Characterization of Weak Collective Neural Coherence

Recently, much attention has been paid to brain rhythms [1,2]. Synchronous neural oscillations may be used for efficient sensory processing (e.g., visual binding) [3]. In addition, neural synchronization is also correlated with pathological rhythms associated with neural diseases (e.g., epileptic seizures and tremors in Parkinson’s disease) [4]. Here, we are interested in the characterization of these synchronized neural rhythms. Collective coherence in a neural population may be well described by the (population-averaged) collective potential VC . For a coherent case, an oscillating (macroscopic) collective potential VC emerges via cooperation of (microscopic) potentials of individual neurons. This collective neural coherence has been characterized mostly in terms of two coherence measures [5]. The first is a “thermodynamic” fluctuation-based coherence measure Mf . Neural coherence is directly related to fluctuations of the collective potential VC . In the thermodynamic limit (N → ∞), a collective state becomes coherent if an oscillating collective potential VC appears. Otherwise (i.e., when the collective potential VC is stationary), it becomes incoherent. Thus, the mean square deviation of the collective potential VC (i.e., time-averaged fluctuations of VC) plays the role of an order parameter to de-