Fast Computation of Generalized Dedekind Sums

We construct an algorithm that reduces the complexity for computing generalized Dedekind sums from exponential to polynomial time. We do so by using an efficient word rewriting process in group theory.Comment: 11 pages, 1 figur

The PIP peptide of INFLORESCENCE DEFICIENT IN ABSCISSION enhances Populus leaf and Elaeis guineensis fruit abscission

The programmed loss of a plant organ is called abscission, which is an important cell separation process that occurs with different organs throughout the life of a plant. The use of floral organ abscission in Arabidopsis thaliana as a model has allowed greater understanding of the complexities of organ abscission, but whether the regulatory pathways are conserved throughout the plant kingdom and for all organ abscission types is unknown. One important pathway that has attracted much attention involves a peptide ligand-receptor signalling system that consists of the secreted peptide IDA (INFLORESCENCE DEFICIENT IN ABSCISSION) and at least two leucine-rich repeat (LRR) receptor-like kinases (RLK), HAESA (HAE) and HAESA-LIKE2 (HSL2). In the current study we examine the bioactive potential of IDA peptides in two different abscission processes, leaf abscission in Populus and ripe fruit abscission in oil palm, and find in both cases treatment with IDA peptides enhances cell separation and abscission of both organ types. Our results provide evidence to suggest that the IDA–HAE–HSL2 pathway is conserved and functions in these phylogenetically divergent dicot and monocot species during both leaf and fruit abscission, respectively