相关论文: Grid Movies

We uncover a connection between two seemingly unrelated notions: lettericity, from structural graph theory, and geometric griddability, from the world of permutation patterns. Both of these notions capture important structural properties of…

Inspired by asymptotically flat manifolds, we introduce the concept of asymptotically flat graphs and define the discrete ADM mass on them. We formulate the discrete positive mass conjecture based on the scalar curvature in the sense of…

We study a gravitating spherically symmetric nonrelativistic configuration consisting of a spinor fluid whose effective equation of state is derived from a consideration of a limiting system supported by a massive nonlinear spinor field.…

Generalizing Milnor's result that an FTC (finite total curvature) knot has an isotopic inscribed polygon, we show that any two nearby knotted FTC graphs are isotopic by a small isotopy. We also show how to obtain sharper constants when the…

We deal with the symmetries of a (2-term) graded vector space or bundle. Our first theorem shows that they define a (strict) Lie 2-groupoid in a natural way. Our second theorem explores the construction of nerves for Lie 2-categories,…

Grid diagrams are special representations of knots in the three-sphere that are used to define a combinatorial version of knot Floer homology. Paolo Ghiggini and Yi Ni showed that knot Floer homology detects fibered knots. Their results…

In this paper we extend the theory of bidimensionality to two families of graphs that do not exclude fixed minors: map graphs and power graphs. In both cases we prove a polynomial relation between the treewidth of a graph in the family and…

By employing the method of moving planes in a novel way we extend some classical symmetry and rigidity results for smooth minimal surfaces to surfaces that have singularities of the sort typically observed in soap films.

We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…

We introduce the warping matrix which is a new description of oriented knots from a viewpoint of warping degree.

Motivated by recent realizations of Dy$_{2}$Ti$_{2}$O$_{7}$ and Ho$_{2}$Ti$_{2}$O$_{7}$ spin ice thin films, and more generally by the physics of confined gauge fields, we study a model of spin ice thin film with surfaces perpendicular to…

We introduce a notion of limit linear series for nodal curves which are not of compact type. We give a construction of a moduli space of limit linear series, which works also in smoothing families, and we prove a corresponding…

Understanding and interacting with everyday physical scenes requires rich knowledge about the structure of the world, represented either implicitly in a value or policy function, or explicitly in a transition model. Here we introduce a new…

This paper is devoted to analytical solutions for the base flow and temporal stability of a liquid film driven by gravity over an inclined plane when the fluid rheology is given by the Carreau-Yasuda model, a general description that…

We prove necessary and sufficient conditions on a family of (generalised) gridding matrices to determine when the corresponding permutation classes are partially well-ordered. One direction requires an application of Higman's Theorem and…

We construct a scattering theory for harmonic one-forms on Riemann surfaces, obtained from boundary value problems through systems of curves and the jump problem. We obtain an explicit expression for the scattering matrix in terms of…

We develop a theory of $\times$-homotopy, fundamental groupoids and covering spaces that apply to non-simple graphs, generalizing existing results for simple graphs. We prove that $\times$-homotopies from finite graphs can be decomposed…

An involutive link is a link which is invariant under the standard rotation by 180 degrees in $S^3$. We establish an equivariant analogue of the work of Carter and Saito aimed at studying equivariant cobordisms between involutive links.…

We present a notion of $\Delta$-stability and stability filtration in arbitrary categories which is equivalent to the existence of Harder-Narasimhan (HN) sequences on objects. Indeed it is equivalent to the existence of a zero morphism, a…

Quantized, compact graphs were shown to be excellent paradigms for quantum chaos in bounded systems. Connecting them with leads to infinity we show that they display all the features which characterize scattering systems with an underlying…