Related papers: Equiangular tight frames from hyperovals
We show that deep ensembles become equivariant for all inputs and at all training times by simply using data augmentation. Crucially, equivariance holds off-manifold and for any architecture in the infinite width limit. The equivariance is…
A geometric perspective involving Grammian and frame operators is used to derive the entire family of Welch bounds. This perspective unifies a number of observations that have been made regarding tightness of the bounds and their…
The concept of balancedly splittable orthogonal designs is introduced along with a recursive construction. As an application, equiangular tight frames over the real, complex, and quaternions meeting the Delsarte-Goethals-Seidel upper bound…
We identify a universal short-time structure in symmetry-resolved entanglement dynamics -- the entanglement channel wave (ECW) -- arising from the decomposition of entanglement into conserved-quantum-number sectors that host robust,…
Topological heavy-fermion systems in three dimensions are usually classified as topological insulators or semimetals. Here, we theoretically predict a different type of heavy-fermion system (dubbed exceptional heavy-fermion semimetal) by…
Finite tight frames play an important role in miscellaneous areas, including quantum information theory. Here we apply a class of tight frames, equiangular tight frames, to address the problem of detecting the entanglement of bipartite…
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…
This paper is concerned with achieving optimal coherence for highly redundant real unit-norm frames. As the redundancy grows, the number of vectors in the frame becomes too large to admit equiangular arrangements. In this case, other…
We develop the general theory for the construction of Extended Topological Quantum Field Theories (ETQFTs) associated with the Costantino-Geer-Patureau quantum invariants of closed 3-manifolds. In order to do so, we introduce relative…
This paper considers the cohomology and bounded interpolation of nonstandard finite element complexes, e.g. Stokes, Hessian, Elasticity, divdiv. Compared to the standard finite element exterior calculus, the main challenge is the existence…
In this paper, we study conditions under which a finite subset $Z$ of the unit sphere $S^{d-1}\subset \mathbb{R}^{d}$ becomes a spherical $t$-design, when $Z$ is constructed by the following procedure: starting from a finite set of…
We present all nontrivial real equiangular tight frames $\{\varphi_m\}_{m=1}^M$ in $\mathbb{R}^N$ obtained as spherical embeddings of primitive rank $3$ graphs on $M$ vertices, and those such that one of their associated $M$ strongly…
The effective field theory (EFT) framework is a precise approximation procedure when the inherent assumptions of a large-scale separation between the Standard Model (SM) and new interactions alongside perturbativity are realised.…
Aerospace design is increasingly incorporating Design Under Uncertainty based approaches to lead to more robust and reliable optimal designs. These approaches require dependable estimates of uncertainty in simulations for their success. The…
In this paper, we begin constructing a new finite-dimensional topological quantum field theory (TQFT) for three-manifolds, based on group PSL(2,C) and its action on a complex variable by fractional-linear transformations, by providing its…
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…
Motivated by a host of recent applications requiring some amount of redundancy, frames are becoming a standard tool in the signal processing toolbox. In this paper, we study a specific class of frames, known as discrete Fourier transform…
Scalable frames are frames with the property that the frame vectors can be rescaled resulting in tight frames. However, if a frame is not scalable, one has to aim for an approximate procedure. For this, in this paper we introduce three…
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…
In this paper we give a new construction of parametric families of complex Hadamard matrices of square orders, and connect them to equiangular tight frames. The results presented here generalize some of the recent ideas of Bodmann et al.…