The geometric measure of entanglement for a symmetric pure state with positive amplitudes

In this paper for a class of symmetric multiparty pure states we consider a conjecture related to the geometric measure of entanglement: 'for a symmetric pure state, the closest product state in terms of the fidelity can be chosen as a symmetric product state'. We show that this conjecture is true for symmetric pure states whose amplitudes are all non-negative in a computational basis. The more general conjecture is still open.Comment: Similar results have been obtained independently and with different methods by T-C. Wei and S. Severini, see arXiv:0905.0012v

The dwarf phenotype of the Arabidopsis acl5 mutant is suppressed by a mutation in an upstream ORF of a bHLH gene

Loss-of-function mutants of the Arabidopsis thaliana ACAULIS 5 (ACL5) gene, which encodes spermine synthase, exhibit a severe dwarf phenotype. To elucidate the ACL5-mediated regulatory pathways of stem internocle elongation, we isolated four suppressor of acaulis (sac) mutants that reverse the acl5 dwarf phenotype. Because these mutants do not rescue the dwarfism of known phytohormone-related mutants, the SAC genes appear to act specifically on the ACL5 pathways. We identify the gene responsible for the dominant sac51-d mutant, which almost completely suppresses the acl5 phenotype. sac51-d disrupts a short upstream open reading frame (uORF) of SAC51, which encodes a bHLH-type transcription factor. Our results indicate that premature termination of the uORF in sac51-d results in an increase in its own transcript level, probably as a result of an increased translation of the main ORF. We suggest a model in which ACL5 plays a role in the translational activation of SAC51, which may lead to the expression of a subset of genes required for stem elongation