Related papers: A general method for rotational averages
We consider an infinitesimal volume where there are many rigid molecules of the same kind, and discuss the description and classification of the local anisotropy in this volume by tensors. First, we examine the symmetry of a rigid molecule,…
The performance of organic optoelectronic devices is critically dependent on how molecules orient within organic thin films. Yet, standard characterization techniques only reveal the first and second moments of the molecular orientation…
We establish the existence of weak solutions of a nonlinear radiation-type boundary value problem for elliptic equation on divergence form with discontinuous leading coefficient. Quantitative estimates play a crucial role on the real…
The point symmetry group is studied for the generalized Webster-type equation describing non-linear acoustic waves in lossy channels with variable cross sections. It is shown that, for certain types of cross section profiles, the admitted…
One of basic difficulties of machine learning is handling unknown rotations of objects, for example in image recognition. A related problem is evaluation of similarity of shapes, for example of two chemical molecules, for which direct…
We argue that in the general relativistic calculation of planetary orbits, the choice of a reference frame which is an obligatory condition in the Newtonian approach is replaced by an appropriate boundary condition on the solution of…
This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…
By a tensor we mean an element of a tensor product of vector spaces over a field. Up to a choice of bases in factors of tensor products, every tensor may be coordinatized, that is, represented as an array consisting of numbers. This note is…
We consider the problem of estimating a rank-one nonsymmetric matrix under additive white Gaussian noise. The matrix to estimate can be written as the outer product of two vectors and we look at the special case in which both vectors are…
We study invariant operators in general tensor models. We show that representation theory provides an efficient framework to count and classify invariants in tensor models. In continuation and completion of our earlier work, we present two…
We obtain a non-linear generalization of the relativistic diffusion of particles with spin. We discuss diffusion equations whose non-linearity is a consequence of quantum statistics. We show that the assumptions of the relativistic…
Invariant tensors are states in the (local) SU(2) tensor product representation but invariant under global SU(2) action. They are of importance in the study of loop quantum gravity. A random tensor is an ensemble of tensor states. An…
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…
We establish a general principle which states that regularizing an inverse problem with a convex function yields solutions which are convex combinations of a small number of atoms. These atoms are identified with the extreme points and…
Time dependent signals in experimental techniques such as Nuclear Magnetic Resonance (NMR) and Muon Spin Relaxation (muSR) are often the result of an ensemble average over many microscopical dynamical processes. While there are a number of…
We introduce a new type of lens that focuses a plane wave into a spherical one, where light comes from all directions. Our method also suggests the design of ideal optical tweezers or, in the reverse direction, photo-detection of nearly all…
A common problem in physics and engineering is determination of the orientation of an object given its angular velocity. When the direction of the angular velocity changes in time, this is a nontrivial problem involving coupled differential…
Matrix concentration inequalities, intimately connected to the Non-Commutative Khintchine inequality, have been an important tool in both applied and pure mathematics. We study tensor versions of these inequalities, and establish…
In applications, a substantial number of problems can be formulated as non-linear least squares problems over smooth varieties. Unlike the usual least squares problem over a Euclidean space, the non-linear least squares problem over a…
Tensor regression is an important tool for tensor data analysis, but existing works have not considered the impact of outliers, making them potentially sensitive to such data points. This paper proposes a low tubal rank robust regression…