46668538
Finding the exact bound of the maximum degrees of class two graphs embeddable in a surface of characteristic epsilon in {-1, -2, -3}
In this paper, we consider the problem of determining the maximum of the set of maximum degrees of class two graphs that can be embedded in a surface. For each surface @S, we define @D(@S)=max{@D(G)|G is a class two graph of maximum degree @D that can be embedded in @S}. Hence Vizing's Planar Graph Conjecture can be restated as @D(@S)=5 if @S is a plane. We show that @D(@S)=7 if @e(@S)=-1 and @D(@S)=8 if @e(@S)@?{-2,-3}.
27555066
On the Edge Reconstruction of Graphs Embedded in Surfaces, III,
In this paper, we prove that if a connected graphGembeddable in a surface?of characteristic?(?) satisfies (1) the minimum degree ofG?5, (2) |V(G)|??43?(?), thenGis edge reconstructible. A direct consequence of the above result is that a triangulationGof a surface of characteristic?(?) is edge reconstructible if |V(G)|??43?(?).
38637293
On spanning trees and walks of low maximum degree
41806675
On Diagonally 10-Coloring Plane Triangulations
This article shows that the vertices of a plane triangulation may be colored with 10 colors such that every pair of vertices has different colors if they are either adjacent or diagonal, that is, that they are not adjacent but are adjacent to two faces which share an edge. This improves a result of Borodin, who showed that 11 colors were sufficient. © 1996 John Wiley & Sons, Inc.
22657577
On cyclic colorings and their generalizations
Abstract A cyclic coloring is a vertex coloring such that vertices in a face receive different colors. Let Δ be the maximum face degree of a graph. This article shows that plane graphs have cyclic 9 5 Δ -colorings, improving results of Ore and Plummer, and of Borodin. The result is mainly a corollary of a best-possible upper bound on the minimum cyclic degree of a vertex of a plane graph in terms of its maximum face degree. The proof also yields results on the projective plane, as well as for d-diagonal colorings. Also, it is shown that plane graphs with Δ=5 have cyclic 8-colorings. This result and also the 9 5 Δ result are not necessarily best possible.
6315714
On the edge-reconstruction of graphs embedded in surfaces IV
In this paper, by applying the discharging method, we give simple proofs that (1) every n-vertex graph with minimum degree at least 3 and girth at least 5 that is embeddable in a surface Σ of Euler characteristic at least -n/8 is edge-reconstructible, and (2) every n-vertex graph with minimum degree at least 4 that is embeddable without faces of length at most 3 in a surface Σ of Euler characteristic at least -n/6 is edge-reconstructible.
5668902
Optimal Spectrum Management in Multiuser Interference Channels
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.
46304006
Identification of Multi-dimensional System based on a Novel Criterion
A device uses two laser beams to assist in parking a vehicle having a windshield at a desired distance relative to a surface forward of the vehicle, such as the wall of a garage. Independent adjustment means are preferably provided for angling one or both of the first and second beams so as to converge in a localized region of the surface forward of the vehicle when the vehicle is positioned at a desired distance. The preferred embodiment further includes means for mounting the device to a visor within the vehicle, such that the first and second beams pass through the windshield. A momentary contact button on a bottom panel of the enclosure may then be used to activate the laser by squeezing the device against the visor, if so mounted. Within the enclosure there is supported a mirror, prism or other light re-directing element in the path of one of the first and second beams prior to exiting enclosure causing the two beams to converge in a localized region of the wall when the vehicle is parked at a desired distance therefrom. The mirror and beamsplitter are preferably disposed on independently adjustable mounts to assist in fixing the desired distance. As a further option, a dispersive optical element such as a lens may be disposed in the path of one of the first and second beams causing that beam to form a line on the surface forward of the vehicle. Method aspects of the invention are also disclosed.
27805594
Research on Query-by-Committee Method of Active Learning and Application
Active learning aims at reducing the number of training examples to be labeled by automatically processing the unlabeled examples, then selecting the most informative ones with respect to a given cost function for a human to label. The major problem is to find the best selection strategy function to quickly reach high classification accuracy. Query-by-Committee (QBC) method of active learning is less computation than other active learning approaches, but its classification accuracy can not achieve the same high as passive learning. In this paper, a new selection strategy for the QBC method is presented by combining Vote Entropy with Kullback-Leibler divergence. Experimental results show that the proposed algorithm is better than previous QBC approach in classification accuracy. It can reach the same accuracy as passive learning with few labeled training examples.
27085331
Design of a real-time interactive tele-exercise classroom for computer exercises over a Gigabit Network
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.
15396012
Silicon Wafer Defect Extraction Based on Morphological Filter and Watershed Algorithm
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.