Related papers: On average coherence of cyclotomic lattices
A common criterion in the design of finite Hilbert space frames is minimal coherence, as this leads to error reduction in various signal processing applications. Frames that achieve minimal coherence relative to all unit-norm frames are…
We discuss as a fundamental characteristic of orthogonal polynomials like the existence of a Lie algebra behind them, can be added to their other relevant aspects. At the basis of the complete framework for orthogonal polynomials we put…
Lattices and partially ordered sets have played an increasingly important role in coding theory, providing combinatorial frameworks for studying structural and algebraic properties of error-correcting codes. Motivated by recent works…
We investigate, theoretically and experimentally,the properties of diffraction spectra of Fibonacci lattices with arbitrary spacings. We show that, by means of a suitable composition rule, a Fibonacci sequence can be mapped into another one…
We examine the behavior of quadrature coherence under the measurement of the same field quadrature. This is carried out with the help of a beam splitter, which implies the contribution of an auxiliary field state impinging at the other…
We study statistical and structural properties of extreme lattices, which are the local minima in the density landscape of lattice sphere packings, in $d$-dimensional Euclidean space $\mathbb{R}^d$. Specifically, we ascertain the…
We count primitive lattices of rank $d$ inside $\mathbb{Z}^{n}$ as their covolume tends to infinity, with respect to certain parameters of such lattices. These parameters include, for example, the subsapce that a lattice spans, namely its…
We study geometric consistency relations between angles on 3-dimensional (3D) circular quadrilateral lattices -- lattices whose faces are planar quadrilaterals inscribable into a circle. We show that these relations generate canonical…
A method by Peres is used to draw spectra of the interacting boson model as lattices in the plane of energy versus an arbitrary observable average (or variance). Ordered (disordered) lattices are signatures of regularity (chaos) in both…
We begin with a short exposition of the theory of lattice varieties. This includes a description of their orbit structure and smooth locus. We construct a flat cover of the lattice variety and show that it is a complete intersection. We…
Finding correspondences between 3D shapes is a crucial problem in computer vision and graphics, which is for example relevant for tasks like shape interpolation, pose transfer, or texture transfer. An often neglected but essential property…
Decoherence has the potential to explain all existing neutrino data including LSND results, without enlarging the neutrino sector. This particular form of CPT violation can preserve the equality of masses and mixing angles between particle…
The detection and characterization of quantum coherence is of fundamental importance both in the foundations of quantum theory as well as for the rapidly developing field of quantum technologies, where coherence has been linked to quantum…
In a galactic halo like the Milky Way, bosonic dark matter particles lighter than about $30$ eV have a de Broglie wavelength larger than the average inter-particle separation and are therefore well described as a set of classical waves.…
We study the shortest vector lengths in module lattices over arbitrary number fields, with an emphasis on cyclotomic fields. In particular, we sharpen the techniques of arXiv:2308.15275v2 to establish improved results for the variance of…
We elaborate on the notion of a filtration of an operad defined in terms of a lattice-valued operad serving as an indexing object. That covers ordinary integer-indexed filtrations of associative algebras and operads as a special case, yet…
Various approaches to physics beyond the Standard Model can lead to small violations of CPT invariance. Since CPT symmetry can be measured with ultrahigh precision, CPT tests offer an interesting phenomenological avenue to search for…
It is known that families of graphs with a semialgebraic edge relation of bounded complexity satisfy much stronger regularity properties than arbitrary graphs, and that they can be decomposed into very homogeneous semialgebraic pieces up to…
We introduce the dual Koenigs lattices, which are the integrable discrete analogues of conjugate nets with equal tangential invariants, and we find the corresponding reduction of the fundamental transformation. We also introduce the notion…
Let $\mathbb{R}^m$ be endowed with the Euclidean metric. The covering radius of a lattice $\Lambda \subset \mathbb{R}^m$ is the least distance $r$ such that, given any point of $\mathbb{R}^m$, the distance from that point to $\Lambda$ is…