Eternal Domination in Grids

In the eternal domination game played on graphs, an attacker attacks a vertex at each turn and a team of guards must move a guard to the attacked vertex to defend it. The guards may only move to adjacent vertices on their turn. The goal is to determine the eternal domination number $\gamma^{\infty}_{all}$ of a graph which is the minimum number of guards required to defend against an infinite sequence of attacks.This paper continues the study of the eternal domination game on strong grids $P_n\boxtimes P_m$. Cartesian grids $P_n \square P_m$ have been vastly studied with tight bounds existing for small grids such as $k\times n$ grids for $k\in \{2,3,4,5\}$. It was recently proven that $\gamma^{\infty}_{all}(P_n \square P_m)=\gamma(P_n \square P_m)+O(n+m)$ where $\gamma(P_n \square P_m)$ is the domination number of $P_n \square P_m$ which lower bounds the eternal domination number [Lamprou et al., CIAC 2017]. We prove that, for all $n,m\in \mathbb{N^*}$ such that $m\geq n$, $\lfloor \frac{n}{3} \rfloor \lfloor \frac{m}{3} \rfloor+\Omega(n+m)=\gamma_{all}^{\infty} (P_{n}\boxtimes P_{m})=\lceil \frac{n}{3} \rceil \lceil \frac{m}{3} \rceil + O(m\sqrt{n})$ (note that $\lceil \frac{n}{3} \rceil \lceil \frac{m}{3} \rceil$ is the domination number of $P_n\boxtimes P_m$). Our technique may be applied to other ``grid-like" graphs

Comparison of Muscle Transcriptome between Pigs with Divergent Meat Quality Phenotypes Identifies Genes Related to Muscle Metabolism and Structure

Background: Meat quality depends on physiological processes taking place in muscle tissue, which could involve a large pattern of genes associated with both muscle structural and metabolic features. Understanding the biological phenomena underlying muscle phenotype at slaughter is necessary to uncover meat quality development. Therefore, a muscle transcriptome analysis was undertaken to compare gene expression profiles between two highly contrasted pig breeds, Large White (LW) and Basque (B), reared in two different housing systems themselves influencing meat quality. LW is the most predominant breed used in pig industry, which exhibits standard meat quality attributes. B is an indigenous breed with low lean meat and high fat contents, high meat quality characteristics, and is genetically distant from other European pig breeds. Methodology/Principal Findings: Transcriptome analysis undertaken using a custom 15 K microarray, highlighted 1233 genes differentially expressed between breeds (multiple-test adjusted P-value,0.05), out of which 635 were highly expressed in the B and 598 highly expressed in the LW pigs. No difference in gene expression was found between housing systems. Besides, expression level of 12 differentially expressed genes quantified by real-time RT-PCR validated microarray data. Functional annotation clustering emphasized four main clusters associated to transcriptome breed differences: metabolic processes, skeletal muscle structure and organization, extracellular matrix, lysosome, and proteolysis, thereb

Evidence that the 16 kDa proteolipid (subunit c) of the vacuolar H(+)-ATPase and ductin from gap junctions are the same polypeptide in Drosophila and Manduca: molecular cloning of the Vha16k gene from Drosophila.

The 16 kDa proteolipid (subunit c) of the eukaryotic vacuolar H(+)-ATPase (V-ATPase) is closely related to the ductin polypeptide that forms the connexon channel of gap junctions in the crustacean Nephrops norvegicus. Here we show that the major protein component of Manduca sexta gap junction preparations is a 16 kDa polypeptide whose N-terminal sequence is homologous to ductin and is identical to the deduced sequence of a previously cloned cDNA from Manduca (Dow et al., Gene, 122, 355-360, 1992). We also show that a Drosophila melanogaster cDNA, highly homologous to the Manduca cDNA, can rescue Saccharomyces cerevisiae, defective in V-ATPase function, in which the corresponding yeast gene, VMA3, has been inactivated. Evidence is presented for a single genetic locus (Vha16) in Drosophila, which in adults at least contains a single transcriptional unit. Taken together, the data suggest that in Drosophila and Manduca, the same polypeptide is both the proteolipid subunit c component of the V-ATPase and the ductin component of gap junctions. The intron/exon structure of the Drosophila Vha16 is identical to that of a human Vha16 gene, and is consistent with an ancient duplication of an 8 kDa domain. A pilot study for gene inactivation shows that transposable P-elements can be easily inserted into the Drosophila ductin Vha16 gene. Although without phenotypic consequences, these can serve as a starting point for generation of null alleles