Related papers: Tensor tomography: progress and challenges

Tensor completion is a natural higher-order generalization of matrix completion where the goal is to recover a low-rank tensor from sparse observations of its entries. Existing algorithms are either heuristic without provable guarantees,…

We propose a new program to quantize and renormalize gravity based on recent progress on the analysis of large random tensors. We compare it briefly with other existing approaches.

Despite encouraging recent progresses in ensemble approaches, classification methods seem to have reached a plateau in development. Further advances depend on a better understanding of geometrical and topological characteristics of point…

This note describes some open problems that can be examined with the purpose of gaining additional insight of how to solve the problem of finding a general classification of geodetic graphs

In this survey paper, we present open problems and conjectures on visibility graphs of points, segments and polygons along with necessary backgrounds for understanding them.

We consider the problem of finding embedded closed geodesics on the two-sphere with an incomplete metric defined outside a point. Various techniques including curve shortening methods are used.

In this article, we consider the problem of finding the support of an inhomogenous possibly anisotropic inclusion in a background of constant electric conductivity from the electrical impedance tomography data at the boundary of a bounded…

We consider the problem of reconstructing the paths of a set of points over time, where, at each of a finite set of moments in time the current positions of points in space are only accessible through some small number of their X-rays. This…

The goal of this survey is to give a list of resent results about topology of manifolds admitting different metrics with the same geodesics. We emphasize the role of the theory of integrable systems in obtaining these results.

In this article, we study various aspects of the mixed ray transform of $(k + \ell)$-tensor fields that are symmetric in its first $k$ and last $\ell$ indices. As a first result, we derive an inversion algorithm to recover the solenoidal…

We present gravitoelectromagnetism and other decompositions of the Riemann tensor from the differential-geometrical point of view.

We give a survey of algorithms for computing topological invariants of semi-algebraic sets with special emphasis on the more recent developments in designing algorithms for computing the Betti numbers of semi-algebraic sets. Aside from…

We survey recent developments in the theory of achievement sets and present a substantial collection of open problems.

An overview is given on those theoretical gravitational lensing results that can be formulated in a spacetime setting, without assuming that the gravitational fields are weak and that the bending angles are small. The first part is devoted…

We present a numerical implementation of the geodesic ray transform and its inversion over functions and solenoidal vector fields on two-dimensional Riemannian manifolds. For each problem, inversion formulas previously derived in…

One of the main issues in computing a tensor decomposition is how to choose the number of rank-one components, since there is no finite algorithms for determining the rank of a tensor. A commonly used approach for this purpose is to find a…

This document is a brief summary of progress that has been made on the problems posed in the document "Twenty Open Problems in Enumeration of Matchings" (also available from this server as math.CO/9801060). NOTE: This article has now been…

One of the main purposes of earth observation is to extract interested information and knowledge from remote sensing (RS) images with high efficiency and accuracy. However, with the development of RS technologies, RS system provide images…

Tensors are a fundamental data structure for many scientific contexts, such as time series analysis, materials science, and physics, among many others. Improving our ability to produce and handle tensors is essential to efficiently address…

Recovery of low-rank matrices from a small number of linear measurements is now well-known to be possible under various model assumptions on the measurements. Such results demonstrate robustness and are backed with provable theoretical…