Path transferability of graphs

AbstractPath transferability of a graph is a notion that arises from the movement of a path along the graph, the behavior of the path seems as a train on a railroad. In this paper, we introduce two graph notions, transferability and reversibility, and study their properties

Memory Immune Responses against Pandemic (H1N1) 2009 Influenza Virus Induced by a Whole Particle Vaccine in Cynomolgus Monkeys Carrying Mafa-A1*052∶02

We made an H1N1 vaccine candidate from a virus library consisting of 144 ( = 16 HA×9 NA) non-pathogenic influenza A viruses and examined its protective effects against a pandemic (2009) H1N1 strain using immunologically naïve cynomolgus macaques to exclude preexisting immunity and to employ a preclinical study since preexisting immunity in humans previously vaccinated or infected with influenza virus might make comparison of vaccine efficacy difficult. Furthermore, macaques carrying a major histocompatibility complex class I molecule, Mafa-A1*052∶02, were used to analyze peptide-specific CD8+ T cell responses. Sera of macaques immunized with an inactivated whole particle formulation without addition of an adjuvant showed higher neutralization titers against the vaccine strain A/Hokkaido/2/1981 (H1N1) than did sera of macaques immunized with a split formulation. Neutralization activities against the pandemic strain A/Narita/1/2009 (H1N1) in sera of macaques immunized twice with the split vaccine reached levels similar to those in sera of macaques immunized once with the whole particle vaccine. After inoculation with the pandemic virus, the virus was detected in nasal samples of unvaccinated macaques for 6 days after infection and for 2.67 days and 5.33 days on average in macaques vaccinated with the whole particle vaccine and the split vaccine, respectively. After the challenge infection, recall neutralizing antibody responses against the pandemic virus and CD8+ T cell responses specific for nucleoprotein peptide NP262-270 bound to Mafa-A1*052∶02 in macaques vaccinated with the whole particle vaccine were observed more promptly or more vigorously than those in macaques vaccinated with the split vaccine. These findings demonstrated that the vaccine derived from our virus library was effective for pandemic virus infection in macaques and that the whole particle vaccine conferred more effective memory and broader cross-reactive immune responses to macaques against pandemic influenza virus infection than did the split vaccine

PATH TRANSFERABILITY OF PLANAR GRAPHS

We regard a path as a train moving on a graph. A graph G is called n-transferable if any path of length n can be moved to any other such path by several steps. We will show that every planar graph with minimum degree at least three is at most 10 transferable