Lower Bounds for Shoreline Searching With 2 or More Robots

Searching for a line on the plane with $n$ unit speed robots is a classic online problem that dates back to the 50's, and for which competitive ratio upper bounds are known for every $n\geq 1$. In this work we improve the best lower bound known for $n=2$ robots from 1.5993 to 3. Moreover we prove that the competitive ratio is at least $\sqrt{3}$ for $n=3$ robots, and at least $1/\cos(\pi/n)$ for $n\geq 4$ robots. Our lower bounds match the best upper bounds known for $n\geq 4$, hence resolving these cases. To the best of our knowledge, these are the first lower bounds proven for the cases $n\geq 3$ of this several decades old problem.Comment: This is an updated version of the paper with the same title which will appear in the proceedings of the 23rd International Conference on Principles of Distributed Systems (OPODIS 2019) Neuchatel, Switzerland, July 17-19, 201

A novel glucagon-related peptide (GCRP) and its receptor GCRPR account for coevolution of their family members in vertebrates

The glucagon (GCG) peptide family consists of GCG, glucagon-like peptide 1 (GLP1), and GLP2, which are derived from a common GCG precursor, and the glucose-dependent insulinotropic polypeptide (GIP). These peptides interact with cognate receptors, GCGR, GLP1R, GLP2R, and GIPR, which belong to the secretin-like G protein-coupled receptor (GPCR) family. We used bioinformatics to identify genes encoding a novel GCG-related peptide (GCRP) and its cognate receptor, GCRPR. The GCRP and GCRPR genes were found in representative tetrapod taxa such as anole lizard, chicken, and Xenopus, and in teleosts including medaka, fugu, tetraodon, and stickleback. However, they were not present in mammals and zebrafish. Phylogenetic and genome synteny analyses showed that GCRP emerged through two rounds of whole genome duplication (2R) during early vertebrate evolution. GCRPR appears to have arisen by local tandem gene duplications from a common ancestor of GCRPR, GCGR, and GLP2R after 2R. Biochemical ligand-receptor interaction analyses revealed that GCRP had the highest affinity for GCRPR in comparison to other GCGR family members. Stimulation of chicken, Xenopus, and medaka GCRPRs activated Gαs-mediated signaling. In contrast to chicken and Xenopus GCRPRs, medaka GCRPR also induced Gαq/11-mediated signaling. Chimeric peptides and receptors showed that the K(16)M(17)K(18) and G(16)Q(17)A(18) motifs in GCRP and GLP1, respectively, may at least in part contribute to specific recognition of their cognate receptors through interaction with the receptor core domain. In conclusion, we present novel data demonstrating that GCRP and GCRPR evolved through gene/genome duplications followed by specific modifications that conferred selective recognition to this ligand-receptor pair

A novel glucagon-related peptide (GCRP) and its receptor GCRPR account for coevolution of their family members in vertebrates

The glucagon (GCG) peptide family consists of GCG, glucagon-like peptide 1 (GLP1), and GLP2, which are derived from a common GCG precursor, and the glucose-dependent insulinotropic polypeptide (GIP). These peptides interact with cognate receptors, GCGR, GLP1R, GLP2R, and GIPR, which belong to the secretin-like G protein-coupled receptor (GPCR) family. We used bioinformatics to identify genes encoding a novel GCG-related peptide (GCRP) and its cognate receptor, GCRPR. The GCRP and GCRPR genes were found in representative tetrapod taxa such as anole lizard, chicken, and Xenopus, and in teleosts including medaka, fugu, tetraodon, and stickleback. However, they were not present in mammals and zebrafish. Phylogenetic and genome synteny analyses showed that GCRP emerged through two rounds of whole genome duplication (2R) during early vertebrate evolution. GCRPR appears to have arisen by local tandem gene duplications from a common ancestor of GCRPR, GCGR, and GLP2R after 2R. Biochemical ligand-receptor interaction analyses revealed that GCRP had the highest affinity for GCRPR in comparison to other GCGR family members. Stimulation of chicken, Xenopus, and medaka GCRPRs activated Gαs-mediated signaling. In contrast to chicken and Xenopus GCRPRs, medaka GCRPR also induced Gαq/11-mediated signaling. Chimeric peptides and receptors showed that the K(16)M(17)K(18) and G(16)Q(17)A(18) motifs in GCRP and GLP1, respectively, may at least in part contribute to specific recognition of their cognate receptors through interaction with the receptor core domain. In conclusion, we present novel data demonstrating that GCRP and GCRPR evolved through gene/genome duplications followed by specific modifications that conferred selective recognition to this ligand-receptor pair