Figure S1: X-ray powder diffraction pattern of the iron oxide nanospheres sample. X-ray Powder diffraction (XRPD) was measured on a conventional in-house powder diffractometer using Cu Kα radiation. Rietveld refinement yields cubic lattice parameters of 8.362(2) Å for the nanospheres and 8.348(1) Å for the nanocubes, which are both close to the cubic spinel lattice parameter of maghemite. The r...

Building upon a famous result due to Ajtai, we propose a sequence of lattice bases with growing dimension, which can be expected to be hard instances of the shortest vector problem (SVP) and which can therefore be used to benchmark lattice reduction algorithms. The SVP is the basis of security for potentially post-quantum cryptosystems. We use our sequence of lattice bases to create a challenge...

We analyze the properties of a class of improved lattice topological charge density operators, constructed by a smearing-like procedure. By optimizing the choice of the parameters introduced in their definition, we find operators having (i) a better statistical behavior as estimators of the topological charge density on the lattice, i.e. less noisy; (ii) a multiplicative renormalization much cl...

Building upon a famous result due to Ajtai, we propose a sequence of lattice bases with growing dimension, which can be expected to be hard instances of the shortest vector problem (SVP) and which can therefore be used to benchmark lattice reduction algorithms. The SVP is the basis of security for potentially post-quantum cryptosystems. We use our sequence of lattice bases to create a challenge...

in this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. also, the fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is characterized. furthermore,...

In this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. Also, the fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is characterized. Furthermore,...

  Nonlinear Dust lattice modes are studied in a hexagonal two-dimensional dusty plasma lattice, in presence of charge gradient of dust particles. In this lattice, such gradients affect nonlinear behavior of dust lattice waves. The amplitude modulation of off-plane transverse dust lattice wave packets is investigated considering the anisotropy of interactions, caused by the height-dependent char...

Symmetry operations of layers periodic in two dimensions restrict the geometry the lattice according to the five two-dimensional Bravais types of lattices. In order-disorder (OD) structures, the operations relating equivalent layers generally leave invariant only a sublattice of the layers. The thus resulting restrictions can be expressed in terms of linear relations of the a, b and a · b scala...

We consider the Gaussian wiretap channel, where two legitimate players Alice and Bob communicate over an additive white Gaussian noise (AWGN) channel, while Eve is eavesdropping, also through an AWGN channel. We propose a coding strategy based on lattice coset encoding. We analyze Eve’s probability of decoding, from which we define the secrecy gain as a design criterion for wiretap lattice code...

By simulating a nonequilibrium coupled map lattice that undergoes an Ising-like phase transition, we show that the Lyapunov spectrum and related dynamical quantities such as the dimension correlation length ξδ are insensitive to the onset of long-range ferromagnetic order. As a function of lattice coupling constant g and for certain lattice maps, the Lyapunov dimension density and other dynamic...