Using a standard definition of fractional powers on the universal cover $\exp:S\to \mathbb{C}^*$ seen as an infinite helicoid embedded in $\mathbb{R}^3$, we study the statistics of pairs from the countable family $\{n^\alpha \, : \, n \in \exp^{-1}(\Lambda) \}$ for every complex grid $\Lambda$ and every real parameter $\alpha \in \, ]0,1[\,$. We pr...
We propose a new framework based on random submersions — that is projection over a random subspace blinded by a small Gaussian noise — for constructing verifiable short secret sharing and showcase it to construct efficient threshold lattice-based signatures in the hash-and-sign paradigm, when based on noise flooding. This is, to our knowledge, the ...
Given a finite set, $A \subseteq \mathbb{R}^2$, and a subset, $B \subseteq A$, the \emph{MST-ratio} is the combined length of the minimum spanning trees of $B$ and $A \setminus B$ divided by the length of the minimum spanning tree of $A$. The question of the supremum, over all sets $A$, of the maximum, over all subsets $B$, is related to the Steine...
status: published
Trigonometric polynomials are usually defined on the lattice of integers.We consider the larger class of weight and root lattices with crystallographic symmetry.This article gives a new approach to minimize trigonometric polynomials, which are invariant under the associated reflection group.The invariance assumption allows us to rewrite the objecti...
One-dimensional (1D) Heisenberg antiferromagnets are of great interest due to their intriguing quantum phenomena. However, the experimental realization of such systems with large spin S remains challenging because even weak interchain interactions induce long-range ordering. In this study, we present an ideal 1D S = 5/2 spin chain antiferromagnet a...
This paper introduces an all-metal series dual-fed continuous transverse stub (CTS) array that enables multi-beam operation at K-band. This capability is obtained by utilizing a reflecting Luneburg lens (RLL) beamformer made of two stacked circular parallel plate waveguides (PPWs). The bottom PPW hosts a graded index medium that collimates the rays...
Humans rely on multimodal perception to form representations of the world. This implies that environmental stimuli must remain consistent and predictable throughout their journey to our sensory organs. When it comes to vision, electromagnetic waves are minimally affected when passing through air or glass treated for chromatic aberrations. Similar c...
Recently, metal sulfides have begun to receive attention as potential cost-effective materials for thermoelectric applications beyond optoelectronic and photovoltaic devices. Herein, based on a comparative analysis of the structural and transport properties of 2D PbSnS2 and 1D PbSnS3, we demonstrate that the intrinsic effects that govern the low la...
