Regional Controllability of Riemann–Liouville Time-Fractional Semilinear Evolution Equations

In this paper, we discuss the exact regional controllability of fractional evolution equations involving Riemann–Liouville fractional derivative of order q ∈ 0,1 . The result is obtained with the help of the theory of fractional calculus, semigroup theory, and Banach fixed-point theorem under several assumptions on the corresponding linear system and the nonlinear term. Finally, some numerical simulations are given to illustrate the obtained result.

Heritability and Cognitive Relevance of Structural Brain Controllability

Cognition and behavior are thought to emerge from the connections and interactions among brain regions. The precise nature of these relationships remains elusive. Here we use tools provided by network control theory to determine how the structural connectivity profile of brain regions may shape individual variation in cognition. In a cohort of healthy young adults (n = 1066), we computed two fundamental brain regional control patterns, average and modal controllability, which index the degree of influence of a region over others. We first established that regional brain controllability measures were both reproducible and heritable. Regions with controllability profiles theoretically conducive to facilitating multiple cognitive operations were over-represented in higher-order resting-state networks. Finally, variation in regional controllability accounted for about 50% of interindividual variability in multiple cognitive domains. We conclude that controllability is a biologically plausible property of the structural connectome and provides a mechanistic explanation for how brain structural architecture may influence cognitive functions.