Partial-Matching RMS Distance Under Translation: Combinatorics and Algorithms

We consider the problem of minimizing the RMS distance (sum of squared distances between pairs of points) under translation between two point sets A and B, in the plane, with (Formula presented.), in the partial-matching setup, in which each point in B is matched to a distinct point in A. Although the problem is not known to be polynomial, we establish several structural properties of the underlying subdivision (Formula presented.) of the plane and derive improved bounds on its complexity. Specifically, we show that this complexity is (Formula presented.), so it is only quadratic in |A|. These results lead to the best known algorithm for finding a translation for which the partial-matching RMS distance between the point sets is minimized. In addition, we show how to compute a local minimum of the partial-matching RMS distance under translation, in polynomial time. © 2017 Springer Science+Business Media New Yor

Galectin-3 Mediates Cross-Talk between K-Ras and Let-7c Tumor Suppressor microRNA

International audienceBACKGROUND: Galectin-3 (Gal-3) and active (GTP-bound) K-Ras contribute to the malignant phenotype of many human tumors by increasing the rate of cell proliferation, survival, and migration. These Gal-3-mediated effects result from a selective binding to K-Ras.GTP, causing increased nanoclustering in the cell membrane and leading to robust Ras signaling. Regulation of the interactions between Gal-3 and active K-Ras is not fully understood. METHODS AND FINDINGS: To gain a better understanding of what regulates the critical interactions between these two proteins, we examined the role of Gal-3 in the regulation of K-Ras by using Gal-3-knockout mouse embryonic-fibroblasts (Gal-3-/- MEFs) and/or Gal-3/Gal-1 double-knockout MEFs. We found that knockout of Gal-3 induced strong downregulation (∼60%) of K-Ras and K-Ras.GTP. The downregulation was somewhat more marked in the double-knockout MEFs, in which we also detected robust inhibition(∼50%) of ERK and Akt activation. These additional effects are probably attributable to inhibition of the weak interactions of K-Ras.GTP with Gal-1. Re-expression of Gal-3 reversed the phenotype of the Gal-3-/- MEFs and dramatically reduced the disappearance of K-Ras in the presence of cycloheximide to the levels seen in wild-type MEFs. Furthermore, phosphorylation of Gal-3 by casein kinase-1 (CK-1) induced translocation of Gal-3 from the nucleus to the cytoplasm and the plasma membrane, leading to K-Ras stabilization accompanied by downregulation of the tumor suppressor miRNA let-7c, known to negatively control K-Ras transcription. CONCLUSIONS: Our results suggest a novel cross-talk between Gal-3-mediated downregulation of let 7c microRNA (which in turn negatively regulates K-Ras transcription) and elucidates the association among Gal-3 let-7c and K-Ras transcription/translation, cellular compartmentalization and activity