We propose two simple upper bounds for the joint spectral radius of sets of nonnegative matrices. These bounds, the joint column radius and the joint row radius, can be computed in polynomial time as solutions of convex optimization problems. We show that for general matrices these bounds are within a factor 1/n of the exact value, where n is the size of the matrices. Moreover, for sets of matr...

In this study, we reported a case with collapse and subluxation of metatarsal-cuneiform joint, navicular-cuneiform joint with subluxed the right first metatarsophalangeal joint. The injured medial column was internally fixed with compression arthrodesis. The fusion site was firmed up with BonGold® Bone Sponge and Bone Putty. The prognosis of fused navicular-cuneiform joint and metatarsal-cuneif...