Related papers: Identify Equivalent Frames
In information fusion, one is often confronted with the following problem: given a preexisting set of measurements about an unknown quantity, what new measurements should one collect in order to accomplish a given fusion task with optimal…
Graph matching is the process of computing the similarity between two graphs. Depending on the requirement, it can be exact or inexact. Exact graph matching requires a strict correspondence between nodes of two graphs, whereas inexact…
The following numerical control over the topological equivalence is proved: two complex polynomials in $n\not= 3$ variables and with isolated singularities are topologically equivalent if one deforms into the other by a continuous family of…
This article suggests that thinking about the role of reference frames can provide new insight into Extended Wigner's Friend scenarios. This involves appealing to symmetries to make a principled distinction between properties of a system…
We study finite systems of vectors whose frame operator matrices are unitarily equivalent, via explicit and computationally efficient unitary transformations, to block-diagonal matrices. We call such systems block-equivalent. We show that a…
The algorithm for finding the optimal consistent approximation of an inconsistent pairwise comparisons matrix is based on a logarithmic transformation of a pairwise comparisons matrix into a vector space with the Euclidean metric.…
A Burling graph is an induced subgraph of some graph in Burling's construction of triangle-free high-chromatic graphs. Equivalently, a Burling graph is a graph that admits a so-called strict frame representation. We provide a…
For any block of a finite group over an algebraically closed field of characteristic $2$ which has dihedral, semidihedral, or generalized quaternion defect groups, we determine explicitly the decomposition of the associated diagonal…
Finite frame theory has become a powerful tool for many applications of mathematics. In this paper we introduce a new area of research in frame theory: Integer frames. These are frames having all integer coordinates with respect to a fixed…
In this paper, we give a new axioms system based on nonseparable flats with their ranks to define a matroid. We deduce a polynomial time algorithm for deciding if a given matroid (respectively, arbitrary structure) is an uniform matroid.…
In this paper we present the construction of an exact dual frame under specific structural assumptions posed on the dual frame. When given a frame $F$ for a finite dimensional Hilbert space, and a set of vectors $H$ that is assumed to be a…
The problem of finding completely positive matrices with equal cp-rank and rank is considered. We give some easy-to-check sufficient conditions on the entries of a doubly nonnegative matrix for it to be completely positive with equal…
Graph embedding is a transformation of nodes of a network into a set of vectors. A good embedding should capture the underlying graph topology and structure, node-to-node relationship, and other relevant information about the graph, its…
A match cut is a transition between a pair of shots that uses similar framing, composition, or action to fluidly bring the viewer from one scene to the next. Match cuts are frequently used in film, television, and advertising. However,…
We provide an algorithm for deciding simple grammar bisimilarity whose complexity is polynomial in the valuation of the grammar (maximum seminorm among production rules). Since the valuation is at most exponential in the size of the…
The aim of this note is to provide a reduction of the Exact Matching problem to the Top-$k$ Perfect Matching Problem. Together with earlier work by El Maalouly, this shows that the two problems are polynomial-time equivalent. The Exact…
This paper concerns the geometric structure of optimizers for frame potentials. We consider finite, real or complex frames and rotation or unitarily invariant potentials, and mostly specialize to Parseval frames, meaning the frame potential…
As neural networks (NNs) are increasingly introduced into safety-critical domains, there is a growing need to formally verify NNs before deployment. In this work we focus on the formal verification problem of NN equivalence which aims to…
Point sets matching method is very important in computer vision, feature extraction, fingerprint matching, motion estimation and so on. This paper proposes a robust point sets matching method. We present an iterative algorithm that is…
Comparability graphs are a popular class of graphs. We introduce as the digraph analogue of comparability graphs the class of comparability digraphs. We show that many concepts such as implication classes and the knotting graph for a…