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In this paper, we propose a fully autonomous density-based clustering algorithm named ‘Ocean’, which is inspired by the oceanic landscape and phenomena that occur in it. Ocean is an improvement over conventional algorithms regarding both distance metric and the clustering mechanism. Ocean defines the distance between two categories as the difference in the relative densities of categories. Unlike existing approaches, Ocean neither assigns the same distance to all pairs of categories, nor assigns arbitrary weights to matches and mismatches between categories that can lead to clustering errors. Ocean uses density ratios of adjacent regions in multidimensional space to detect the edges of the clusters. Ocean is robust against clusters of identical patterns. Unlike conventional approaches, Ocean neither makes any assumption regarding the data distribution within clusters, nor requires tuning of free parameters. Empirical evaluations demonstrate improved performance of Ocean over existing approaches.

An in silico study of mRNA secondary structure has found a bias within the coding sequences of genes that favors "in-frame" pairing of nucleotides. This pairing of codons, each with its reverse-complement, partitions the 20 amino acids into three subsets. The genetic code can therefore be represented by a three-component graph. The composition of proteins in terms of amino acid membership in the three subgroups has been measured, and sequence runs of members within the same subgroup have been analyzed using a runs statistic based on Z-scores. In a GENBANK database of over 416,000 protein sequences, the distribution of this runs-test statistic is negatively skewed. To assess whether this statistical bias was due to a chance grouping of the amino acids in the real genetic code, several alternate partitions of the genetic code were examined by permuting the assignment of amino acids to groups. A metric was constructed to define the difference, or "distance", between any two such partitions, and an exhaustive search was conducted among alternate partitions maximally distant from the natural partition of the genetic code, to select sets of partitions that were also maximally distant from one another. The statistical skewness of the runs statistic distribution for native protein sequences were significantly more negative under the natural partition than they were under all of the maximally different partition of codons, although for all partitions, including the natural one, the randomized sequences had quite similar skewness. Hence under the natural graph theory partition of the genetic code there is a preference for more protein sequences to contain fewer runs of amino acids, than they do under the other partitions, meaning that the average run must be longer under the natural partition. This suggests that a corresponding bias may exist in the coding sequences of the actual genes that code for these proteins.

In this paper, a new distance metric between interval-valued fuzzy sets is pro-posed. The four special interval-valued fuzzy metric spaces are studied, which are induced by four well-known interval-valued residual implication operations. It proved that the interval-valued fuzzy metric spaces induced by Łukasiewicz implication and Goguen implication are more suitable for interval-valued fuzzy reasoning. Moreover, based on these two interval-valued fuzzy metric spaces, we discuss the robustness of interval-valued fuzzy reasoning triple I methods.

A new distance metric between interval-valued fuzzy sets is proposed. And based on this metric, we analyze robustness of the interval-valued fuzzy reasoning algorithms based on two well-known interval-valued residual implication operations. It was proved that the interval-valued fuzzy reasoning algorithm based the Łukasiewicz interval-valued implication and Goguen interval-valued implication are robust.