Relative Entropy, Gaussian Concentration and Uniqueness of Equilibrium States.

For a general class of lattice spin systems, we prove that an abstract Gaussian concentration bound implies positivity of the lower relative entropy density. As a consequence, we obtain uniqueness of translation-invariant Gibbs measures from the Gaussian concentration bound in this general setting. This extends earlier results with a different and very short proof.

Rejuvenating functional responses with renewal theory.

Functional responses are widely used to describe interactions and resource exchange between individuals in ecology. The form given to functional responses dramatically affects the dynamics and stability of populations and communities. Despite their importance, functional responses are generally considered with a phenomenological approach, without clear mechanistic justifications from individual traits and behaviours.

Multivalued mappings in generalized chaos synchronization.

The onset of generalized synchronization of chaos in directionally coupled systems corresponds to the formation of a continuous mapping that enables one to persistently define the state of the response system from the trajectory of the drive system. A recently developed theory of generalized synchronization of chaos deals only with the case where this synchronization mapping is a single-valued function. In this paper, we explore generalized synchronization in a regime where the synchronization mapping can become a multivalued function.