Subgraphs of 4-Regular Planar Graphs

We shall present an algorithm for determining whether or not a given planar graph H can ever be a subgraph of a 4-regular planar graph. The algorithm has running time O(|H|^2.5) and can be used to find an explicit 4-regular planar graph G⊃H if such a graph exists. It shall not matter whether we specify that H and G must be simple graphs or allow them to be multigraphs.     

A GPU framework for parallel segmentation of volumetric images using discrete deformable models

Despite the ability of current GPU processors to treat heavy parallel computation tasks, its use for solving medical image segmentation problems is still not fully exploited and remains challenging. A lot of difficulties may arise related to, for example, the different image modalities, noise and artifacts of source images, or the shape and appearance variability of the structures to segment. Motivated by practical problems of image segmentation in the medical field, we present in this paper a GPU framework based on explicit discrete deformable models, implemented over the NVidia CUDA architecture, aimed for the segmentation of volumetric images. The framework supports the segmentation in parallel of different volumetric structures as well as interaction during the segmentation process and real-time visualization of the intermediate results. Promising results in terms of accuracy and speed on a real segmentation experiment have demonstrated the usability of the system.     

Illustrating volume data sets and layered models with importance-aware composition

Non-photorealistic (illustrative) rendering augments typical rendering models to selectively emphasize or de-emphasize specific structures of rendered objects. Illustrative techniques may affect not only the rendering style of specific portions of an object but also their visibility, ensuring that less important regions do not occlude more important ones. Cutaway views completely remove occluding, unimportant structures—possibly also removing valuable context information—while existing solutions for smooth reduction of occlusion based on importance lack precise visibility control, simplicity and generality. We introduce a new front-to-back fragment composition equation that directly takes into account a measure of sample importance and allows smooth and precise importance-based visibility control. We demonstrate the generality of our composition equation with several illustrative effects, which were obtained by using a set of importance measures calculated on the fly or defined by the user. The presented composition method is suitable for direct volume rendering as well as rendering of layered 3D models. We discuss both cases and show examples, though focusing mainly on illustration of volumetric data.     

Linear-Time Recognition of Helly Circular-Arc Models and Graphs

A circular-arc model ℳ is a circle C together with a collection A\mathcal{A} of arcs of C. If A\mathcal{A} satisfies the Helly Property then ℳ is a Helly circular-arc model. A (Helly) circular-arc graph is the intersection graph of a (Helly) circular-arc model. Circular-arc graphs and their subclasses have been the object of a great deal of attention in the literature. Linear-time recognition algorithms have been described both for the general class and for some of its subclasses. However, for Helly circular-arc graphs, the best recognition algorithm is that by Gavril, whose complexity is O(n ³). In this article, we describe different characterizations for Helly circular-arc graphs, including a characterization by forbidden induced subgraphs for the class. The characterizations lead to a linear-time recognition algorithm for recognizing graphs of this class. The algorithm also produces certificates for a negative answer, by exhibiting a forbidden subgraph of it, within this same bound.     

Product selection for promotion planning

This paper addresses a very important question—how to select the right products to promote in order to maximize promotional benefit. We set up a framework to incorporate promotion decisions into the data-mining process, formulate the profit maximization problem as an optimization problem, and propose a heuristic search solution to discover the right products to promote. Moreover, we are able to get access to real supermarket data and apply our solution to help achieve higher profits. Our experimental results on both synthetic data and real supermarket data demonstrate that our framework and method are highly effective and can potentially bring huge profit gains to a marketing campaign.     

Theories of initial segments of standard models of arithmetics and their complete extensions

We investigate families of finite initial segments of standard models for various arithmetics. We give an axiomatization of the theory of sentences true in almost all finite models with addition. We also characterize its complete extensions and relate its infinite models to models of Presburger arithmetic.We also estimate the complexity of complete extensions of the arithmetic with addition and multiplication.     

Parameterized complexity of coloring problems: Treewidth versus vertex cover

We compare the fixed parameter complexity of various variants of coloring problems (including List Coloring, Precoloring Extension, Equitable Coloring, L(p,1)-Labeling and Channel Assignment) when parameterized by treewidth and by vertex cover number. In most (but not all) cases we conclude that parametrization by the vertex cover number provides a significant drop in the complexity of the problems.     

NC图形验证与仿真技术的研究概况

数控程序图形验证与仿真技术的研究对保证加工质量提高加工效率具有重要意义,同时也是虚拟制造技术的主要研究内容之一,该文从国外NC几何验证、NC物理验证以及我国的NC图形验证三个方面对NC图形验证技术的发展概况作了较全面的论述,并指出其中存在的不足和尚待解决的问题。最后提出一种新的复杂曲面NC图形验证的体系结构。     

Convergence analysis of convex incremental neural networks

Recently, a convex incremental algorithm (CI-ELM) has been proposed in Huang and Chen (Neurocomputing 70:3056–3062, 2007), which randomly chooses hidden neurons and then analytically determines the output weights connecting with the hidden layer and the output layer. Though hidden neurons are generated randomly, the network constructed by CI-ELM is still based on the principle of universal approximation. The random approximation theory breaks through the limitation of most conventional theories, eliminating the need for tuning hidden neurons. However, due to the random characteristic, some of the neurons contribute little to decrease the residual error, which eventually increase the complexity and computation of neural networks. Thus, CI-ELM cannot precisely give out its convergence rate. Based on Lee’s results (Lee et al., IEEE Trans Inf Theory 42(6):2118–2132, 1996), we first show the convergence rate of a maximum CI-ELM, and then systematically analyze the convergence rate of an enhanced CI-ELM. Different from CI-ELM, the hidden neurons of the two algorithms are chosen by following the maximum or optimality principle under the same structure as CI-ELM. Further, the proof process also demonstrates that our algorithms achieve smaller residual errors than CI-ELM. Since the proposed neural networks remove these “useless” neurons, they improve the efficiency of neural networks. The experimental results on benchmark regression problems will support our conclusions. The work is under the funding of Singapore MOE AcRF Tier 1 grant WBS No: R 252-000-221-112.     

An adaptive learning approach for 3-D surface reconstruction from point clouds.

In this paper, we propose a multiresolution approach for surface reconstruction from clouds of unorganized points representing an object surface in 3-D space. The proposed method uses a set of mesh operators and simple rules for selective mesh refinement, with a strategy based on Kohonen's self-organizing map (SOM). Basically, a self-adaptive scheme is used for iteratively moving vertices of an initial simple mesh in the direction of the set of points, ideally the object boundary. Successive refinement and motion of vertices are applied leading to a more detailed surface, in a multiresolution, iterative scheme. Reconstruction was experimented on with several point sets, including different shapes and sizes. Results show generated meshes very close to object final shapes. We include measures of performance and discuss robustness.