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Symmetric informationally complete measurements (SICs) are elegant, celebrated and broadly useful discrete structures in Hilbert space. We introduce a more sophisticated discrete structure compounded by several SICs. A SIC-compound is…

A partial interference cancellation (PIC) group decoding based space-time block code (STBC) design criterion was recently proposed by Guo and Xia, where the decoding complexity and the code rate trade-off is dealt when the full diversity is…

Crystals which have a uniform distribution of defects are endowed with a Lie group description which allows one to construct an associated discrete structure. These structures are in fact the discrete subgroups of the ambient Lie group. The…

Semidefinite programs have recently been developed for the problem of community detection, which may be viewed as a special case of the stochastic blockmodel. Here, we develop a semidefinite program that can be tailored to other instances…

Coherent bremsstrahlung of high energy electrons moving in a three-dimensional imperfect periodic lattice consisting of a complicated system of atoms is considered. On the basis of the normalized probability density function of the…

Block-transitive Steiner $t$-designs form a central part of the study of highly symmetric combinatorial configurations at the interface of several disciplines, including group theory, geometry, combinatorics, coding and information theory,…

I give an elementary proof that a quasi-symmetric design without repeated blocks on $v$ points has at most $v\choose2$ blocks, with equality if and only if it is a tight $4$-design.

A barred preferential arrangement is a preferential arrangement onto which a number of identical bars are inserted in between the blocks of the preferential arrangement. In this study we examine combinatorial properties of barred…

Nonlinearity in coherent fiber links is fundamentally driven by the temporal statistics and spectral structure of signal intensity. This paper develops a unified framework that links block-level energy statistics of shaped constellations to…

A strong $s$-blocking set in a projective space is a set of points that intersects each codimension-$s$ subspace in a spanning set of the subspace. We present an explicit construction of such sets in a $(k - 1)$-dimensional projective space…

One of the main open problems in quantum communication is the design of efficient quantum-secured networks. This is a challenging goal, because it requires protocols that guarantee both unconditional security and high communication rates,…

Speckle patterns are formed by random interferences of mutually coherent beams. While speckles are often considered as an unwanted noise in many areas, they also formed the foundation for the development of numerous speckle-based imaging,…

We have performed electronic structure calculations to explore the band-gap dependence on polytypes for $sp^3$-bonded semiconducting materials, i.e., SiC, AlN, BN, GaN, Si, and diamond. In this comprehensive study, we have found that…

There are exactly 35 inequivalent (36, 15, 6) difference sets in nine groups. Eight of the nine groups have a normal Sylow 3-subgroup. We give a straightforward spread construction which explains the 32 inequivalent difference sets in these…

A difference matrix over a group is a discrete structure that is intimately related to many other combinatorial designs, including mutually orthogonal Latin squares, orthogonal arrays, and transversal designs. Interest in constructing…

In this work, a group theory-based formulation that introduces new classes of dihedral-symmetric beams is presented. Our framework leverages the algebraic properties of the dihedral group of rotations and reflections to transform input…

The dimension of a linear space is the maximum positive integer $d$ such that any $d$ of its points generate a proper subspace. For a set $K$ of integers at least two, recall that a pairwise balanced design PBD$(v,K)$ is a linear space on…

Split-plot designs find wide applicability in multifactor experiments with randomization restrictions. Practical considerations often warrant the use of unbalanced designs. This paper investigates randomization based causal inference in…

Beam splitters are not-free operations with regard to quantum coherence. As a consequence, they can create coherence from both coherent and incoherent states. We investigate the increase in coherence produced by cascades of beam splitters.…

A $t\text{-}(n,K,\lambda;q)$ design, also called the $q$-analog of a $t$-wise balanced design, is a set ${\mathcal B}$ of subspaces with dimensions contained in $K$ of the $n$-dimensional vector space ${\mathbb F}_q^n$ over the finite field…