Related papers: $k$-Homogeneous Equiangular Tight Frames
This note provides an introduction to selected topics in algebraic graph theory, including strongly regular graphs, Steiner systems, and automorphism groups. We describe constructions and properties of notable graphs such as the Petersen…
For a finite point set $E\subset \mathbb{R}^d$ and a connected graph $G$ on $k+1$ vertices, we define a $G$-framework to be a collection of $k + 1$ points in E such that the distance between a pair of points is specified if the…
Let $X$ be an abelian variety defined over an algebraically closed field $k$. We consider theta groups associated to \emph{simple semi-homogenous vector bundles of separable type} on $X$. We determine the structure and representation theory…
We introduce and study a $K$-theory of twisted bundles for associative algebras $A(\mathfrak g)$ of formal series with an infinite-Lie algebra coefficients over arbitrary compact topological spaces. Fibers of such bundles are given by…
We introduce a class of finite tight frames called prime tight frames and prove some of their elementary properties. In particular, we show that any finite tight frame can be written as a union of prime tight frames. We then characterize…
Frame theory has been a popular subject in the design of structured signals and codes in recent years, with applications ranging from the design of measurement matrices in compressive sensing, to spherical codes for data compression and…
Physically, disordered ensembles of non-homopolymeric polypeptides are expected to be heterogeneous; i.e., they should differ from those homogeneous ensembles of homopolymers that harbor an essentially unique relationship between average…
We consider the set of all linear combinations with integer coefficients of the vectors of a unit tight equiangular $(k,n)$ frame and are interested in the question whether this set is a lattice, that is, a discrete additive subgroup of the…
We present a topological framework for finding low-flop algorithms for evaluating element stiffness matrices associated with multilinear forms for finite element methods posed over straight-sided affine domains. This framework relies on…
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…
By following the ideas underpinning the well-established ``homogeneous model'' of an $n$-dimensional Euclidean space, we investigate whether the motion group or the weak motion group of an $n$-dimensional affine metric space on a vector…
We compare the invariants of flat vector bundles defined by Atiyah et al. and Jones et al. and prove that, up to weak homotopy, they induce the same map, denoted by $e$, from the $0$-connective algebraic $K$-theory space of the complex…
The concepts of symmetry and symmetry groups are at the heart of several developments in modern theoretical and mathematical physics. The present paper is devoted to a number of selected topics within this framework: Euclidean and rotation…
A finite collection of unit vectors $S \subset \mathbb{R}^n$ is called a spherical two-distance set if there are two numbers $a$ and $b$ such that the inner products of distinct vectors from $S$ are either $a$ or $b$. We prove that if $a\ne…
This paper is mainly motivated by the analysis of the so-called Bounded Generation property (BG) of linear groups (in characteristic $0$), which is known to admit far-reaching group-theoretic implications. We achieve complete answers to…
Scheme-theoretic methods are used to classify ternary quadratic forms with values in line bundles over arbitrary schemes and to canonically determine the isomorphisms between them. The association of a quadratic bundle to its even Clifford…
We draw a random subset of $k$ rows from a frame with $n$ rows (vectors) and $m$ columns (dimensions), where $k$ and $m$ are proportional to $n$. For a variety of important deterministic equiangular tight frames (ETFs) and tight non-ETF…
This is a draft of a monograph to appear in the Springer series "Encyclopaedia of Mathematical Sciences", subseries "Invariant Theory and Algebraic Transformation Groups". The subject is homogeneous spaces of algebraic groups and their…
We consider $m$ spinless Fermions in $l > m$ degenerate single-particle levels interacting via a $k$-body random interaction with Gaussian probability distribution and $k <= m$ in the limit $l$ to infinity (the embedded $k$-body random…
We study open equivariant projective embeddings of homogeneous spaces such that the complement of the open orbit does not contain divisors. Criterions of existence of such an embedding are considered and finiteness of isomorphism classes of…