Databases of consistent, directed- and weighted inter-areal connectivity for mouse, macaque and marmoset monkeys have recently become available and begun to be used to build structural and dynamical models. A structural hierarchy can be defined based by laminar patterns of cortical connections. A large-scale dynamical model of the macaque cortex endowed with a laminar structure accounts for empirically observed frequency-modulated interplay between bottom-up and top-down processes. Signal propagation in the model with spiking neurons displays a threshold of stimulus amplitude for the activity to gain access to the prefrontal cortex, reminiscent of the ignition phenomenon associated with conscious perception. These two examples illustrate how connectomics inform structurally based dynamic models of multi-regional brain systems. Theory raises novel questions for future anatomical and physiological empirical research, in a back-and-forth collaboration between experimentalists and theorists. Directed- and weighted inter-areal cortical connectivity matrices of macaque, marmoset and mouse exhibit similarities as well as marked differences. The new connectomic data provide quantitative information for structural and dynamical modeling of multi-regional cortical circuit providing insight to the global cortical function. Quantification of cortical hierarchy guides investigations of interplay between bottom-up and top-down information processes.
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