Global Existence and Asymptotic Behavior for Functional Evolution Equations

In this paper we present some results of global existence and attrac-tivity of mild solutions for semilinear evolution equations with innitedelay in a Banach space. The considerations of this paper are basedon the Schauder's xed point theorem and the theory of evolutionsystem.     

Scale-free brain functional networks

Functional magnetic resonance imaging is used to extract functional networks connecting correlated human brain sites. Analysis of the resulting networks in different tasks shows that (a) the distribution of functional connections, and the probability of finding a link versus distance are both scale-free, (b) the characteristic path length is small and comparable with those of equivalent random networks, and (c) the clustering coefficient is orders of magnitude larger than those of equivalent random networks. All these properties, typical of scale-free small-world networks, reflect important functional information about brain states.