On matrix differential equations in the Hopf algebra of renormalization
  We establish Sakakibara's differential equations in a matrix setting for the counter term (respectively renormalized character) in Connes-Kreimer's Birkhoff decomposition in any connected graded Hopf algebra, thus including Feynman rules in perturbative renormalization as a key example. 
Kurusch Ebrahimi-Fard, Dominique Manchon