38623555
Domination number and neighbourhood conditions
Abstract The domination number γ of a graph G is the minimum cardinality of a subset D of vertices of G such that each vertex outside D is adjacent to at least one vertex in D . For any subset A of the vertex set of G , let ∂ + ( A ) be the set of vertices not in A which are adjacent to at least one vertex in A . Let N (A) be the union of A and ∂ + ( A ), and d ( A ) be the sum of degrees of all the vertices of A . In this paper we prove the inequality 2q ⩽ (p−γ)(p−γ+2)−|∂ + (A)| (p−γ+1)+d( N (A)) , and characterize the extremal graphs for which the equality holds, where p and q are the numbers of vertices and edges of G , respectively. From this we then get an upper bound for γ which generalizes the known upper bound γ⩽p+1− 2q+1 . Let I ( A ) be the set of vertices adjacent to all vertices of A , and I (A) be the union of A and I ( A ). We prove that 2q ⩽ (p − γ − | I (A)| + 2)(p − γ + 4) + d( I (A)) − min {p − γ − | I (A)| + 2, |A|, |I(A)|, 3} , which implies an upper bound for γ as well.
2040851
Decycling numbers of random regular graphs
The decycling number φ(G) of a graph G is the smallest number of vertices which can be removed from G so that the resultant graph contains no cycles. In this paper, we study the decycling numbers of random regular graphs. For a random cubic graph G of order n, we prove that φ(G) = ⌈n/4 + 1/2⌉ holds asymptotically almost surely. This is the result of executing a greedy algorithm for decycling G making use of a randomly chosen Hamilton cycle. For a general random d-regular graph G of order n, where d ≥ 4, we prove that φ(G)/n can be bounded below and above asymptotically almost surely by certain constants b(d) and B(d), depending solely on d, which are determined by solving, respectively, an algebraic equation and a system of differential equations.
32007375
Interpolation theorems for graphs, hypergraphs and matroids
Abstract Let P and Q be, respectively, hereditary and cohereditary properties defined on the subsets of a finite set S . We first prove that several functions related to P and Q interpolate over some families of subsets of S . By using this we then derive a number of interpolation results for graphs, hypergraphs and matroids.
1717304
Shape Regression Machine
We present a machine learning approach called shape regression machine (SRM) to segmenting in real time an anatomic structure that manifests a deformable shape in a medical image. Traditional shape segmentation methods rely on various assumptions. For instance, the deformable model assumes that edge defines the shape; the Mumford-Shah variational method assumes that the regions inside/outside the (closed) contour are homogenous in intensity; and the active appearance model assumes that shape/appearance variations are linear. In addition, they all need a good initialization. In contrast, SRM poses no such restrictions. It is a two-stage approach that leverages (a) the underlying medical context that defines the anatomic structure and (b) an annotated database that exemplifies the shape and appearance variations of the anatomy. In the first stage, it solves the initialization problem as object detection and derives a regression solution that needs just one scan in principle. In the second stage, it learns a nonlinear regressor that predicts the nonrigid shape from image appearance. We also propose a boosting regression approach that supports real time segmentation. We demonstrate the effectiveness of SRM using experiments on segmenting the left ventricle endocardium from an echocardiogram of an apical four chamber view.
7007263
The rich-club phenomenon in the Internet topology
We show that the Internet topology at the autonomous system (AS) level has a rich-club phenomenon. The rich nodes, which are a small number of nodes with large numbers of links, are very well connected to each other. The rich-club is a core tier that we measured using the rich-club connectivity and the node-node link distribution. We obtained this core tier without any heuristic assumption between the ASs. The rich-club phenomenon is a simple qualitative way to differentiate between power law topologies and provides a criterion for new network models. To show this, we compared the measured rich-club of the AS graph with networks obtained using the Baraba/spl acute/si-Albert (BA) scale-free network model, the Fitness BA model and the Inet-3.0 model.
17046861
Appearance modeling under geometric context
We propose a unified framework based on a general definition of geometric transform (GeT) for modeling appearance. GeT represents the appearance by applying designed functionals over certain geometric sets. We show that image warping, Radon transform, trace transform, etc. are special cases of our definition. Moreover, three different types of GeTs are designed to handle deformation, articulation and occlusion and applied to fingerprinting the appearance inside a contour. They include the contour-driven GeT, the feature curve based GeT and selecting functionals to model the appearance inside the convex hull of the contour. A multi-resolution representation that combines both shape and appearance information is also proposed. We apply our approach to image synthesis and object recognition. The proposed approach produces promising results when applied to fingerprinting the appearance of human and body parts despite the challenges due to articulated motion and deformations
62771282
Robust appearance-based tracking of moving object from moving platform
We present a robust algorithm for tracking moving objects from a moving platform. Robustness is achieved by incorporating temporal differencing and shape detection in an appearance-based object tracking algorithm. In addition, the incorporation of these two methods also improves accuracy and computational efficiency of detection. Some experimental results using airborne-video tracking are given to illustrate the effectiveness of this method.
728
Analyzing and modelling the AS-level Internet topology
Recently we introduced the rich-club phenomenon as a quantitative metric to characterize the tier structure of the Autonomous Systems level Internet topology (AS graph) and we proposed the Interactive Growth (IG) model, which closely matches the degree distribution and hierarchical structure of the AS graph and compares favourble with other available Internet power-law topology generators. Our research was based on the widely used BGP AS graph obtained from the Oregon BGP routing tables. Researchers argue that Traceroute AS graph, extracted from the traceroute data collected by the CAIDA's active probing tool, Skitter, is more complete and reliable. To be prudent, in this paper we analyze and compare topological structures of Traceroute AS graph and BGP AS graph. Also we compare with two synthetic Internet topologies generated by the IG model and the well-known Barabasi-Albert (BA) model. Result shows that both AS graphs show the rich-club phenomenon and have similar tier structures, which are closely matched by the IG model, however the BA model does not show the rich-club phenomenon at all.