Related papers: Cubical convex ear decompositions

In this paper we show that the set of closure relations on a finite poset P forms a supersolvable lattice, as suggested by Rota. Furthermore this lattice is dually isomorphic to the lattice of closed sets in a convex geometry (in the sense…

We prove that the order complex of a geometric lattice has a convex ear decomposition. As a consequence, if D(L) is the order complex of a rank (r+1) geometric lattice L, then for all i \leq r/2 the h-vector of D(L) satisfies h(i-1) \leq…

In this paper, we present a Localized Orthogonal Decomposition (LOD) in Petrov-Galerkin formulation for a two-scale Helmholtz-type problem. The two-scale problem is, for instance, motivated from the homogenization of the Helmholtz equation…

This paper proposes a new method for rigid body pose estimation based on spectrahedral representations of the tautological orbitopes of $SE(2)$ and $SE(3)$. The approach can use dense point cloud data from stereo vision or an RGB-D sensor…

We consider a novel clustering task in which clusters can have compositional relationships, e.g., one cluster contains images of rectangles, one contains images of circles, and a third (compositional) cluster contains images with both…

A convex cone is said to be projectionally exposed (p-exposed) if every face arises as a projection of the original cone. It is known that, in dimension at most four, the intersection of two p-exposed cones is again p-exposed. In this paper…

We propose an Ensemble of Robust Constrained Local Models for alignment of faces in the presence of significant occlusions and of any unknown pose and expression. To account for partial occlusions we introduce, Robust Constrained Local…

Decomposition of shapes into (approximate) convex parts is essential for applications such as part-based shape representation, shape matching, and collision detection. In this paper, we propose a novel convex decomposition using a…

The concept of a Kleene algebra (sometimes also called Kleene lattice) was already generalized by the first author for non-distributive lattices under the name pseudo-Kleene algebra. We extend these concepts to posets and show how…

Deep networks have strong capacities of embedding data into latent representations and finishing following tasks. However, the capacities largely come from high-quality annotated labels, which are expensive to collect. Noisy labels are more…

The aim of the present paper is to extend the concept of a congruence from lattices to posets. We use an approach different from that used by the first author and V. Sn\'a\v{s}el. By using our definition we show that congruence classes are…

The basic tool for solving problems in metric geometry and isotonic regression is the metric projection onto closed convex cones. Isotonicity of these projections with respect to a given order relation can facilitate finding the solutions…

In this paper, we present a new perspective on cut generation in the context of Benders decomposition. The approach, which is based on the relation between the alternative polyhedron and the reverse polar set, helps us to improve…

Dilated convolution with learnable spacings (DCLS) is a recent convolution method in which the positions of the kernel elements are learned throughout training by backpropagation. Its interest has recently been demonstrated in computer…

In this paper, we study the posets of classes of subgroups of finite group having same set of orders of elements. We show that this poset is a chain only in the case of p-groups and moreover, we characterize all finite groups for which this…

While faces of a polytope form a well structured lattice, in which faces of each possible dimension are present, this is not true for general compact convex sets. We address the question of what dimensional patterns are possible for the…

We investigate a poset structure that extends the weak order on a finite Coxeter group $W$ to the set of all faces of the permutahedron of $W$. We call this order the facial weak order. We first provide two alternative characterizations of…

Bj\"orner and Wachs introduced CL-shellability as a technique for studying the topological structure of order complexes of partially ordered sets (posets). They also introduced the notion of recursive atom ordering, and they proved that a…

Existing fake audio detection systems perform well in in-domain testing, but still face many challenges in out-of-domain testing. This is due to the mismatch between the training and test data, as well as the poor generalizability of…

We generalize the concept of combinatorial nested set complexes to posets and exhibit the topological relationship between the arising nested set complexes and the order complex of the underlying poset. In particular, a sufficient condition…