View source for Scale-free neocortical dynamics

==Implications of scale-free neocortical dynamics==

===Hubs===
Preferentiality in a scale-free network, depending on the probabilities of input and output connections, supports the emergence of ''hubs'', which are nodes of exceptionally high density of connectivity including long-distance links (Bollobás, 2001). Commonly studied networks with hubs include the route maps of major airlines and the patterns of connectivity on the Internet (Barabási, 2002). If neocortical connectivity and dynamics are scale-free, then for every cognitive function that can be adequately controlled, one or more hubs should be observable at which connection and activity densities are maximal. Then the ''hot spots'' of high metabolic activity revealed by macroscopic imaging ([[fMRI]], etc.) provide evidence not for localized functions but for hubs in non-local macroscopic states that organize mesoscopic and microscopic functions. Achard et al. (2006) recently describe the existence of such hubs in low frequency functional connectivity of human cortex. Recent computational modelling also gives insight into the dynamic relationship between structural hubs and their dynamic expression (Honey et al. 2007).

===State transitions===

Above a certain threshold of connection density, a scale-free network can undergo an abrupt state transition and re[[synchronization]] globally and virtually instantaneously no matter how large its diameter. Scale-free dynamics can explain how mammalian brains operate on the same time scales despite differences in size ranging to 10<sup>4</sup> (mouse to whale). 

===Focal lesions===
Random lesions of scale-free networks have negligible effects; lesions of hubs are catastrophic. Examples in humans are [[coma]] and [[Parkinson’s disease]] from small [[brain stem]] lesions. Other examples ripe for exploration by teams of clinicians and mathematicians may include studies of the effects of lesions of the perforant path from entorhinal cortex to dentate gyrus; Broca's area; Wernicke's area; anterior cingulate; and ventromedial prefrontal cortex.