Title: Robustness of functional networks at criticality against structural defects,
Abstract: The robustness of dynamical properties of neuronal networks against
structural damages is a central problem in computational and experimental
neuroscience. Research has shown that the cortical network of a healthy brain
works near a critical state, and moreover, that functional neuronal networks
often have scale-free and small-world properties. In this work, we study how
the robustness of simple functional networks at criticality is affected by
structural defects. In particular, we consider a 2D Ising model at the critical
temperature and investigate how its functional network changes with the
increasing degree of structural defects. We show that the scale-free and
small-world properties of the functional network at criticality are robust
against large degrees of structural lesions while the system remains below the
percolation limit. Although the Ising model is only a conceptual description of
a two-state neuron, our research reveals fundamental robustness properties of
functional networks derived from classical statistical mechanics models.