Related papers: Parametrizing the Grassmannian using pipe dreams

This paper proposes a generalized framework with joint normalization which learns lower-dimensional subspaces with maximum discriminative power by making use of the Riemannian geometry. In particular, we model the similarity/dissimilarity…

Let $\Pi$ be a polar space of type $\textsf{D}_{n}$. Denote by ${\mathcal G}_{\delta}(\Pi)$, $\delta\in \{+,-\}$ the associated half-spin Grassmannians and write $\Gamma_{\delta}(\Pi)$ for the corresponding half-spin Grassmann graphs. In…

In this paper, we explore the discriminative power of Grassmannian persistence diagrams of 1-parameter filtrations, examine their relationships with other related constructions, and study their computational aspects. Grassmannian…

A G-gain graph is a graph whose oriented edges are labeled invertibly from a group G. Zaslavsky proposed two matroids of G-gain graphs, called frame matroids and lift matroids, and investigated linear representations of them. Each matroid…

We study the dimer model for a planar bipartite graph N embedded in a disk, with boundary vertices on the boundary of the disk. Counting dimer configurations with specified boundary conditions gives a point in the totally nonnegative…

Positroids are families of matroids introduced by Postnikov in the study of non-negative Grassmannians. In particular, positroids enumerate a CW decomposition of the totally non-negative Grassmannian. Furthermore, Postnikov has identified…

Let $\Pi$ be a polar space of rank $n$ and let ${\mathcal G}_{k}(\Pi)$, $k\in \{0,\dots,n-1\}$ be the polar Grassmannian formed by $k$-dimensional singular subspaces of $\Pi$. The corresponding Grassmann graph will be denoted by…

Franco, Galloni, Penante, and Wen have proposed a boundary measurement map for a graph on any closed orientable surface with boundary. We consider this boundary measurement map which takes as input an edge weighted directed graph embedded…

A novel Gromov-Wasserstein learning framework is proposed to jointly match (align) graphs and learn embedding vectors for the associated graph nodes. Using Gromov-Wasserstein discrepancy, we measure the dissimilarity between two graphs and…

The syndrome decoding problem has been proposed as a computational hardness assumption for code based cryptosystem that are safe against quantum computing. The problem has been reduced to finding the codeword with the smallest non-zero…

We study the parameterized complexity of the graph isomorphism problem when parameterized by width parameters related to tree decompositions. We apply the following technique to obtain fixed-parameter tractability for such parameters. We…

Dendrograms used in data analysis are ultrametric spaces, hence objects of nonarchimedean geometry. It is known that there exist $p$-adic representation of dendrograms. Completed by a point at infinity, they can be viewed as subtrees of the…

Research on automated image enhancement has gained momentum in recent years, partially due to the need for easy-to-use tools for enhancing pictures captured by ubiquitous cameras on mobile devices. Many of the existing leading methods…

Treewidth is a graph parameter that plays a fundamental role in several structural and algorithmic results. We study the problem of decomposing a given graph $G$ into node-disjoint subgraphs, where each subgraph has sufficiently large…

In this paper we construct an explicit map from planar bicolored (plabic) trivalent graphs representing a given irreducible positroid cell $S$ in the totally non-negative Grassmannian $Gr^{\mbox{TNN}}(k,n)$ to the spectral data for the…

An embedding of a point-line geometry \Gamma is usually defined as an injective mapping \epsilon from the point-set of \Gamma to the set of points of a projective space such that \epsilon(l) is a projective line for every line l of \Gamma,…

UMAP is a non-parametric graph-based dimensionality reduction algorithm using applied Riemannian geometry and algebraic topology to find low-dimensional embeddings of structured data. The UMAP algorithm consists of two steps: (1) Compute a…

We initiate a systematic study of non-planar on-shell diagrams in N=4 SYM and develop powerful technology for doing so. We introduce canonical variables generalizing face variables, which make the dlog form of the on-shell form explicit. We…

Let $V$ be an $n$-dimensional left vector space over a division ring $R$. We write ${\mathcal G}_{k}(V)$ for the Grassmannian formed by $k$-dimensional subspaces of $V$ and denote by $\Gamma_{k}(V)$ the associated Grassmann graph. Let also…

We propose a class of methods for graphon estimation based on exploiting connections with nonparametric regression. The idea is to construct an ordering of the nodes in the network, similar in spirit to Chan and Airoldi (2014). However,…