  Synchronization phenomena are pervasive in biology. In neuronal networks, the
mechanisms of synchronization have been extensively studied from both
physiological and computational viewpoints. The functional role of
synchronization has also attracted much interest and debate. In particular,
synchronization may allow distant sites in the brain to communicate and
cooperate with each other, and therefore it may play a role in temporal binding
and in attention and sensory-motor integration mechanisms.
  In this article, we study another role for synchronization: the so-called
"collective enhancement of precision." We argue, in a full nonlinear dynamical
context, that synchronization may help protect interconnected neurons from the
influence of random perturbations -- intrinsic neuronal noise -- which affect
all neurons in the nervous system. This property may allow reliable
computations to be carried out even in the presence of significant noise (as
experimentally found e.g., in retinal ganglion cells in primates), as
mathematically it is key to obtaining meaningful downstream signals, whether in
terms of precisely-timed interaction (temporal coding), population coding, or
frequency coding. Using stochastic contraction theory, we show how
synchronization of nonlinear dynamical systems helps protect these systems from
random perturbations.
  Our main contribution is a mathematical proof that, under specific quantified
conditions, the impact of noise on each individual system and on the spatial
mean can essentially be cancelled through synchronization. Similar concepts may
be applicable to questions in systems biology.
