The migrative functional equations provide a very powerful tool for constructing and characterizing new fuzzy logic connectives by convex combination, and have particularly important applications in image processing. So far, the migrativity between conjunctive logic connectives has been extensively studied, the obtained results do not, however, work well for triangular conorms. This paper is devoted to an in-depth investigation on three types of migrativity for continuous triangular conorms S with respect to N -ordinal sum implications I , which have distinctive features from ordinary ordinal sum implications. We will provide first detailed characterizations on the ( α , I ) -migrativity of S for each case according to the position relation of α in the range of N , by giving the corresponding ordinal sum decompositions of the t-conorm and implication solutions. Then the ( α , I ) -migrativity is extended to internal and global cases, and their characterizations are given under some additional constraints.

Motif discovery in sequence data is fundamental to many biological problems such as antibody biomarker identification. Recent advances in instrumental techniques make it possible to generate thousands of protein sequences at once, which raises a big data issue for the existing motif finding algorithms: They either work only in a small scale of several hundred sequences or have to trade accuracy for efficiency. In this work, we demonstrate that by intelligently clustering sequences, it is possible to significantly improve the scalability of all the existing motif finding algorithms without losing accuracy at all. An anchor based sequence clustering algorithm (ASC) is thus proposed to divide a sequence dataset into multiple smaller clusters so that sequences sharing the same motif will be located into the same cluster. Then an existing motif finding algorithm can be applied to each individual cluster to generate motifs. In the end, the results from multiple clusters are merged together as final output. Experimental results show that our approach is generic and orders of magnitude faster than traditional motif finding algorithms. It can discover motifs from protein sequences in the scale that no existing algorithm can handle. In particular, ASC reduces the running time of a very popular motif finding algorithm, MEME, from weeks to a few minutes with even better accuracy.