30370540
On (d, 2)-dominating numbers of binary undirected de Bruijn graphs
Abstract In this paper, we show that: (i) For n-dimensional undirected binary de Bruijn graphs, UB(n), n⩾4, there is a vertex x=x 1 x 1 x 1 ⋯ x 1 x 1 (x1=1 or 0) such that for any other vertex t there exist at least two internally disjoint paths of length at most n−1 between x and t in UB(n), i.e., the (n−1,2)-dominating number of UB(n) is equal to one. (ii) For n⩾5, let S={100⋯01,011⋯10}. For any other vertex t there exist at least two internally disjoint paths of length at most n−2 between t and S in UB(n), i.e., the (n−2,2)-dominating number of UB(n) is no more than 2.
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.
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 ) .
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.
29686713
A note on Ramsey numbers with two parameters
The Ramsey number R(G1, G2) is the smallest integer p such that for any graph G on p vertices either G contains G1 or G- contains G2, where G- denotes the complement of G. In this paper, some new bounds with two parameters for the Ramsey number R(G1, G2), under some assumptions, are obtained. Especially, we prove that R(K6 - e, K6) ≤ 116 and R(K6 - e, K7) ≤ 202, these improve the two upper bounds for the classical Ramsey number in [S.P. Radziszowski, Small Ramsey number, Electron. J. Combin. DSI (2002) 1-36].
14716028
New Upper Bounds for Ramsey Numbers
The Ramsey numberR(G1,G2) is the smallest integerpsuch that for any graphGonpvertices eitherGcontainsG1orGcontainsG2, whereGdenotes the complement ofG. LetR(m,n)=R(Km,Kn). Some new upper bound formulas are obtained forR(G1,G2andR(m,n), and we derive some new upper bounds for Ramsey numbers here.
1201195
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. Several approaches have been applied to this problem, including analyzing gene expression patterns, phylogenetic profiles, protein fusions and protein-protein interactions. 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 (YPD), using the protein-protein interaction data from the Munich Information Center for Protein Sequences (MIPS, http://mips.gsf.de). We show that our approach outperforms other available methods for function prediction based on protein interaction data.
6145819
HapBlock: haplotype block partitioning and tag SNP selection software using a set of dynamic programming algorithms
UNLABELLED
Recent studies have revealed that linkage disequilibrium (LD) patterns vary across the human genome with some regions of high LD interspersed with regions of low LD. Such LD patterns make it possible to select a set of single nucleotide polymorphism (SNPs; tag SNPs) for genome-wide association studies. We have developed a suite of computer programs to analyze the block-like LD patterns and to select the corresponding tag SNPs. Compared to other programs for haplotype block partitioning and tag SNP selection, our program has several notable features. First, the dynamic programming algorithms implemented are guaranteed to find the block partition with minimum number of tag SNPs for the given criteria of blocks and tag SNPs. Second, both haplotype data and genotype data from unrelated individuals and/or from general pedigrees can be analyzed. Third, several existing measures/criteria for haplotype block partitioning and tag SNP selection have been implemented in the program. Finally, the programs provide flexibility to include specific SNPs (e.g. non-synonymous SNPs) as tag SNPs.


AVAILABILITY
The HapBlock program and its supplemental documents can be downloaded from the website http://www.cmb.usc.edu/~msms/HapBlock.
17536436
Combining visual and automated data mining for near-real-time anomaly detection and analysis in BGP
The security of Internet routing is a major concern because attacks and errors can result in data packets not reaching their intended destination and/or falling into the wrong hands. A key step in improving routing security is to analyze and understand it. In the past, we and other researchers have presented various visual-based, statistical-based, and signature-based methods of analyzing Internet routing data.
 In this paper, we describe an integration of visual and automated data mining methods for discovering and investigating anomalies in Internet routing. We show how these different components are combined in such a way as to complement each other, creating a very effective and useful analysis tool. In addition to performing analysis on archived data, our system is able to collect, process and visualize data in near-real-time.
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.
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.