Related papers: A Commentary on "Breaking Row and Column Symmetrie…
Persistence diagrams, combining geometry and topology for an effective shape description used in pattern recognition, have already proven to be an effective tool for shape representation with respect to a certainfiltering function.…
Selection rules are often considered a hallmark of symmetry. When a symmetry is broken, e.g., by an external perturbation, the system exhibits selection rule deviations which are often analyzed by perturbation theory. Here, we employ…
In this paper, we present and analyze methods for solving a system of linear equations over idempotent semifields. The first method is based on the pseudo-inverse of the system matrix. We then present a specific version of Cramer's rule…
The Nystrom method is an efficient technique to speed up large-scale learning applications by generating low-rank approximations. Crucial to the performance of this technique is the assumption that a matrix can be well approximated by…
Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown low-rank matrix. Our goal is to decompose the given matrix into its sparse and low-rank components. Such a problem arises in a number of…
In finance, economics and many other fields, observations in a matrix form are often observed over time. For example, many economic indicators are obtained in different countries over time. Various financial characteristics of many…
We study integer-valued matrices with bounded determinants. Such matrices appear in the theory of integer programs (IP) with bounded determinants. For example, Artmann et al. showed that an IP can be solved in strongly polynomial time if…
Multilinear and tensor decompositions are a popular tool in linear and multilinear algebra and have a wide range of important applications to modern computing. Our paper of 1972 presented the first nontrivial application of such…
This work is devoted to the study of the relationships between graph theory and the qualitative analysis of ordinary differential equations, with a special focus on two-dimensional systems. In particular, we reinterpret classical results…
We show that schemes for sparsifying matrices based on iteratively resampling rows yield guarantees matching classic 'offline' sparsifiers (see e.g. Spielman and Srivastava [STOC 2008]). In particular, this gives a formal analysis of a…
We present a novel methodology to detect imperfect bilateral symmetry in CT of human anatomy. In this paper, the structurally symmetric nature of the pelvic bone is explored and is used to provide interventional image augmentation for…
These lectures are intended to provide an introduction to heavy meson decays and CP violation. The first lecture contains a brief review of the standard model and how the CKM matrix and CP violation arise, mixing and CP violation in neutral…
We show that a rational normal scroll can in general be set-theoretically defined by a proper subset of the 2-minors of the associated two-row matrix. This allows us to find a class of rational normal scrolls that are almost set-theoretic…
Benders' decomposition (BD) is a framework for solving optimization problems by removing some variables and modeling their contribution to the original problem via so-called Benders cuts. While many advanced optimization techniques can be…
Complex networks are frequently employed to model physical or virtual complex systems. When certain entities exist across multiple systems simultaneously, unveiling their corresponding relationships across the networks becomes crucial. This…
This is the first of a series of papers in which we initiate and develop the theory of reflection monoids, motivated by the theory of reflection groups. The main results identify a number of important inverse semigroups as reflection…
Position operator $\hat{r}$ appears as $i{\partial_p}$ in wave mechanics, while its matrix form is well known diverging in diagonals, causing serious difficulties in basis transformation, observable yielding, etc. We aim to find a…
This paper examines the problem of locating outlier columns in a large, otherwise low-rank, matrix. We propose a simple two-step adaptive sensing and inference approach and establish theoretical guarantees for its performance; our results…
This paper addresses matrix approximation problems for matrices that are large, sparse and/or that are representations of large graphs. To tackle these problems, we consider algorithms that are based primarily on coarsening techniques,…
We provide some insights in the study of branching problems of reductive groups, and a method of investigations into symmetry breaking operators. First, we give geometric criteria for finiteness property of linearly independent continuous…