Advances in analytical techniques that adapt new mathematical methods have aided the study of complex cognitive processes and neural communication in normal (Hummel and Gerloff, 2005; Chen et al., 2008b; Chorlian et al., 2009) as well as pathological conditions (Uhlhaas and Singer, 2006). Important state-of-the-art analysis tools based on mathematical approaches include: (1) phase synchrony in oscillations (Varela et al., 2001); and (2) methods of source localization (e.g., sLORETA (low-resolution brain electromagnetic tomography) which solves the “inverse problem” to generate anatomically constrained solutions of active sources within the brain that underlie the event-related scalp activity (Pascual-Marqui, 2002). The ERP and ERO analyses are supplemented by source localization techniques to infer anatomical substrates and have been successfully used to study several psychiatric disorders including AUDs (Coutin-Churchman and Moreno, 2008; Holmes and Pizzagalli, 2008; Kamarajan et al., 2010; Itoh et al., 2011; Pandey et al., 2012). Hence, these tools are instrumental in translating and comparing findings from electrophysiological studies with those from imaging methodologies, or using them in conjunction with each other, to create a multimodal approach.
