19566771
Nowhere-Zero 4-Flows and Cayley Graphs on Solvable Groups
We prove that every Cayley graph on a finite solvable group admits a nowhere-zero 4-flow. In particular, every cubic Cayley graph on a solvable group is 3-edge-colorable.
17466332
Nowhere-zero 3-flows in products of graphs
A graph G is an odd-circuit tree if every block of G is an odd length circuit. It is proved in this paper that the product of every pair of graphs G and H admits a nowhere-zero 3-flow unless G is an odd-circuit tree and H has a bridge. This theorem is a partial result to the Tutte’s 3-flow conjecture and generalizes a result by Imrich and Skrekovski [7] that the product of two bipartite graphs admits a nowhere-zero 3-flow. A byproduct of this theorem is that every bridgeless Cayley graph G 1⁄4 Cayð ;SÞ on an abelian group with a minimal generating set S admits a nowhere-zero 3-flow except for odd prisms. 2005 Wiley Periodicals, Inc. J Graph Theory 50: 79–89, 2005
11462933
On flows in bidirected graphs
Bouchet conjectured that every bidirected graph which admits a nowhere-zero bidirected flow will admit a nowhere-zero bidirected 6-flow [A. Bouchet, Nowhere-zero integer flows on a bidirected graph, J. Combin. Theory Ser. B 34 (1983) 279-292]. He proved that this conjecture is true with 6 replaced by 216. Zyka proved in his Ph.D dissertation that it is true with 6 replaced by 30. Khelladi proved it is true with 6 replaced with 18 for 4-connected graphs [A. Khelladi, Nowhere-zero integer chains and flows in bidirected graphs, J. Combin. Theory Ser. B 43 (1987) 95-115]. In this paper, we prove that Bouchet's conjecture is true for 6-edge connected bidirected graphs.
13303898
Chords of longest circuits in 3-connected graphs
Thomassen conjectured that every longest circuit of a 3-connected graph has a chord. The conjecture is verified in this paper for projective planar graphs with minimum degree at least 4.
46565546
Arc-disjoint circuits in digraphs
80453
Chords of longest circuits in locally planar graphs
It was conjectured by Thomassen ([B. Alspach, C. Godsil, Cycle in graphs, Ann. Discrete Math. 27 (1985)], p. 466) that every longest circuit of a 3-connected graph must have a chord. This conjecture is verified for locally 4-connected planar graphs, that is, let N be the set of natural numbers; then there is a function h : N → N such that, for every 4-connected graph G embedded in a surface S with Euler genus g and face-width at least h(g), every longest circuit of G has a chord.
8628384
Fingerprint Indexing Based on LAS Registration
Fingerprint indexing is an efficient technique that greatly improves the performance of fingerprint based person authentication systems by reducing the number of comparison. In this paper, we propose an indexing method based on fingerprint registration with a novel feature called local axial symmetry (LAS). The location and direction estimation of reference point are achieved in a straightforward way after the LAS field is achieved. Then the registered orientation field is utilized as a feature vector to perform the following indexing. A new scheme of the experiment is introduced and satisfactory experimental results are achieved on FVC2000 DB2 that the average search space is only 2.34% of all fingers in the condition of equal-sized training set and testing set.
6853058
Markov chain correlation based clustering of gene expression data
An efficient Markov chain correlation based clustering method (MCC) has been proposed for clustering gene expression data. The gene expression data is first normalized and Markov chains (MC) are constructed from the dynamics of the gene expressions, in which the behavior of the genes at each step of the experiment can be taken into account. Based on the correlation of one-step Markov chain transition probabilities, an agglomerative method is employed to group the series that have similar behavior at each point. The proposed MCC clustering method has been applied to four gene expression datasets to obtain a number of clusters. The results show that the MCC method outperforms the commonly used K-means method and produces clusters that are more meaningful in terms of the similarity of the grouped genes. Another advantage of the proposed method over the existing clustering methods is that the knowledge of the group number is not required.
14923326
Co-histogram and Image Degradation Evaluation
The tool for image degradation evaluation addressed in this paper is called co-histogram, which is a statistic graph generated by counting the corresponding pixel pairs of two images. The graph is a two-dimensional joint probability distribution of the two images. A co-histogram shows how the pixels are distributed among combinations of two image pixel values. By means of co-histogram, we can have a visual understanding of PSNR, and the symmetry of a co-histogram is also significant for objective evaluation of image degradation. Our experiments with image degradation models of image compression, convolution blurring and geometric distortion perform the importance of the co-histogram.
10875476
Affinity relation discovery in image database clustering and content-based retrieval
In this paper, we propose a unified framework, called <i>Markov Model Mediator</i> (MMM), to facilitate image database clustering and to improve the query performance. The structure of the MMM framework consists of two hierarchical levels: local MMMs and integrated MMMs, which model the affinity relations among the images within a single image database and within a set of image databases, respectively, via an effective data mining process. The effectiveness and efficiency of the MMM framework for database clustering and image retrieval are demonstrated over a set of image databases which contain various numbers of images with different dimensions and concept categories.
12113641
Neighbor number, valley seeking and clustering
This paper proposes a novel nonparametric clustering algorithm capable of identifying shape-free clusters. This algorithm is based on a nonparametric estimation of the normalized density derivative (NDD) and the local convexity of the density distribution function, both of which are represented in a very concise form in terms of neighbor numbers. We use NDD to measure the dissimilarity between each pair of observations in a local neighborhood and to build a connectivity graph. Combined with the local convexity, this similarity measure can detect observations in local minima (valleys) of the density function, which separate observations in different major clusters. We demonstrate that this algorithm has a close relationship with the single-linkage hierarchical clustering and can be viewed as its extension. The performance of the algorithm is tested with both synthetic and real datasets. An example of color image segmentation is also given. Comparisons with several representative existing algorithms show that the proposed method can robustly identify major clusters even when there are complex configurations and/or large overlaps.