On the Stability of Periodic Multi-Solitons of the KdV Equation.

In this paper we obtain the following stability result for periodic multi-solitons of the KdV equation: We prove that under any given semilinear Hamiltonian perturbation of small size , a large class of periodic multi-solitons of the KdV equation, including ones of large amplitude, are orbitally stable for a time interval of length at least . To the best of our knowledge, this is the first stability result of such type for periodic multi-solitons of large size of an integrable PDE.

Nekhoroshev theorem for the periodic Toda lattice.

The periodic Toda lattice with N sites is globally symplectomorphic to a two parameter family of N-1 coupled harmonic oscillators. The action variables fill out the whole positive quadrant of R(N-1). We prove that in the interior of the positive quadrant as well as in a neighborhood of the origin, the Toda Hamiltonian is strictly convex and therefore Nekhoroshev's theorem applies on (almost) all parts of phase space (2000 Mathematics Subject Classification: 37J35, 37J40, 70H06).

OntoGene in BioCreative II.

Background: Research scientists and companies working in the domains of biomedicine and genomics are increasingly faced with the problem of efficiently locating, within the vast body of published scientific findings, the critical pieces of information that are needed to direct current and future research investment.

Results: In this report we describe approaches taken within the scope of the second BioCreative competition in order to solve two aspects of this problem: detection of novel protein interactions reported in scientific articles, and detection of the experimental method that was used to confirm the interaction. Our approach to the former problem is based on a high-recall protein annotation step, followed by two strict disambiguation steps.