Related papers: Cubical convex ear decompositions

We propose a Su-Schrieffer-Heeger type electron-phonon model for C_{60} with O defects and solve by the adiabatic approximation. Two new properties are obtained. (1) The dimerization becomes weaker around the oxygen. Two localized states…

In this paper, two high order complex contour discretization methods are proposed to simulate wave propagation in locally perturbed periodic closed waveguides. As is well known the problem is not always uniquely solvable due to the…

A specialization semilattice is a join semilattice together with a coarser preorder $ \sqsubseteq $ satisfying an appropriate compatibility condition. If $X$ is a topological space, then $(\mathcal P(X), \cup, \sqsubseteq )$ is a…

We present a CNN architecture for speech enhancement from multichannel first-order Ambisonics mixtures. The data-dependent spatial filters, deduced from a mask-based approach, are used to help an automatic speech recognition engine to face…

We study the Convex Set Disjointness (CSD) problem, where two players have input sets taken from an arbitrary fixed domain~$U\subseteq \mathbb{R}^d$ of size $\lvert U\rvert = n$. Their mutual goal is to decide using minimum communication…

Let F be a finite set of circles in the plane. We point out that the usual convex closure restricted to F yields a convex geometry, that is, a combinatorial structure introduced by P. H Edelman in 1980 under the name "anti-exchange closure…

In our previous papers, together with J. Paseka we introduced so-called sectionally pseudocomplemented lattices and posets and illuminated their role in algebraic constructions. We believe that - similar to relatively pseudocomplemented…

Liquid crystals can self-organize into a layered smectic phase. While the smectic layers are typically straight forming a lamellar pattern in bulk, external confinement may drastically distort the layers due to the boundary conditions…

We initiate the study of absorbing representations of $C^\ast$-algebras with respect to closed operator convex cones. We completely determine when such absorbing representations exist, which leads to the question of characterising when a…

We introduce a novel multi-resolution Localized Orthogonal Decomposition (LOD) for time-harmonic acoustic scattering problems that can be modeled by the Helmholtz equation. The method merges the concepts of LOD and operator-adapted wavelets…

In 1979, Shearer and Kleitman conjectured that there exist $\lfloor n/2 \rfloor+1$ orthogonal chain decompositions of the hypercube $Q_n$, and constructed two orthogonal chain decompositions. In this paper, we make the first non-trivial…

Auscultation for neonates is a simple and non-invasive method of providing diagnosis for cardiovascular and respiratory disease. Such diagnosis often requires high-quality heart and lung sounds to be captured during auscultation. However,…

The Wythoff construction takes a $d$-dimensional polytope $P$, a subset $S$ of $\{0,..., d\}$ and returns another $d$-dimensional polytope $P(S)$. If $P$ is a regular polytope, then $P(S)$ is vertex-transitive. This construction builds a…

With the advancement of neural networks, there has been a notable increase, both in terms of quantity and variety, in research publications concerning the application of autoencoders to reduced-order models. We propose a polytopic…

We create a framework for studying symmetric chain decompositions of families of finite posets based on the geometry of polytopes. Our framework unifies almost all known results regarding symmetric chain decompositions of the Young posets…

Articulated objects exist widely in the real world. However, previous 3D generative methods for unsupervised part decomposition are unsuitable for such objects, because they assume a spatially fixed part location, resulting in inconsistent…

We propose a new shape-based modeling technique for applications in imaging problems. Given a collection of shape priors (a shape dictionary), we define our problem as choosing the right dictionary elements and geometrically composing them…

We consider the convected Helmholtz equation with a generalized Myers boundary condition (a boundary condition of the second-order) and characterize the set of physical parameters for which the problem is weakly well-posed. The model comes…

This paper studies topological properties of the lattices of non-crossing partitions of types A and B and of the poset of injective words. Specifically, it is shown that after the removal of the bottom and top elements (if existent) these…

Let $N$ be a lattice of rank $n$ and let $M = N^{\vee}$ be its dual lattice. In this note we show that given two compact, bounded, full-dimensional convex sets $K_1 \subseteq K_2 \subseteq M_{\R} \coloneqq M \otimes_{\Z} \R$, there is a…