Related papers: Polyhedral combinatorics of bisectors
In this article we present theoretical and computational results on the existence of polyhedral embeddings of graphs. The emphasis is on cubic graphs. We also describe an efficient algorithm to compute all polyhedral embeddings of a given…
In this paper we discuss bimeron pseudo spin textures for double layer quantum hall systems with filling factor $\nu =1$. Bimerons are excitations corresponding to bound pairs of merons and anti-merons. Bimeron solutions have already been…
We show that the linear map defined by multiplication with a general bi-homogeneous form between two bi-graduated pieces of the first cohomology of a nonsingular quadric in the projective space is of maximal rank. This is the first non…
We present a discrete Morse-theoretic method for proving that a regular CW complex is homeomorphic to a sphere. We use this method to define bisimplices, the cells of a class of regular CW complexes we call bisimplicial complexes. The…
For the binary discs packed in two dimensions, the packing fraction of disc assembly becomes lower than that of the monodisperse system when the size ratio is close to unity. We show that the suppressed packing fraction is caused by an…
In this paper we extend recent results of Fiorini et al. on the extension complexity of the cut polytope and related polyhedra. We first describe a lifting argument to show exponential extension complexity for a number of NP-complete…
Bilayer graphene is a recently isolated and intriguing class of many-body systems with massive chiral quasiparticles. We present theoretical results for the electronic compressibility of bilayer graphene that are based on a four-band…
We present a theory of bilayer two-dimensional electron systems that host a spatially indirect exciton condensate when in thermal equilibrium. Equilibrium bilayer exciton condensates (BXCs) are expected to form when two nearby semiconductor…
The shellability of the boundary complex of an unbounded polyhedron is investigated. To this end, it is necessary to pass to a suitable compactification, e.g., by one point. This observation can be exploited to prove that any tropical…
In this paper we bring together tropical linear algebra and convex 3-dimensional bodies. We show how certain convex 3-dimensional bodies having 20 vertices and 12 facets can be encoded in a $4\times 4$ integer zero-diagonal matrix $A$. A…
This work introduces a multidimensional generalization of the maximum bisection problem. A mixed integer linear programming formulation is proposed with the proof of its correctness. The numerical tests, made on the randomly generated…
Let $A,B \subseteq \mathbb{R}^d $ both span $\mathbb{R}^d$ such that $\langle a, b \rangle \in \{0,1\}$ holds for all $a \in A$, $b \in B$. We show that $ |A| \cdot |B| \le (d+1) 2^d $. This allows us to settle a conjecture by Bohn, Faenza,…
Superfluidity has recently been reported in double electron-hole bilayer graphene. The multiband nature of the bilayers is important because of the very small band gaps between conduction and valence bands. The long range nature of the…
This paper presents a physics-consistent framework for bistatic sensing incorporating a 2-Dimensional (2D) waveguide-fed metasurface antenna array capable of realizing eXtremely-Large Multiple-Input Multiple-Output (XL MIMO) apertures. A…
We consider binary classification restricted to a class of continuous piecewise linear functions whose decision boundaries are (possibly nonconvex) starshaped polyhedral sets, supported on a fixed polyhedral simplicial fan. We investigate…
A conjecture of May states that there is an up-to-adjunction strictification of symmetric bimonoidal functors between bipermutative categories. The main result of this paper proves a weaker form of May's conjecture that starts with…
The bilayer Hubbard model with electron-hole doping is an ideal platform to study excitonic orders due to suppressed recombination via spatial separation of electrons and holes. However, suffering from the sign problem, previous quantum…
Collision detection is a critical functionality for robotics. The degree to which objects collide cannot be represented as a continuously differentiable function for any shapes other than spheres. This paper proposes a framework for…
Recent angle-resolved photoemission data for overdoped Bi2212 are explained. Of the peak-dip-hump structure, the peak corresponds the $\vec q =0$ component of a hole condensate which appears at $T_c$. The fluctuating part of this same…
We study thresholds for the appearance of a 2-core in random hypergraphs that are a mixture of a constant number of random uniform hypergraphs each with a linear number of edges but with different edge sizes. For the case of two overlapping…