SLYRB measures:natural invariant measures for chaotic systems

In many applications it is useful to consider not only the set that constitutes an attractor but also (if it exists) the asymptotic distribution of a typical trajectory converging to the attractor. Indeed, in the physics literature such a distribution is often assumed to exist. When it exists, it is called a "natural invariant measure". The results by Lasota and Yorke, and by Sinai, Ruelle and Bowen represent two approaches both of which establish the existence of an invariant measure. The goal of this paper is to relate the "Lasota-Yorke measure" for chaotic attractors in one-dimensional maps and the "Sinai-Ruelle-Bowen measure" for chaotic attractors in higher-dimensional dynamical systems. We introduce the notion of "SLYRB measure". (We pronounce the term "SLYRB" as a single word "slurb".) The SRB concept of measure can be motivated by asking how a trajectory from a typical initial point is distributed asymptotically. Similarly the SLYRB concept of measure can be motivated by asking what the average distribution is for trajectories of a large collection of initial points in some region not necessarily restricted to a single basin. The latter is analogous to ask where all the rain drops from a rain storm go and the former asks about where a single rain drop goes, perhaps winding up distributed throughout a particular lake. (C) 2002 Elsevier Science B.V. All rights reserved

Function of a retrotransposon nucleocapsid protein

Long terminal repeat (LTR) retrotransposons are not only the ancient predecessors of retroviruses, but they constitute significant fractions of the genomes of many eukaryotic species. Studies of their structure and function are motivated by opportunities to gain insight into common functions of retroviruses and retrotransposons, diverse mechanisms of intracellular genomic mobility and host factors that diminish or enhance retrotransposition. This review focuses on the nucleocapsid (NC) protein of a Saccharomyces cerevisiae LTR retrotransposon, the metavirus, Ty3. Retrovirus NC promotes genomic (g)RNA dimerization and packaging, tRNA primer annealing, reverse transcription strand transfers, and host protein interactions with gRNA. Studies of Ty3 NC have revealed key roles for Ty3 NC in formation of retroelement assembly sites (retrosomes), and in chaperoning primer tRNA to both dimerize and circularize Ty3 gRNA. We speculate that Ty3 NC, together with P-body and stress-granule proteins, plays a role in transitioning Ty3 RNA from translation template to gRNA, and that interactions between the acidic spacer domain of Ty3 Gag3 and the adjacent basic NC domain control condensation of the virus-like particle