1204298
An implicit degree condition for long cycles in 2-connected graphs
Abstract Let id ( v ) denote the implicit degree of a vertex v . In this work we prove that: If G is a 2-connected graph with max { id ( u ) , id ( v ) } ≥ c / 2 for each pair of nonadjacent vertices u and v that are vertices of an induced claw or an induced modified claw of G , then G contains either a Hamilton cycle or a cycle of length at least c . This extends several previous results on the existence of long cycles in graphs.
13607587
Heavy cycles passing through some specified vertices in weighted graphs
A weighted graph is one in which every edge e is assigned a nonnegative number, called the weight of e. The sum of the weights of the edges incident with a vertex v is called the weighted degree of v. The weight of a cycle is defined as the sum of the weights of its edges. In this paper, we prove that: (1) if G is a 2-connected weighted graph such that the minimum weighted degree of G is at least d, then for every given vertices x and y, either G contains a cycle of weight at least 2d passing through both of x and y or every heaviest cycle in G is a hamiltonian cycle, and (2) if G is a 2-connected weighted graph such that the weighted degree sum of every pair of nonadjacent vertices is at least s, then for every vertex y, G contains either a cycle of weight at least s passing through y or a hamiltonian cycle. AMS classification: 05C45 05C38 05C35
6391408
Computing the Scattering Number of Graphs
The scattering number of a noncomplete connected graph G is defined by s ( G )= max{ y ( G m X ) m X X ² V ( G ), y ( G m X ) S 2}, where y ( G m X ) denotes the number of components of G m X . This parameter can be used to measure the vulnerability of networks. It shows not only the difficulty to break down the network but also the damage that has been caused. In this paper, we prove that the problem of computing the scattering number of a graph is NP-complete. At the same time, the scattering numbers of grids and those of Cartesian products of two complete graphs are determined.
40273501
Pattern Discovery in Probabilistic Databases
Modeling probabilistic data is one of important issues in databases due to the fact that data is often uncertainty in real-world applications. So, it is necessary to identify potentially useful patterns in probabilistic databases. Because probabilistic data in 1NF relations is redundant, previous mining techniques don't work well on probabilistic databases. For this reason, this paper proposes a new model for mining probabilistic databases. A partition is thus developed for preprocessing probabilistic data in a probabilistic databases. We evaluated the proposed technique, and the experimental results demonstrate that our approach is effective and efficient.
29457354
A novel shape matching method using biological sequence dynamic alignment
Shape description and its corresponding matching algorithm is one of the main concerns in MPEG-7. A novel dynamic shape matching algorithm is proposed. First, the conventional 8-directional chain code is exploited to describe the binary shape. A dynamic shape matching algorithm, which is derived from the solution for the biological sequence similarity analysis based on molecular evolutionary theory, is proposed to measure the similarity distance between the shapes by computing their similarity score (SS). Based on a large set of MPEG-7 binary shapes, simulation results have shown that the proposed dynamic alignment matching algorithm is fairly promising and also robust to scale changes, small non-rigid deformation, and similarity based shape matching defined in MPEG-7 core experiments.
2378459
Visualization of Topological Defects in Nematic Liquid Crystals Using Streamtubes, Streamsurfaces and Ellipsoids
Researchers in computational condensed matter physics deal with complex data sets consisting of time varying 3D tensor, vector, and scalar quantities. Particularly, in the research of topological defects in nematic liquid crystals (LC) displaying the results of the computer simulation of molecular dynamics presents a challenge. Combining existing immersive and interactive visualization methods we developed new methods that attempt to provide a clear, efficient, and intuitive way to visualize and explore LC data. In addition, the visualization of the data has presented us with a novel method of obtaining the locations of the topological defects present in a liquid crystal system.
9519800
Turbulent Decay and Mixing of Accelerated Inhomogeneous Flows Via a Feature Based Analysis
In this paper, we focus on the late time turbulence of an accelerated inhomogeneous flow environment, which is a generalization of the Richtmyer--Meshkov environment. The numerical investigation is based on two-dimensional (2D) compressible Euler simulation, which is initiated by a shock wave hitting a gas layer (curtain). Although our unforced study is based on the intrinsic numerical dissipation, we observe excellent agreement with the previous decay analysis on 2D viscous isotropic homogeneous turbulence at inertial range [J. R. Chasnov, Phys. Fluids, 9 (1997), pp. 171--180]. The baroclinic circulation in our environment plays a major role in the mass transport and mixing. The mass-transport induced density gradient intensification, in turn, enhances the circulation baroclinically and provides an intrinsic forcing at intermediate to high wave number range. With the assistance of a computer graphics based feature extraction and tracking algorithm, we address quantitatively the spatial and temporal diffusivity of the mixing zone. We study and compare both the slow/fast/slow and fast/slow/fast cases to illustrate heuristically the correlation of mass and momentum diffusivity.
15381284
Color Rapid Prototyping for Diffusion-Tensor MRI Visualization
We describe work toward creating color rapid prototyping (RP) plaster models as visualization tools to support scientific research in diffusion-tensor (DT) MRI analysis. We currently give surgeons and neurologists virtual-reality (VR) applications to visualize different aspects of their brain data, but having physical representations of those virtual models allows them to review the data with a very robust, natural, and fast haptic interface: their own hands. Our initial results are encouraging, and end users are excited about the possibilities of this technique. For example, using these models in conjunction with digital models on the computer screen or VR environment provides a static frame of reference that helps keep users oriented during their analysis tasks.