Related papers: Correlations in totally symmetric self-complementa…
We investigate a rich new class of exactly solvable particle systems generalizing the Totally Asymmetric Simple Exclusion Process (TASEP). Our particle systems can be thought of as new exactly solvable examples of tandem queues, directed…
An equiangular tight frame (ETF) is a sequence of vectors in a Hilbert space that achieves equality in the Welch bound and so has minimal coherence. More generally, an equichordal tight fusion frame (ECTFF) is a sequence of equi-dimensional…
We give a sufficient criterion, which we call stability, for a coarse Lipschitz map $f$ from a complete manifold $X$ with Ricci curvature bounded below to a proper Hadamard space $Y$ to be within bounded distance of a harmonic map. We prove…
Theoretical prediction of topological superconductivity is key to their discovery. Recently, it is proved that in 199 out of 230 space groups, topological superconductivity coexists with an $s$-wave-like pairing symmetry, raising the hope…
The ability to tailor a coherent surface plasmon polariton (SPP) field is an important step towards a number of new opportunities for a broad range of nanophotonic applications such as sensing [1,2], nano-circuitry [3,4], optical data…
The most general form of non-static plane symmetric space-times is considered to study proper curvature collineations by using the rank of the 6X6 Riemann matrix and direct integration techniques. Studying proper curvature collineations in…
This is the second paper in the series devoted to the study of the dimer model on t-embeddings of planar bipartite graphs. We introduce the notion of perfect t-embeddings and assume that the graphs of the associated origami maps converge to…
In this work, we introduce a new type of topological order which is protected by subsystem symmetries which act on lower dimensional subsets of lattice many-body system, e.g. along lines or planes in a three dimensional system. The symmetry…
We lay out the foundations of the theory of second-order conformal superintegrable systems. Such systems are essentially Laplace equations on a manifold with an added potential: $(\Delta_n+V({\bf x}))\Psi=0$. Distinct families of…
This paper is a self-contained exposition of the geometry of symmetric positive-definite real $n\times n$ matrices $\operatorname{SPD}(n)$, including necessary and sufficent conditions for a submanifold $\mathcal{N}…
Correlation matrices are standardized covariance matrices. They form an affine space of symmetric matrices defined by setting the diagonal entries to one. We study the geometry of maximum likelihood estimation for this model and linear…
A perfect matching in a bipartite graph embedded on a torus defines a height function on the graph's faces and an associated height change vector in $\Z^2$. These matchings are enumerated by a combination of four evaluations of a bivariate…
We introduce symmetric Poisson structures as pairs consisting of a symmetric bivector field and a torsion-free connection satisfying an integrability condition analogous to that in usual Poisson geometry. Equivalent conditions in Poisson…
Symmetric edge polytopes are a recent and well-studied family of centrally symmetric polytopes arising from graphs. In this paper, we introduce a generalization of this family to arbitrary simplicial complexes. We show how topological…
We consider the monomer-dimer partition function on arbitrary finite planar graphs and arbitrary monomer and dimer weights, with the restriction that the only non-zero monomer weights are those on the boundary. We prove a Pfaffian formula…
Matrices are the most common representations of graphs. They are also used for the representation of algebras and cluster algebras. This paper shows some properties of matrices in order to facilitate the understanding and locating…
We introduce the class of almost symmetric submanifolds of Euclidean space, a close relative of symmetric submanifolds and (contact) sub-Riemannian symmetric spaces. More specifically, we prove that every full irreducible almost symmetric…
We examine connections between combinatorial notions that arise in machine learning and topological notions in cubical/simplicial geometry. These connections enable to export results from geometry to machine learning. Our first main result…
Plane symmetric self-similar solutions to Einstein's four-dimensional theory of gravity are studied and all such solutions are given analytically in closed form. The local and global properties of these solutions are investigated and it is…
A set of n segments in the plane may form a Euclidean TSP tour, a tree, or a matching, among others. Optimal TSP tours as well as minimum spanning trees and perfect matchings have no crossing segments, but several heuristics and…