Neural collapse provides an elegant mathematical characterization of learned last layer
representations (aka features) and classifier weights in deep classification models. Such …

We propose a construction of $ d^ 2$ complex equiangular lines in $\mathbb {C}^ d $, also
known as SICPOVMs, which were conjectured by Zauner to exist for all d. The construction …

We show that naturally associated to a SIC (symmetric informationally complete positive
operator valued measure or SIC-POVM) in dimension d there are a number of higher …

We describe a flexible technique that constructs tight fusion frames with prescribed transitive
symmetry. Applying this technique with representations of the symmetric and alternating …

We prove the following two results.\begin {enumerate}\item Let $\mathcal {A} $ be a unital
commutative C*-algebra and $\mathcal {A}^ d $ be the standard Hilbert C*-module over …

We consider sets of trace‐normalized non‐negative operators in Hilbert–Schmidt balls that
maximize their mutual Hilbert–Schmidt distance; these are optimal arrangements in the sets …

Consider the fundamental problem of arranging r-dimensional subspaces of R d in such a
way that maximizes the minimum distance between unit vectors in different subspaces. It is …

In this chapter, several metric problems in projective and Grassmann spaces are presented,
such as the determination of their congruence order and their superposability order. For that …

We show the optimal coherence of $2 d $ lines in $\mathbb {C}^{d} $ is given by the Welch
bound whenever a skew Hadamard of order $ d+ 1$ exists. Our proof uses a variant of …

Abstract In 1992, Godsil and Hensel published a ground-breaking study of distance-regular
antipodal covers of the complete graph that, among other things, introduced an important …