Shared information in stationary states at criticality

We consider bipartitions of one-dimensional extended systems whose probability distribution functions describe stationary states of stochastic models. We define estimators of the information shared between the two subsystems. If the correlation length is finite, the estimators stay finite for large system sizes. If the correlation length diverges, so do the estimators. The definition of the estimators is inspired by information theory. We look at several models and compare the behaviors of the estimators in the finite-size scaling limit. Analytical and numerical methods as well as Monte Carlo simulations are used. We show how the finite-size scaling functions change for various phase transitions, including the case where one has conformal invariance.

Symmetry in biology: from genetic code to stochastic gene regulation

Mathematical models, as instruments for understanding the workings of nature, are a traditional tool of physics, but they also play an ever increasing role in biology - in the description of fundamental processes as well as that of complex systems. In this review, the authors discuss two examples of the application of group theoretical methods, which constitute the mathematical discipline for a quantitative description of the idea of symmetry, to genetics. The first one appears, in the form of a pseudo-orthogonal (Lorentz like) symmetry, in the stochastic modelling of what may be regarded as the simplest possible example of a genetic network and, hopefully, a building block for more complicated ones: a single self-interacting or externally regulated gene with only two possible states: ` on` and ` off`. The second is the algebraic approach to the evolution of the genetic code, according to which the current code results from a dynamical symmetry breaking process, starting out from an initial state of complete symmetry and ending in the presently observed final state of low symmetry. In both cases, symmetry plays a decisive role: in the first, it is a characteristic feature of the dynamics of the gene switch and its decay to equilibrium, whereas in the second, it provides the guidelines for the evolution of the coding rules.

Contextual, but not auditory, fear conditioning is disrupted by neurotoxic selective lesion of the basal nucleus of amygdala in rats

The basolateral amygdala complex (BLA) is involved in acquisition of contextual and auditory fear conditioning. However, the BLA is not a single structure but comprises a group of nuclei, including the lateral (LA), basal (BA) and accessory basal (AB) nuclei. While it is consensual that the LA is critical for auditory fear conditioning, there is controversy on the participation of the BA in fear conditioning. Hodological and neurophysiological findings suggest that each of these nuclei processes distinct information in parallel; the BA would deal with polymodal or contextual representations, and the LA would process unimodal or elemental representations. Thus, it seems plausible to hypothesize that the BA is required for contextual, but not auditory, fear conditioning. This hypothesis was evaluated in Wistar rats submitted to multiple-site ibotenate-induced damage restricted to the BA and then exposed to a concurrent contextual and auditory fear conditioning training followed by separated contextual and auditory conditioning testing. Differing from electrolytic lesion and lidocaine inactivation, this surgical approach does not disturb fibers of passage originating in other brain areas, restricting damage to the aimed nucleus. Relative to the sham-operated controls, rats with selective damage to the BA exhibited disruption of performance in the contextual, but not the auditory, component of the task. Thus, while the BA seems required for contextual fear conditioning, it is not critical for both an auditory-US association, nor for the expression of the freezing response. (C) 2009 Elsevier Inc. All rights reserved.