`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

Groupoids, imaginaries and internal covers

Let $T$ be a first-order theory. A correspondence is established between internal covers of models of $T$ and definable groupoids within $T$. We also consider amalgamations of independent diagrams of algebraically closed substructures, and find strong relation between: covers, uniqueness for 3-amalgamation, existence of 4-amalgamation, imaginaries of T^\si, and definable groupoids. As a corollary, we describe the imaginary elements of families of finite-dimensional vector spaces over pseudo-finite fields.Comment: Local improvements; thanks to referee of Turkish Mathematical Journal. First appeared in the proceedings of the Paris VII seminar: structures alg\'ebriques ordonn\'ee (2004/5

On finite imaginaries

We study finite imaginaries in certain valued fields, and prove a conjecture of Cluckers and Denef.Comment: 15p

On Second-Order Monadic Monoidal and Groupoidal Quantifiers

We study logics defined in terms of second-order monadic monoidal and groupoidal quantifiers. These are generalized quantifiers defined by monoid and groupoid word-problems, equivalently, by regular and context-free languages. We give a computational classification of the expressive power of these logics over strings with varying built-in predicates. In particular, we show that ATIME(n) can be logically characterized in terms of second-order monadic monoidal quantifiers