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This correspondence describes extensions to the k-modes algorithm for clustering categorical data. By modifying a simple matching dissimilarity measure for categorical objects, a heuristic approach was developed in [4], [12] which allows the use of the k-modes paradigm to obtain a cluster with strong intrasimilarity and to efficiently cluster large categorical data sets. The main aim of this paper is to rigorously derive the updating formula of the k-modes clustering algorithm with the new dissimilarity measure and the convergence of the algorithm under the optimization framework.

Semi-mangroves form a group of transitional species between glycophytes and halophytes, and hold unique potential for learning molecular mechanisms underlying plant salt tolerance. Millettia pinnata is a semi-mangrove plant that can survive a wide range of saline conditions in the absence of specialized morphological and physiological traits. By employing the Illumina sequencing platform, we generated ∼192 million short reads from four cDNA libraries of M. pinnata and processed them into 108 598 unisequences with a high depth of coverage. The mean length and total length of these unisequences were 606 bp and 65.8 Mb, respectively. A total of 54 596 (50.3%) unisequences were assigned Nr annotations. Functional classification revealed the involvement of unisequences in various biological processes related to metabolism and environmental adaptation. We identified 23 815 candidate salt-responsive genes with significantly differential expression under seawater and freshwater treatments. Based on the reverse transcription–polymerase chain reaction (RT–PCR) and real-time PCR analyses, we verified the changes in expression levels for a number of candidate genes. The functional enrichment analyses for the candidate genes showed tissue-specific patterns of transcriptome remodelling upon salt stress in the roots and the leaves. The transcriptome of M. pinnata will provide valuable gene resources for future application in crop improvement. In addition, this study sets a good example for large-scale identification of salt-responsive genes in non-model organisms using the sequencing-based approach.

Genomic regions that are unusually divergent between closely related species or racial groups can be particularly informative about the process of speciation or the operation of natural selection. The two sequenced genomes of cultivated Asian rice, Oryza sativa, reveal that at least 6% of the genomes are unusually divergent. Sequencing of ten unlinked loci from the highly divergent regions consistently identified two highly divergent haplotypes with each locus in nearly complete linkage disequilibrium among 25 O. sativa cultivars and 35 lines from six wild species. The existence of two highly divergent haplotypes in high divergence regions in species from all geographical areas (Africa, Asia, and Oceania) was in contrast to the low polymorphism and low linkage disequilibrium that were observed in other parts of the genome, represented by ten reference loci. While several natural processes are likely to contribute to this pattern of genomic variation, domestication may have greatly exaggerated the trend. In this hypothesis, divergent haplotypes that were adapted to different geographical and ecological environments migrated along with humans during the development of domesticated varieties. If true, these high divergence regions of the genome would be enriched for loci that contribute to the enormous range of phenotypic variation observed among domesticated breeds.

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