The domination number and the least QQ-eigenvalue

A vertex set $D$ of a graph $G$ is said to be a dominating set if every vertex of $V(G)\setminus D$ is adjacent to at least a vertex in $D$, and the domination number $\gamma(G)$ ($\gamma$, for short) is the minimum cardinality of all dominating sets of $G$. For a graph, the least $Q$-eigenvalue is the least eigenvalue of its signless Laplacian matrix. In this paper, for a nonbipartite graph with both order $n$ and domination number $\gamma$, we show that $n\geq 3\gamma-1$, and show that it contains a unicyclic spanning subgraph with the same domination number $\gamma$. By investigating the relation between the domination number and the least $Q$-eigenvalue of a graph, we minimize the least $Q$-eigenvalue among all the nonbipartite graphs with given domination number.Comment: 13 pages, 3 figure

Dual KS: Defining Gene Sets with Tissue Set Enrichment Analysis

Background: Gene set enrichment analysis (GSEA) is an analytic approach which simultaneously reduces the dimensionality of microarray data and enables ready inference of the biological meaning of observed gene expression patterns. Here we invert the GSEA process to identify class-specific gene signatures. Because our approach uses the Kolmogorov-Smirnov approach both to define class specific signatures and to classify samples using those signatures, we have termed this methodology “Dual-KS” (DKS). Results: The optimum gene signature identified by the DKS algorithm was smaller than other methods to which it was compared in 5 out of 10 datasets. The estimated error rate of DKS using the optimum gene signature was smaller than the estimated error rate of the random forest method in 4 out of the 10 datasets, and was equivalent in two additional datasets. DKS performance relative to other benchmarked algorithms was similar to its performance relative to random forests. Conclusions: DKS is an efficient analytic methodology that can identify highly parsimonious gene signatures useful for classification in the context of microarray studies. The algorithm is available as the dualKS package for R as part of the bioconductor project

Genomic epidemiology of Vibrio cholerae reveals the regional and global spread of two epidemic non-toxigenic lineages

Non-toxigenic Vibrio cholerae isolates have been found associated with diarrheal disease globally, however, the global picture of non-toxigenic infections is largely unknown. Among non-toxigenic V. cholerae, ctxAB negative, tcpA positive (CNTP) isolates have the highest risk of disease. From 2001 to 2012, 71 infectious diarrhea cases were reported in Hangzhou, China, caused by CNTP serogroup O1 isolates. We sequenced 119 V. cholerae genomes isolated from patients, carriers and the environment in Hangzhou between 2001 and 2012, and compared them with 850 publicly available global isolates. We found that CNTP isolates from Hangzhou belonged to two distinctive lineages, named L3b and L9. Both lineages caused disease over a long time period with usually mild or moderate clinical symptoms. Within Hangzhou, the spread route of the L3b lineage was apparently from rural to urban areas, with aquatic food products being the most likely medium. Both lineages had been previously reported as causing local endemic disease in Latin America, but here we show that global spread of them has occurred, with the most likely origin of L3b lineage being in Central Asia. The L3b lineage has spread to China on at least three occasions. Other spread events, including from China to Thailand and to Latin America were also observed. We fill the missing links in the global spread of the two non-toxigenic serogroup O1 V. cholerae lineages that can cause human infection. The results are important for the design of future disease control strategies: surveillance of V. cholerae should not be limited to ctxAB positive strains

Strings And Colorings Of Topological Coding Towards Asymmetric Topology Cryptography

We, for anti-quantum computing, will discuss various number-based strings, such as number-based super-strings, parameterized strings, set-based strings, graph-based strings, integer-partitioned and integer-decomposed strings, Hanzi-based strings, as well as algebraic operations based on number-based strings. Moreover, we introduce number-based string-colorings, magic-constraint colorings, and vector-colorings and set-colorings related with strings. For the technique of encrypting the entire network at once, we propose graphic lattices related with number-based strings, Hanzi-graphic lattices, string groups, all-tree-graphic lattices. We study some topics of asymmetric topology cryptography, such as topological signatures, Key-pair graphs, Key-pair strings, one-encryption one-time and self-certification algorithms. Part of topological techniques and algorithms introduced here are closely related with NP-complete problems or NP-hard problems.Comment: Asymmetric topology encryption is a new topic of topological coding towards the certificateless public key cryptograph