Neuronal networks are controlled by a combination of the dynamics of individual neurons and the connectivity of the network that links them together. We study a minimal model of the preBotzinger complex, a small neuronal network that controls the bre
athing rhythm of mammals through periodic firing bursts. We show that the properties of a such a randomly connected network of identical excitatory neurons are fundamentally different from those of uniformly connected neuronal networks as described by mean-field theory. We show that (i) the connectivity properties of the networks determines the location of emergent pacemakers that trigger the firing bursts and (ii) that the collective desensitization that terminates the firing bursts is determined again by the network connectivity, through k-core clusters of neurons.
We present a statistical-mechanical analysis of the positioning of nucleosomes along one of the chromosomes of yeast DNA as a function of the strength of the binding potential and of the chemical potential of the nucleosomes. We find a significant de
nsity of two-level nucleosome switching regions where, as a function of the chemical potential, the nucleosome distribution undergoes a micro first-order transition. The location of these nucleosome switches shows a strong correlation with the location of transcription-factor binding sites.
