Related papers: Equiangular tight frames and unistochastic matrice…
We introduce the $\star_G$ tensor algebra, in which any finite group $G$ defines the multiplication rule, making equivariance an intrinsic algebraic property rather than an architectural constraint. The framework rests on three…
The restricted isometry property (RIP) is a well-known matrix condition that provides state-of-the-art reconstruction guarantees for compressed sensing. While random matrices are known to satisfy this property with high probability,…
The elasticity tensor that describes the elastic response of a material to external forces is among the most fundamental properties of materials. The availability of full elasticity tensors for inorganic crystalline compounds, however, is…
We analyze the set of real and complex Hadamard matrices with additional symmetry constrains. In particular, we link the problem of existence of maximally entangled multipartite states of $2k$ subsystems with $d$ levels each to the set of…
True-time-delay (TTD) beamformers can produce wideband, squint-free beams in both analog and digital signal domains, unlike frequency-dependent FFT beams. Our previous work showed that TTD beamformers can be efficiently realized using the…
It follows from the GKM description of equivariant cohomology that the GKM graph of a GKM manifold has free equivariant graph cohomology, and satisfies a Poincar\'e duality condition. We prove that these conditions are sufficient for an…
We study the properties of a set of vectors called tight frames that obtained as the orthogonal projection of some orthonormal basis of $\R^n$ onto $\R^k.$ We show that a set of vectors is a tight frame if and only if the set of all cross…
The recently discovered Neural collapse (NC) phenomenon states that the last-layer weights of Deep Neural Networks (DNN), converge to the so-called Equiangular Tight Frame (ETF) simplex, at the terminal phase of their training. This ETF…
An orthogonal n-frame is an ordered set of n pairwise orthogonal vectors. The set of all orthogonal n-frames in a d-dimensional quadratic vector space is an algebraic variety V(d,n). In this paper, we investigate the variety V(d,n) as well…
Marshall and Olkin (1997, Biometrika, 84, 641 - 652) introduced a very powerful method to introduce an additional parameter to a class of continuous distribution functions and hence it brings more flexibility to the model. They have…
To enumerate 3-manifold triangulations with a given property, one typically begins with a set of potential face pairing graphs (also known as dual 1-skeletons), and then attempts to flesh each graph out into full triangulations using an…
We construct a 2-parameter family of 4-dimensional polytopes with extreme combinatorial structure: In this family, the ``fatness'' of the f-vector gets arbitrarily close to 9, the ``complexity'' (given by the flag vector) gets arbitrarily…
Extensions of the Standard Model have been attempted from the bottom up and from the top down yet there remains a largely unexplored middle ground. In this paper, using the Mathematica package LieART, we exhaustively enumerate embeddings of…
In twisted Diophantine approximation, for a fixed $m\times n$ matrix $\boldsymbol\alpha$ one is interested in sets of vectors $\boldsymbol\beta\in\mathbb R^m$ such that the system of affine forms $\mathbb R^n \ni \mathbf q \mapsto…
When constructing finite frames for a given application, the most important consideration is the spectrum of the frame operator. Indeed, the minimum and maximum eigenvalues of the frame operator are the optimal frame bounds, and the frame…
The low-energy expansion of genus-one string amplitudes produces infinite families of non-holomorphic modular forms after each step of integrating over a point on the torus worldsheet which are known as elliptic modular graph forms (eMGFs).…
Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated quantum many-particle systems. For the simplest spinless fermion (or boson) systems with say $m$ fermions (or bosons) in $N$ single…
In this work, the concept of mutually unbiased frames is introduced as the most general notion of unbiasedness for sets composed by linearly independent and normalized vectors. It encompasses the already existing notions of unbiasedness for…
We present a new probabilistic algorithm that characterizes the equidimensional components of the affine algebraic variety defined by an arbitrary sparse polynomial system with prescribed supports. For each equidimensional component, the…
We present a kind of construction for a class of special matrices with at most two different eigenvalues, in terms of some interesting multiplicators which are very useful in calculating eigenvalue polynomials of these matrices. This class…