Related papers: On the Area of Hypercube Layouts
Because of its novel physical properties, two-dimensional materials have attracted great attention. From first-principle calculations and vibration frequenceis analysis, we predict a new family of two-dimensional materials based on the idea…
In several parent iron-pnictide compounds the resistivity has an extended range of linear magnetic field dependence. We argue that there is a simple and natural explanation of this behavior. Spin density wave transition leads to…
We introduce the idea that the electronic band structure of a charge density wave system may mimic the electronic structure of graphene. In that case a class of materials quite different from graphene might be opened up to exploit…
Multi-channel wireless systems have become a standard solution to address our information society's ever-increasing demand for more information transfer. The ultimate bound on the capacity such systems can achieve is the limited channel…
Let $Q_d$ denote the hypercube of dimension $d$. Given $d\geq m$, a spanning subgraph $G$ of $Q_d$ is said to be $(Q_d,Q_m)$-saturated if it does not contain $Q_m$ as a subgraph but adding any edge of $E(Q_d)\setminus E(G)$ creates a copy…
Graphene, one of the strongest materials ever discovered, triggered the exploration of many 2D materials in the last decade. However, the successful synthesis of a stable nanomaterial requires a rudimentary understanding of the relationship…
Nanowires are formed by indenting and subsequently retracting two pieces of sodium metal. Their cross-section gradually reduces upon retraction and the diameters can be obtained from the conductance. In previous work we have demonstrated…
How many hyperplanes in $\mathbb{R}^n$ are needed in order to slice every edge of the $n$-dimensional hypercube with vertex set $\{\pm 1\}^n$? Here, we say that a hyperplane $H\subseteq \mathbb{R}^n$ slices an edge of the hypercube if it…
In this note we provide an improved upper bound on the biplanar crossing number of the 8-dimensional hypercube. The $k$-planar crossing number of a graph $cr_k(G)$ is the number of crossings required when every edge of $G$ must be drawn in…
Several commonly observed physical and biological systems are arranged in shapes that closely resemble an honeycomb cluster, that is, a tessellation of the plane by regular hexagons. Although these shapes are not always the direct product…
This paper investigates the \emph{Wiring Diagram Problem} (WDP), a three-dimensional layout design problem arising in industrial applications such as cable harness design and pipeline routing in constrained environments. In these settings,…
We investigate electronic quantum transport through nano-wires with one-sided surface roughness. A magnetic field perpendicular to the scattering region is shown to lead to exponentially diverging localization lengths in the…
Dropout Regularization, serving to reduce variance, is nearly ubiquitous in Deep Learning models. We explore the relationship between the dropout rate and model complexity by training 2,000 neural networks configured with random…
It is hypothetized that the algebra of the configuration of twenty-seven lines lying on a general cubic surface underlines the dimensional hierarchy of heterotic string spacetimes.
A $d$-dimensional hypercube drawing of a graph represents the vertices by distinct points in $\{0,1\}^d$, such that the line-segments representing the edges do not cross. We study lower and upper bounds on the minimum number of dimensions…
We study dense packings of a large number of congruent non-overlapping circles inside a square by looking for configurations which maximize the packing density, defined as the ratio between the area occupied by the disks and the area of the…
The transition in random fiber networks from two-dimensional to three-dimensional planar structure driven by increasing coverage (total fiber length per unit area) is studied with a deposition model. At low coverage the network geometry…
Density functional theory has been used to study the adsorption of molecular H2 on a graphene layer. Different adsorption sites on top of atoms, bonds and the center of carbon hexagons have been considered and compared. We conclude that the…
A local permittivity model is proposed to accurately characterize spatial dispersion in non-local wire-medium (WM) structures with arbitrary terminations. A closed-form expression for the local thickness-dependent permittivity is derived…
Superconducting $MgB_2$ wires in Cu, GlidCop or Monel sheath with Nb or Fe barrier are prepared. Wires vary by sheath material, number of superconducting cores and their chemical composition. Wires are HIP-ed (Hot Isostatic Pressing) at…