Related papers: A Large Scale Approach to Decomposition Spaces
We develop a folding approach to study two-dimensional symmetry-enriched topological (SET) phases with the mirror reflection symmetry. Our folding approach significantly transforms the mirror SETs, such that their properties can be…
With a simple generic approach, we develop a classification that encodes and measures the strength of completeness (or compactness) properties in various types of spaces and ordered structures. The approach also allows us to encode notions…
We investigate the relationship between the compactness of embeddings of Sobolev spaces built upon rearrangement-invariant spaces into rearrangement-invariant spaces endowed with $d$-Ahlfors measures under certain restriction on the speed…
We study central configurations when the set of positions is symmetric. We use a theorem from representation theory of finite groups to explore the symmetry properties of equations for central configurations. This approach simplifies…
We introduce structured decompositions, category-theoretic structures which simultaneously generalize notions from graph theory (including treewidth, layered treewidth, co-treewidth, graph decomposition width, tree independence number,…
In this paper, we consider the problem of partitioning a polygon into a set of connected disjoint sub-polygons, each of which covers an area of a specific size. The work is motivated by terrain covering applications in robotics, where the…
Assemblies of anisotropic particles commonly appear in studies of active many-body systems. However, in two dimensions, the geometric ramifications of the finite density of such objects are not entirely understood. To fully characterize…
Learning from unordered sets is a fundamental learning setup, recently attracting increasing attention. Research in this area has focused on the case where elements of the set are represented by feature vectors, and far less emphasis has…
Deep metric learning (DML) is a cornerstone of many computer vision applications. It aims at learning a mapping from the input domain to an embedding space, where semantically similar objects are located nearby and dissimilar objects far…
We introduce decomposition complexes of posets, which generalize order complexes. The main advantage of our construction is that decomposition complexes are closed under taking products. Other special instances of this theory include nested…
The slice decomposition is a bijective method for enumerating planar maps (graphs embedded in the sphere) with control over face degrees. In this paper, we extend the slice decomposition to the richer setting of hypermaps, naturally…
We introduce a notion of equivariant coarse cohomology of the complement of a subspace in a metric space. We use this cohomology to define a notion of coarse cohomology of the configuration space of a metric space and develop tools to…
We use a continuous mesoscopic model to address the yielding properties of plastic composites, formed by a host material and inclusions with different elastic and/or plastic properties. We investigate the flow properties of the composed…
This paper examines a stochastic deconvolution problem on compact symmetric spaces which is referred to as decompounding. This involves estimating the step distributions of a random walk, where in addition the number of steps between…
Existing scene understanding systems mainly focus on recognizing the visible parts of a scene, ignoring the intact appearance of physical objects in the real-world. Concurrently, image completion has aimed to create plausible appearance for…
We prove that a conformal mapping defined on the unit disk belongs to a weighted Bergman space if and only if certain integrals involving the harmonic measure converge. With the aid of this theorem, we give a geometric characterization of…
We study the quantitative properties of Lipschitz mappings from Euclidean spaces into metric spaces. We prove that it is always possible to decompose the domain of such a mapping into pieces on which the mapping "behaves like a projection…
We investigate the existence of embeddings of shearlet coorbit spaces associated to weighted mixed $L^p$-spaces into classical Sobolev spaces in dimension three by using the description of coorbit spaces as decomposition spaces. This…
The visual world around us can be described as a structured set of objects and their associated relations. An image of a room may be conjured given only the description of the underlying objects and their associated relations. While there…
A stratified space is a topological space equipped with a \emph{stratification}, which is a decomposition or partition of the topological space satisfying certain extra conditions. More recently, the notion of poset-stratified space, i.e.,…