13354529
Edge-pancyclicity of coupled graphs
The coupled graph c(G) of a plane graph G is the graph defined on the vertex set V(G)∪F(G) so that two vertices in c(G) are joined by an edge if and only if they are adjacent or incident in G. We prove that the coupled graph of a 2-connected plane graph is edge-pancyclic. However, there exists a 2-edge-connected plane graph G such that c(G) is not Hamiltonian.
41406916
A bound for multicolor Ramsey numbers
Abstract The Ramsey number R(G 1 , G 2 , …, G n ) is the smallest integer p such that for any n -edge coloring (E 1 ,E 2 , …, E n ) of K p , K p [E i ] contains G i for some i , G i as a subgraph in K p [E i ] . Let R(m 1 ,m 2 , …, m n )≔R(K m 1 ,K m 2 , …, K m n ),R(m;n)≔R(m 1 ,m 2 ,…,m n ) if m i =m for i=1, 2,…,n . A formula is obtained for R(G 1 ,G 2 , …, G n ) .
15445426
An Ore-type Condition for Cyclability
A graph G is said to be cyclable if for each orientation D of G, there exists a set S(D) ?V(G) such that reversing all the arcs with one end in S results in a Hamiltonian digraph. Let G be a simple graph of even ordern? 8. In this paper, we show that if the degree sum of any two nonadjacent vertices is not less thann+ 1, then G is cyclable and the lower bound is sharp.
45980557
A new idea for Hamiltonian problem
6176366
The Ramsey numbers of stars versus wheels
For two given graphs G 1 and G 2 , the Ramsey number R(G 1 , G 2 ) is the smallest positive integer n such that for any graph G of order n, either G contains G 1 or the complement of G contains G 2 . Let S n denote a star of order n and W m a wheel of order m + 1. This paper shows that R(S n , W 6 )=2n + 1 for n ≥ 3 and R(S n , W m )=3n - 2 for m odd and n ≥ m - 1 ≥ 2.
27951187
The Ramsey numbers of trees versus W6 or W7
Let Tn denote a tree of order n and Wm a wheel of order m + 1. In this paper, we show the Ramsey numbers R(Tn, W6) = 2n - 1 + µ for n ≥ 5, where µ = 2 if Tn = Sn, µ = 1 if Tn = Sn(1, 1) or Tn = Sn(1, 2) and n ≡ 0 (mod 3), and µ = 0 otherwise; R(Tn, W7) = 3n - 2 for n ≥ 6.
901722
Dynamic programming algorithms for haplotype block partitioning: applications to human chromosome 21 haplotype data
Recent studies have shown that the human genome has a haplotype block structure such that it can be divided into discrete blocks of limited haplotype diversity. Patil et al. [6] and Zhang et al. [12] developed algorithms to partition haplotypes into blocks with minimum number of tag SNPs for the entire chromosome. However, it is not clear how to partition haplotypes into blocks with restricted number of SNPs when only limited resources are available. In this paper, we first formulated this problem as finding a block partition with a fixed number of tag SNPs that can cover the maximal percentage of a genome. Then we solved it by two dynamic programming algorithms, which are fairly flexible to take into account the knowledge of functional polymorphism. We applied our algorithms to the published SNP data of human chromosome 21 combining with the functional information of these SNPs and demonstrated the effectiveness of them. Statistical investigation of the relationship between the starting points of a block partition and the coding and non-coding regions illuminated that the SNPs at these starting points are not significantly enriched in coding regions. We also developed an efficient algorithm to find all possible long local maximal haplotypes across a subset of samples. After applying this algorithm to the human chromosome 21 haplotype data, we found that samples with long local haplotypes are not necessarily globally similar.
16277587
On Detection of Anomalous Routing Dynamics in BGP
BGP, the de facto inter-domain routing protocol, is the core component of current Internet infrastructure. BGP traffic deserves thorough exploration, since abnormal BGP routing dynamics could impair global Internet connectivity and stability. In this paper, two methods, signature-based detection and statistics-based detection, are designed and implemented to detect BGP anomalous routing dynamics in BGP UPDATEs. Signature-based detection utilizes a set of fixed patterns to search and identify routing anomalies. For the statistics-based detection, we devise five measures to model BGP UPDATEs traffic. In the training phase, the detector is trained to learn the expected behaviors of BGP from the historical long-term BGP UPDATEs dataset. It then examines the test dataset to detect “anomalies” in the testing phase. An anomaly is flagged when the tested behavior significantly differs from the expected behaviors. We have applied these two approaches to examine the BGP data collected by RIPE-NCC servers for a number of IP prefixes. Through manual analysis, we specify possible causes of some detected anomalies. Finally, comparing the two approaches, we highlight the advantages and limitations of each. While our evaluation is still preliminary, we have demonstrated that, by combining both signature-based and statistics-based anomaly detection approaches, our system can effectively and accurately identify certain BGP events that are worthy of further investigation.
31567164
Prediction of protein function using protein-protein interaction data
Assigning functions to novel proteins is one of the most important problems in the post-genomic era. We develop a novel approach that applies the theory of Markov random fields to infer a protein's functions using protein-protein interaction data and the functional annotations of its interaction protein partners. For each function of interest and a protein, we predict the probability that the protein has that function using Bayesian approaches. Unlike in other available approaches for protein annotation where a protein has or does not have a function of interest, we give a probability for having the function. This probability indicates how confident we are about the prediction. We apply our method to predict cellular functions (43 categories including a category "others") for yeast proteins defined in the Yeast Proteome Database, using the protein-protein interaction data from the Munich Information Center for Protein Sequences. We show that our approach outperforms other available methods for function prediction based on protein interaction data.
29387350
Efficient and robust feature extraction by maximum margin criterion
In pattern recognition, feature extraction techniques are widely employed to reduce the dimensionality of data and to enhance the discriminatory information. Principal component analysis (PCA) and linear discriminant analysis (LDA) are the two most popular linear dimensionality reduction methods. However, PCA is not very effective for the extraction of the most discriminant features, and LDA is not stable due to the small sample size problem . In this paper, we propose some new (linear and nonlinear) feature extractors based on maximum margin criterion (MMC). Geometrically, feature extractors based on MMC maximize the (average) margin between classes after dimensionality reduction. It is shown that MMC can represent class separability better than PCA. As a connection to LDA, we may also derive LDA from MMC by incorporating some constraints. By using some other constraints, we establish a new linear feature extractor that does not suffer from the small sample size problem, which is known to cause serious stability problems for LDA. The kernelized (nonlinear) counterpart of this linear feature extractor is also established in the paper. Our extensive experiments demonstrate that the new feature extractors are effective, stable, and efficient.
52799334
On the Editing Distance Between Undirected Acyclic Graphs
We consider the problem of comparing CUAL graphs (Connected, Undirected, Acyclic graphs with nodes being Labeled). This problem is motivated by the study of information retrieval for bio-chemical and molecular databases. Suppose we define the distance between two CUAL graphs G1 and G2 to be the weighted number of edit operations (insert node, delete node and relabel node) to transform G1 to G2. By reduction from exact cover by 3-sets, one can show that finding the distance between two CUAL graphs is NP-complete. In view of the hardness of the problem, we propose a constrained distance metric, called the degree-2 distance, by requiring that any node to be inserted (deleted) have no more than 2 neighbors. With this metric, we present an efficient algorithm to solve the problem. The algorithm runs in time O(N1N2D2) for general weighting edit operations and in time for integral weighting edit operations, where Ni, i=1, 2, is the number of nodes in Gi, D=min{d1, d2} and di is the maximum degree of Gi.