Related papers: Constructing Toeplitz arrays via cut and project s…
We investigate tameness of Toeplitz shifts. By introducing the notion of extended Bratteli-Vershik diagrams, we show that such shifts with finite Toeplitz rank are tame if and only if there are at most countably many orbits of singular…
To a Toeplitz flow $(X,T)$ we associate an ordered $K^0$-group, denoted $K^0(X,T)$, which is order isomorphic to the $K^0$-group of the associated (non-commutative) $C^\ast$-crossed product $C(X)\rtimes_T \mathbb{Z}$. However, $K^0(X,T)$…
We show how to reconstruct a finite directed graph E from its Toeplitz algebra, its gauge action, and the canonical finite-dimensional abelian subalgebra generated by the vertex projections. We also show that if E has no sinks, then we can…
We present a new superfast algorithm for solving Toeplitz systems. This algorithm is based on a relation between the solution of such problems and syzygies of polynomials or moving lines. We show an explicit connection between the…
We consider partial symmetric Toeplitz matrices where a positive definite completion exists. We characterize those patterns where the maximum determinant completion is itself Toeplitz. We then extend these results with positive definite…
A large part of the geometry of array antennas is often partially defined by finite translational symmetries. Applying the method of moments (MoM) with the RWG-like element on an appropriately structured mesh to these arrays results in an…
We give a general construction of topological groups from combinatorial structures such as trees, towers, gaps, and subadditive functions. We connect topological properties of corresponding groups with combinatorial properties of these…
We show that the maximum rank of block lower triangular Toeplitz block matrices equals their term rank if the blocks fulfill a structural condition, i.e., only the locations but not the values of their nonzeros are fixed.
In this work, we propose a novel method for quantifying distances between Toeplitz structured covariance matrices. By exploiting the spectral representation of Toeplitz matrices, the proposed distance measure is defined based on an optimal…
Every countable graph can be built from finite graphs by a suitable infinite process, either adding new vertices randomly or imposing some rules on the new edges. On the other hand, a profinite topological graph is built as the inverse…
In this paper, we analyze the Borel complexity of the topological conjugacy relation on Toeplitz subshifts. More specifically, we prove that topological conjugacy of Toeplitz subshifts with separated holes is hyperfinite. Indeed, we show…
We present a sublinear query algorithm for outputting a near-optimal low-rank approximation to any positive semidefinite Toeplitz matrix $T \in \mathbb{R}^{d \times d}$. In particular, for any integer rank $k \leq d$ and $\epsilon,\delta >…
Orthogonal array and a large set of orthogonal arrays are important research objects in combinatorial design theory, and they are widely applied to statistics, computer science, coding theory and cryptography. In this paper, some new series…
We construct ergodic probability measures with infinite metric entropy for typical continuous maps and homeomorphisms on compact manifolds. We also construct sequences of such measures that converge to a zero-entropy measure.
Given a uniformly expanding transitive Markov interval map, we show that within the set of ergodic measures the set of nonadapted ergodic measures is residual in with respect to the topology induced by the $\overline{d}$-metric. This set of…
The problems of uniform linear array (with uniform mutual coupling) calibration and Toeplitz covariance matrix estimation are re-examined for application in the receive arrays of modern High Frequency Over-the-Horizon Radars (HF OTHR).…
We present explicit algorithms for computing structured matrix-vector products that are optimal in the sense of Strassen, i.e., using a provably minimum number of multiplications. These structures include Toeplitz/Hankel/circulant,…
We define a class of automorphisms of rational function fields of finite characteristic and employ these to construct different types of optimal linear rank-metric codes. The first construction is of generalized Gabidulin codes over…
The set of infinite upper-triangular totally positive Toeplitz matrices has a classical parametrisation proved by Edrei et al and originally conjectured by Schoenberg, that involves pairs of sequences of positive real parameters. These…
Motivated by the analysis and geometry of metric-measure structures in infinite dimensions, we study the category of extended metric-topological spaces, along with many of its distinguished subcategories (such as the one of compact spaces).…