On spanning trees and walks of low maximum degree

title: Coloring edges of graphs embedded in a surface of characteristic zero
abstract: Consider graphs that are embeddable in a surface of characteristic zero. Class two graphs of this type with maximum degree Δ ≤ 6 are known to exist. Hind and Zhao showed that such graphs with maximum degree Δ ge; 8 must be class one. This article shows that such graphs with maximum degree Δ = 7 also must be class one, completing the analysis of these surfaces. These are the first surfaces where the maximum degree of class two graphs has been determined.

title: Optimal Spectrum Management in Multiuser Interference Channels
abstract: In this paper, we study the problem of continuous frequency optimal spectrum management in multiuser frequency selective interference channels. We assume that interference is treated as noise by the decoders, and separate encoding is applied. First, a simple pair-wise channel condition for frequency division multiple access schemes to achieve all Pareto optimal points of the rate region is derived. It enables fully distributed global optimal decision making on whether any two users should use orthogonal channels. Next, we present an analytical solution to finding the maximum sum-rate in two-user symmetric frequency flat channels. Generalizing this solution to frequency selective channels, a convex optimization is established that yields the global optimum. Finally, we show that our method generalizes to K-user (K ≥ 2) weighted sum-rate maximization in asymmetric frequency selective channels, and we transform this classic nonconvex optimization to an equivalent convex optimization in the primal domain.

title: Design of a real-time interactive tele-exercise classroom for computer exercises over a Gigabit Network
abstract: This paper proposes a tele-exercise classroom for computer exercises over the Japan Gigabit Network. The requirements for constructing the tele-exercise classroom be discussed. The main features of the classroom are (1) a teacher can monitor a strident's operations, (2) give instructions to the student, (3) show a demonstration to the student. Besides, exercise materials and/or problems happening during the exercise class can be presented by using a synchronous/asynchronous white board, and discussions between the teacher and a student (students) can be carried out through interactive real-time video/audio. We present a systems model which shows the configuration of the system, user computer terminal types, system modes, and action modes. In addition, the extendibility of the system is considered in the model.

title: Silicon Wafer Defect Extraction Based on Morphological Filter and Watershed Algorithm
abstract: Defect extraction techniques are studied regarding the silicon wafer surface defect. We design a new filter based on multiple structuring elements and suggest an improved marker-based and region merging watershed. To begin with, the filter which generalized close-opening and open-closing filter based on the morphological filter with multiple structuring elements is introduced to eliminate the noise and simplify the image and morphological gradient image while preserving the details. And then in order to reduce the over-segmentation of the watershed algorithm, this paper suggests an improved marker-based and region merging method, region average gray value and edge strength criterion is used in merging operation and has a good effect on segmentation. Finally, the improved watershed algorithm is applied to the filtered gradient image to get the defect contours. The experiments show that this method can eliminate the noises and extract accurately location and closed region contours, which lays a good foundation for defect feature extraction and selection.

title: A Neighborhood-Based Clustering Algorithm
abstract: In this paper, we present a new clustering algorithm, NBC, i.e., Neighborhood Based Clustering, which discovers clusters based on the neighborhood characteristics of data. The NBC algorithm has the following advantages: (1) NBC is effective in discovering clusters of arbitrary shape and different densities; (2) NBC needs fewer input parameters than the existing clustering algorithms; (3) NBC can cluster both large and high-dimensional databases efficiently.

title: Evolving Model for Small-World Network Based on Benefit Choice
abstract: Based on reviewing the research progress of evolving model for small-world network, the defects of present studies were pointed out. Taking a square grid as the basis, an evolving model for small-world network based on benefit choice was built. This model is different from other papers in which limitation of vector' degree was considered. Then, the author proposed a simulation scheme and compared the network generated by simulation with a same scale random network. The results show that this network has small-world characteristic. Finally, several directions were given.