Stable Vertex Research Articles

Frequency-dependent functional renormalization group for interacting fermionic systems

We derive an expansion of the functional renormalization (fRG) equations that treats the frequency and momentum dependencies of the vertices in a systematic manner. The scheme extends the channel-decomposed fRG equations to the frequency domain and reformulates them as a series of linear integral equations in the particle-particle, particle-hole and particle-hole exchange channels. We show that the linearity of the equations offers numerous computational advantages and leads to converged, stable solutions for a variety of Hamiltonians. As the expansion is in the coupling between channels, the truncations that are necessary to making the scheme computationally viable still lead to equations that treat contributions from all channels equally. As a first benchmark we apply the two-loop fRG equations to the single impurity Anderson model. We consider the sources of error within the fRG, the computational cost associated with each, and how the choice of regulator affects the flow of the fRG. We then use the optimal truncation scheme to study the Extended Hubbard Hamiltonian in one and two dimensions. We find that in many cases of interest the fRG flow converges to a stable vertex and self-energy from which we can extract the various correlation functions and susceptibilities of interest.

Perfect Matching Interdiction Problem Restricted to a Stable Vertex

Suppose v is the stable vertex of a weighted graph G. The purpose of the perfect matching interdiction problem restricted to the stable vertex v in G is to remove v and a vertex adjacent to v such that the weight of the maximum perfect matching in the resulting graph is minimized. In this paper, we present an approximate solution for this problem. According to the approximate and optimal solutions, a special ratio is introduced for this problem. This ratio is not bounded from above and we obtain it for some special classes of graphs.

A zero-watermarking scheme for three-dimensional mesh models based on multi-features

The aim of this study is to devise a zero-watermarking algorithm, the main challenge of which is the selection and construction of resilient features of three-dimensional(3D) models while improving the resilience of the zero-watermarking algorithm to common attacks. A novel zero-watermarking scheme for 3D mesh models based on multi-features is proposed in this paper. Using the Ordered Statistics Vertex Extraction and Tracing Algorithm, the stable vertices of a 3D model are determined. Then, the skewness measure of the shape diameter function values and vertex norms of the stable vertices are determined. Combined with the distribution feature of the number of stable vertices, a resilient watermark is applied. Experimental results show that the proposed scheme is not affected by a similarity transformation (such as translation, rotation, or uniform scaling) or vertex reordering. The scheme is also sufficiently resilient to noise, simplification, smoothing, and subdivision attacks. In addition, the scheme can resist cropping to a certain extent. The scheme proposed in this paper is suitable for applications that require 3D models with a higher accuracy and that cannot be embedded with a watermark that would modify the data of those models.

On minimal non [h,2,1] graphs

The class of graphs which admits a VPT representation in a host tree with maximum degree at most h is denoted by [h,2,1]. The classes [h,2,1] are closed by taking induced subgraphs, therefore each one can be characterized by a family of minimal forbidden induced subgraphs. In this paper we associate the minimal forbidden induced subgraphs for [h,2,1] which are VPT with (color) critical graphs. We describe how to obtain minimal forbidden induced subgraphs from critical graphs, even more, we show that the family of graphs obtained using our procedure is exactly the family of minimal forbidden induced subgraphs which are VPT, split and have no dominated stable vertices. We conjecture that there are no other VPT minimal forbidden induced subgraphs. We also prove that the minimal forbidden induced subgraphs for [h,2,1] that are VPT graphs belong to the class [h+1,2,1].

Properties of edge-deleted distance stable graphs

The distance from a vertex u to a vertex v in a connected graph G is the length of a shortest u–v path in G. The distance of a vertex v of G is the sum of the distances from v to the vertices of G. For a vertex v in a 2-edge-connected graph G, we define the edge-deleted distance of v as the maximum distance of v in G −e over all edges e of G. A vertex is an edge-deleted distance stable vertex if the difference between its edge-deleted distance and distance is 1. A 2-edge-connected graph G is an edge-deleted distance stable graph if each vertex of G is an edge-deleted distance stable vertex. In this paper, we investigate the edge-deleted distance of vertices and describe properties of edge-deleted distance stable graphs. © 1999 John Wiley & Sons, Inc. Networks 34: 279–282, 1999

On the robust control via reflection coefficients

Abstract A robust version of the modal controller design for discrete-time systems is introduced. Instead of a single stable point a stable simplex must be preselected in the closed loop characteristic polynomials coefficients space. A constructive procedure for generating simplexis inside the “nice stability region” is given starting from the unit hypercube of reflection coefficients of monic polynomials. This procedure is quite straightforward because, first, n edges are generated by a linear Schur invariant transformation and, second, the most critical edge is determined by the difference of reflection coefficients numbers. The procedure of robust controller design makes use of a stability measure defined as the minimal distance between a preselected stable simplex and vertices of an uncertain polytopic plant.