Related papers: On the Area of Hypercube Layouts
The CuO-planes of high-T_c superconductors were found to consist of geometric stripes with alternating superconducting and antiferromagnetic areas. Here we will investigate the repulsive Hubbard model of striped clusters as a possible…
We prove that at least $\Omega(n^{0.51})$ hyperplanes are needed to slice all edges of the $n$-dimensional hypercube. We provide a couple of applications: lower bounds on the computational complexity of parity, and a lower bound on the…
The full distribution of the conductance $P(G)$ in quasi-one-dimensional wires with rough surfaces is analyzed from the diffusive to the localization regime. In the crossover region, where the statistics is dominated by only one or two…
Consider the $n$-cube graph with vertices $\{-1,1\}^n$ and edges connecting vertices with hamming distance $1$. How many hyperplanes in $\mathbb{R}^n$ are needed in order to dissect all edges? We show that at least…
We consider arbitrary dense wireless networks, in which $n$ nodes are placed in an arbitrary (deterministic) manner on a square region of unit area and communicate with each other over Gaussian fading channels. We provide inner and outer…
We introduce a framework for emulating graphs and, through them, curved spaces of arbitrary dimension, using arrays of superconducting wires. The array consists of two stacked layers of wires, horizontal and vertical, such that wires are…
The superconducting properties of a two-dimensional superconducting wire network with a new geometry have been measured as a function of the external magnetic field. The extreme localization effect recently predicted for this periodic…
Over an infinite field $K$, we investigate the minimal free resolution of some configurations of lines. We explicitly describe the minimal free resolution of "complete grids of lines" and obtain an analogous result about the so-called…
We propose a new principle to realize flatbands which are robust in real materials, based on a network superstructure of one-dimensional segments. This mechanism is naturally realized in the nearly commensurate charge-density wave of…
All previously published work on isomorphic grid embeddings into n-cubes has been restricted to binary n-cubes. This paper describes a straightforward method for embedding a A x B grid isomorphically into a k-ary n-cube with k>2.
The generation of high magnetic fields requires materials with high electric conductivity and good strength properties. Cu/Nb composites are considered to be good candidates for this purpose. In this work we aim to predict, from theory, the…
We consider constructions of covering-radius-1 completely regular codes, or, equivalently, equitable 2-partitions (regular 2-partitions, perfect 2-colorings), of halved n-cubes. Keywords: completely regular code, equitable partition,…
The largest possible average diameter of a bounded cell of a simple hyperplane arrangement is conjectured to be not greater than the dimension. We prove that this conjecture holds in dimension 2, and is asymptotically tight in fixed…
Current distribution for a thin superconducting strip shielded by two ideally conducting plains has been calculated. It is shown that at microwave requencies the current density has maximum over the center of the strip in contrast to the dc…
We show that the minimal number of skewed hyperplanes that cover the hypercube $\{0,1\}^{n}$ is at least $\frac{n}{2}+1$, and there are infinitely many $n$'s when the hypercube can be covered with $n-\log_{2}(n)+1$ skewed hyperplanes. The…
We first show that the union of a projective curve with one of its extremal secant lines satisfies the linear general position principle for hyperplane sections. We use this to give an improved approximation of the Betti numbers of curves…
A key concept for many graph layout algorithms is planarity, a graph property that allows to draw vertices and edges crossing-free in the plane. Important is the generalization to $k$-planar graphs, which can be drawn in the plane with at…
Certain binary asymmetric channels, such as Z-channels in which one of the two crossover probabilities is zero, demand optimal ones densities different from 50%. Some broadcast channels, such as broadcast binary symmetric channels (BBSC)…
Nanostructured and architectured copper niobium composite wires are excellent candidates for the generation of intense pulsed magnetic fields (>90T) as they combine both high strength and high electrical conductivity. Multi-scaled Cu-Nb…
The magnetic field dependent localization in a disordered quantum wire is considered nonperturbatively. An increase of an averaged localization length with the magnetic field is found, saturating at twice its value without magnetic field.…