Related papers: Parametrizing the Grassmannian using pipe dreams

Linear structural equation models, which relate random variables via linear interdependencies and Gaussian noise, are a popular tool for modeling multivariate joint distributions. These models correspond to mixed graphs that include both…

A (possibly denerate) drawing of a graph $G$ in the plane is approximable by an embedding if it can be turned into an embedding by an arbitrarily small perturbation. We show that testing, whether a straight-line drawing of a planar graph…

Using the Plucker map between grassmannians, we study basic aspects of classic grassmannian geometries. For `hyperbolic' grassmannian geometries, we prove some facts (for instance, that the Plucker map is a minimal isometric embedding) that…

We reconsider the problem of calculating a general spectral correlation function containing an arbitrary number of products and ratios of characteristic polynomials for a N x N random matrix taken from the Gaussian Unitary Ensemble (GUE).…

We give new characterizations for the class of uniformly dense matroids and study applications of these characterizations to graphic and real representable matroids. We show that a matroid is uniformly dense if and only if its base polytope…

Bayesian optimization (BO) is a powerful framework for optimizing expensive black-box objectives, yet extending it to graph-structured domains remains challenging due to the discrete and combinatorial nature of graphs. Existing approaches…

Let H be a graph, and let C_H(G) be the number of (subgraph isomorphic) copies of H contained in a graph G. We investigate the fundamental problem of estimating C_H(G). Previous results cover only a few specific instances of this general…

Let $\Gamma(n,k)$ be the Grassmann graph formed by the $k$-dimensional subspaces of a vector space of dimension $n$ over a field $\mathbb F$ and, for $t\in \mathbb{N}\setminus \{0\}$, let $\Delta_t(n,k)$ be the subgraph of $\Gamma(n,k)$…

Procedural modeling is now the de facto standard of material modeling in industry. Procedural models can be edited and are easily extended, unlike pixel-based representations of captured materials. In this paper, we present a semi-automatic…

In this work, we propose a parameter-free and efficient method to tackle the structure-texture image decomposition problem. In particular, we present a neural network LPR-NET based on the unrolling of the Low Patch Rank model. On the one…

Given a graph $G$, a subgraph $H$ is isometric if $d_H(u,v) = d_G(u,v)$ for every pair $u,v\in V(H)$, where $d$ is the distance function. A graph $G$ is distance preserving (dp) if it has an isometric subgraph of every possible order. A…

We show an algorithm that, given an $n$-vertex graph $G$ and a parameter $k$, in time $2^{O(k \log k)} n^{O(1)}$ finds a tree decomposition of $G$ with the following properties: * every adhesion of the tree decomposition is of size at most…

This paper employs techniques from metric geometry and optimal transport theory to address questions related to the analysis of functional data on metric or metric-measure spaces, which we refer to as fields. Formally, fields are viewed as…

In this paper, we propose a graph classification approach for automatically determining whether to use a monolithic or a decomposition-based solution method. In this approach, an optimization problem is represented as a graph that captures…

We state a combinatorial optimization problem whose feasible solutions define both a decomposition and a node labeling of a given graph. This problem offers a common mathematical abstraction of seemingly unrelated computer vision tasks,…

We introduce a generalized framework for studying higher-order versions of the multiscale method known as Localized Orthogonal Decomposition. Through a suitable reformulation, we are able to accommodate both conforming and nonconforming…

Graph embedding is a transformation of nodes of a network into a set of vectors. A good embedding should capture the underlying graph topology and structure, node-to-node relationship, and other relevant information about the graph, its…

In this paper we give a method to associate a graph with an arbitrary density matrix referred to a standard orthonormal basis in the Hilbert space of a finite dimensional quantum system. We study the related issues like classification of…

The dichotomy conjecture for the parameterized embedding problem states that the problem of deciding whether a given graph $G$ from some class $K$ of "pattern graphs" can be embedded into a given graph $H$ (that is, is isomorphic to a…

We propose a functional view of matrix decomposition problems on graphs such as geometric matrix completion and graph regularized dimensionality reduction. Our unifying framework is based on the key idea that using a reduced basis to…