Mutual information rate and bounds for it

The amount of information exchanged per unit of time between two nodes in a dynamical network or between two data sets is a powerful concept for analysing complex systems. This quantity, known as the mutual information rate (MIR), is calculated from the mutual information, which is rigorously defined only for random systems. Moreover, the definition of mutual information is based on probabilities of significant events. This work offers a simple alternative way to calculate the MIR in dynamical (deterministic) networks or between two data sets (not fully deterministic), and to calculate its upper and lower bounds without having to calculate probabilities, but rather in terms of well known and well defined quantities in dynamical systems. As possible applications of our bounds, we study the relationship between synchronisation and the exchange of information in a system of two coupled maps and in experimental networks of coupled oscillators

Seasonal changes in patterns of gene expression in avian song control brain regions.

This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Photoperiod and hormonal cues drive dramatic seasonal changes in structure and function of the avian song control system. Little is known, however, about the patterns of gene expression associated with seasonal changes. Here we address this issue by altering the hormonal and photoperiodic conditions in seasonally-breeding Gambel's white-crowned sparrows and extracting RNA from the telencephalic song control nuclei HVC and RA across multiple time points that capture different stages of growth and regression. We chose HVC and RA because while both nuclei change in volume across seasons, the cellular mechanisms underlying these changes differ. We thus hypothesized that different genes would be expressed between HVC and RA. We tested this by using the extracted RNA to perform a cDNA microarray hybridization developed by the SoNG initiative. We then validated these results using qRT-PCR. We found that 363 genes varied by more than 1.5 fold (>log(2) 0.585) in expression in HVC and/or RA. Supporting our hypothesis, only 59 of these 363 genes were found to vary in both nuclei, while 132 gene expression changes were HVC specific and 172 were RA specific. We then assigned many of these genes to functional categories relevant to the different mechanisms underlying seasonal change in HVC and RA, including neurogenesis, apoptosis, cell growth, dendrite arborization and axonal growth, angiogenesis, endocrinology, growth factors, and electrophysiology. This revealed categorical differences in the kinds of genes regulated in HVC and RA. These results show that different molecular programs underlie seasonal changes in HVC and RA, and that gene expression is time specific across different reproductive conditions. Our results provide insights into the complex molecular pathways that underlie adult neural plasticity