Related papers: Signotopes Induce Unique Sink Orientations on Grid…
We develop objective linear algebra in a new setting with a cardinality functor that can take negative values. The signs arise as little homotopies, as ratios between orientations. To illustrate the workings of the theory we give an…
This document is a practical guide to computations using an automatic structure for the mapping class group of a once-punctured, oriented surface $S$. We describe a quadratic time algorithm for the word problem in this group, which can be…
We describe how self-adjoint ordered operator spaces, also called non-unital operator systems in the literature, can be understood as $*$-vector spaces equipped with a matrix gauge structure. We explain how this perspective has several…
Singletons are those unitary irreducible modules of the Poincare or (anti) de Sitter group that can be lifted to unitary modules of the conformal group. Higher-spin algebras are the corresponding realizations of the universal enveloping…
A graph G is said to be 1-perfectly orientable (1-p.o. for short) if it admits an orientation such that the out-neighborhood of every vertex is a clique in G. The class of 1-p.o. graphs forms a common generalization of the classes of…
The way of reduction of metal oxyde semiconductor (MOS) structures is going to reach limitations and new devices have to be explored as an alternative to MOS technology. Molecular electronic and more particularly self-assembly-molecular…
Let $K\subseteq\mathbb{R}$ be the unique attractor of an iterated function system. We consider the case where $K$ is an interval and study those elements of $K$ with a unique coding. We prove under mild conditions that the set of points…
Zonotopes are studied from the point of view of central symmetry and how volumes of facets and the angles between them determine a zonotope uniquely. New proofs are given for theorems of Shephard and McMullen characterizing a zonotope by…
We investigate realizations of topological insulators with spin-1 bosons loaded in a honeycomb optical lattice and subjected to a $SU(3)$ spin-orbit coupling - a situation which can be realized experimentally using cold atomic gases. In…
We give an $O(n^{1.5} \log n)$ algorithm that, given a directed planar graph with arc capacities, a set of source nodes and a single sink node, finds a maximum flow from the sources to the sink . This is the first subquadratic-time strongly…
Let $S$ be a set of $n$ points in a polygon $P$ with $m$ vertices. The geodesic unit-disk graph $G(S)$ induced by $S$ has vertex set $S$ and contains an edge between two vertices whenever their geodesic distance in $P$ is at most one. In…
This paper presents "oriented pivoting systems" as an abstract framework for complementary pivoting. It gives a unified simple proof that the endpoints of complementary pivoting paths have opposite sign. A special case are the Nash…
A previous article was devoted to an analysis of the symmetry properties of a class of first-order delay ordinary differential systems (DODSs). Here we concentrate on linear DODSs. They have infinite-dimensional Lie point symmetry groups…
We show that any isomorphism between mapping class groups of orientable infinite-type surfaces is induced by a homeomorphism between the surfaces. Our argument additionally applies to automorphisms between finite-index subgroups of these…
We prove that every closed orientable surface S of negative Euler characteristic admits a pair of finite-degree covers which are length isospectral over S but generically not simple length isospectral over S. To do this, we first…
It is shown that in SO(10) and SU(5) models having a $U(1)_R$ symmetry, the requirement of breaking the unified group to the Standard Model leads to flat directions in the scalar potential. These can lead to a ``cosmological modulus…
Transparent Conductive Oxides (TCOs) are a class of materials that combine high optical transparency with high electrical conductivity. This property makes them uniquely appealing as transparent-conductive electrodes in solar cells and…
We study schemes for interpolating functions that take values in the special orthogonal group $SO(n)$. Our focus is on interpolation schemes obtained by embedding $SO(n)$ in a linear space, interpolating in the linear space, and mapping the…
We theoretically demonstrate that screw dislocation (SD), a 1D topological defect widely present in semiconductors, exhibits ubiquitously a new form of spin-orbit coupling (SOC) effect. Differing from the widely known conventional 2D…
Stacked metasurfaces are being investigated in light of exploring exotic optical effects that cannot be achieved with single-layered metasurfaces. In this Letter, we theoretically demonstrate that stacks of metallic wire-grid metasurfaces…