Scale-Free Exponents of Resting State provide a Biomarker for Typical   and Atypical Brain Activity
  Scale-free networks (SFN) arise from simple growth processes, which can encourage efficient, centralized and fault tolerant communication (1). Recently its been shown that stable network hub structure is governed by a phase transition at exponents (>2.0) causing a dramatic change in network structure including a loss of global connectivity, an increasing minimum dominating node set, and a shift towards increasing connectivity growth compared to node growth. Is this SFN shift identifiable in atypical brain activity? The Pareto Distribution (P(D)~D^-\b{eta}) on the hub Degree (D) is a signature of scale-free networks. During resting-state, we assess Degree exponents across a large range of neurotypical and atypical subjects. We use graph complexity theory to provide a predictive theory of the brain network structure. Results. We show that neurotypical resting-state fMRI brain activity possess scale-free Pareto exponents (1.8 se .01) in a single individual scanned over 66 days as well as in 60 different individuals (1.8 se .02). We also show that 60 individuals with Autistic Spectrum Disorder, and 60 individuals with Schizophrenia have significantly higher (>2.0) scale-free exponents (2.4 se .03, 2.3 se .04), indicating more fractionated and less controllable dynamics in the brain networks revealed in resting state. Finally we show that the exponent values vary with phenotypic measures of atypical disease severity indicating that the global topology of the network itself can provide specific diagnostic biomarkers for atypical brain activity. 
S.J. Hanson, D. Mastrovito, C. Hanson, J. Ramsey, and C. Glymour
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