We prove that a binomial edge ideal of a graph G has a quadratic Gröbner basis with respect to some term order if and only if the graph G is closed with respect to a given labelling of the vertices. We also state some criteria for the closedness of a graph G that do not depend on the labelling of its vertex set.

We survey some recent results on the minimal graded free resolution of a square-free monomial ideal. The theme uniting these results is the point-of-view that the generators of a monomial ideal correspond to the maximal faces (the facets) of a simplicial complex ∆. This correspondence gives us a new method, distinct from the Stanley-Reisner correspondence, to associate to a square-free monomial...

We study the topology of the lcm-lattice of edge ideals and derive upper bounds on the Castelnuovo-Mumford regularity of the ideals. In this context it is natural to restrict to the family of graphs with no induced 4-cycle in their complement. Using the above method we obtain sharp upper bounds on the regularity when the complement is a chordal graph, or a cycle, or when the primal graph is cla...

This work presents a new approach for analyzing the problem of edge-preserving image smoothing using convex minimization and for selecting smoothing parameters. The close-form (global) solution is derived as the response of a convex smoothing model to the ideal step edge. Insights into how the minimal solution responds to edges in the data and how the parameter values aaect resultant edges in t...

Transport in an ideal two-dimensional quantum spin Hall device is dominated by the counterpropagating edge states of electrons with opposite spins, giving the universal value of the conductance, 2e(2)/h. We study the effect on the conductance of a magnetic impurity, which can backscatter an electron from one edge state to the other. In the case of isotropic Kondo exchange we find that the corre...

We present a current and charge conserving theory for the low frequency admittance of a two-dimensional electron gas connected to ideal metallic contacts and subject to a quantizing magnetic field. In the framework of the edge-channel picture, we calculate the admittance up to first order with respect to frequency. The transport coefficients in first order with respect to frequency, which are c...

A numerical investigation of ideal magnetohydrodynamic stability in finite aspect ratio tokamaks with zero edge current density is carried out. It is shown that, assuming a conventionally D-shaped cross section and a safety factor on axis greater than 2.1, both n = oo and n = 1 modes are stable for any beta, even in the absence of any surrounding conductors.

Let G be a bipartite graph with edge ideal I(G) whose quotient ring R/I(G) is sequentially Cohen-Macaulay. We prove: (1) the independence complex of G must be vertex decomposable, and (2) the Castelnuovo-Mumford regularity of R/I(G) can be determined from the invariants of G.

Correctly interpreting a natural image requires dealing properly with the effects of occlusion, and hence, contour grouping across occlusions is a major component of many natural visual tasks. To better understand the mechanisms of contour grouping across occlusions, we (a) measured the pair-wise statistics of edge elements from contours in natural images, as a function of edge element geometry...

We introduce the concept of minimum edge cover for an induced subgraph in a graph. Let [Formula: see text] be unicyclic graph with unique odd cycle and its ideal. compute exact values all symbolic defects using describe one method to find quasi-polynomial associated ideal text]. classify class graphs when some power maximal annihilates any fixed Also those graphs, we Hilbert function module