Critical behavior of a bounded Kardar-Parisi-Zhang equation

A host of spatially extended systems, both in physics and in other disciplines, are well described at a coarse-grained scale by a Langevin equation with multiplicative-noise. Such systems may exhibit non-equilibrium phase transitions, which can be classified into universality classes. Here we study in detail one of such classes that can be mapped into a Kardar-Parisi-Zhang (KPZ) interface equation with a positive (negative) non-linearity in the presence of a bounding lower (upper) wall. The wall limits the possible values taken by the height variable, introducing a lower (upper) cut-off, and induce a phase transition between a pinned (active) and a depinned (absorbing) phase. This transition is studied here using mean field and field theoretical arguments, as well as from a numerical point of view. Its main properties and critical features, as well as some challenging theoretical difficulties, are reported. The differences with other multiplicative noise and bounded-KPZ universality classes are stressed, and the effects caused by the introduction of ``attractive'' walls, relevant in some physical contexts, are also analyzed.Comment: Invited paper to a special issue of the Brazilian J. of Physics. 5 eps Figures. 9 pagres. Revtex

OPTIMIZING SMITH-WATERMAN ALIGNMENTS

Mutual correlation between segments of DNA or protein sequences can be detected by Smith-Waterman local alignments. We present a statistical analysis of alignment of such sequences, based on a recent scaling theory. A new delity measure is introduced and shown to capture the signi cance of the local alignment, i.e., the extent to which the correlated subsequences are correctly identi ed. It is demonstrated how the delity may be optimized in the space of penalty parameters using only the alignment score data of a single sequence pair.