`The frozen accident' as an evolutionary adaptation: A rate distortion theory perspective on the dynamics and symmetries of genetic coding mechanisms

We survey some interpretations and related issues concerning the frozen hypothesis due to F. Crick and how it can be explained in terms of several natural mechanisms involving error correction codes, spin glasses, symmetry breaking and the characteristic robustness of genetic networks. The approach to most of these questions involves using elements of Shannon's rate distortion theory incorporating a semantic system which is meaningful for the relevant alphabets and vocabulary implemented in transmission of the genetic code. We apply the fundamental homology between information source uncertainty with the free energy density of a thermodynamical system with respect to transcriptional regulators and the communication channels of sequence/structure in proteins. This leads to the suggestion that the frozen accident may have been a type of evolutionary adaptation

kk-Schur functions and affine Schubert calculus

This book is an exposition of the current state of research of affine Schubert calculus and $k$-Schur functions. This text is based on a series of lectures given at a workshop titled "Affine Schubert Calculus" that took place in July 2010 at the Fields Institute in Toronto, Ontario. The story of this research is told in three parts: 1. Primer on $k$-Schur Functions 2. Stanley symmetric functions and Peterson algebras 3. Affine Schubert calculusComment: 213 pages; conference website: http://www.fields.utoronto.ca/programs/scientific/10-11/schubert/, updates and corrections since v1. This material is based upon work supported by the National Science Foundation under Grant No. DMS-065264

Conjugacy of unimodular Pisot substitutions subshifts to domain exchanges

We prove that any unimodular Pisot substitution subshift is measurably conjugate to a domain exchange in Euclidean spaces which factorizes onto a minimal rotation on a torus. This generalizes the pioneer works of Rauzy and Arnoux-Ito providing geometric realizations to any unimodular Pisot substitution without any additional combinatorial condition.Comment: 29 p. In this new version, a gap in the proof of the main theorem has been fixe