor product systems of Hilbert spaces introduced by Arveson for classifying…

Designing novel diffusion-weighted pulse sequences to probe tissue microstructure beyond the conventional Stejskal-Tanner family is currently of broad interest. One such technique, multidimensional diffusion MRI, has been recently proposed…

In the recent articles \cite{PSU1,PSU3}, a number of tensor tomography results were proved on two-dimensional manifolds. The purpose of this paper is to extend some of these methods to manifolds of any dimension. A central concept is the…

The modelling of off-axis simple tension experiments on transversely isotropic nonlinearly elastic materials is considered. A testing protocol is proposed where normal force is applied to one edge of a rectangular specimen with the opposite…

Anisotropic Diffusion is widely used for noise reduction with simultaneous preservation of vascular structures in maximum intensity projected (MIP) angiograms. However, extension to minimum intensity projected (mIP) venograms in…