Lagrangian-Hamiltonian unified formalism for field theory

The Rusk-Skinner formalism was developed in order to give a geometrical unified formalism for describing mechanical systems. It incorporates all the characteristics of Lagrangian and Hamiltonian descriptions of these systems (including dynamical equations and solutions, constraints, Legendre map, evolution operators, equivalence, etc.). In this work we extend this unified framework to first-order classical field theories, and show how this description comprises the main features of the Lagrangian and Hamiltonian formalisms, both for the regular and singular cases. This formulation is a first step toward further applications in optimal control theory for PDE's.Comment: LaTeX file, 23 pages. Minor changes have been made. References are update

Respiratory Complex III Is Required to Maintain Complex I in Mammalian Mitochondria

A puzzling observation in patients with oxidative phosphorylation (OXPHOS) deficiencies is the presence of combined enzyme complex defects associated with a genetic alteration in only one protein-coding gene. In particular, mutations in the mtDNA encoded cytochrome b gene are associated either with combined complex I+III deficiency or with only complex III deficiency. We have reproduced the combined complex I+III defect in mouse and human cultured cell models harboring cytochrome b mutations. In both, complex III assembly is impeded and causes a severe reduction in the amount of complex I, not observed when complex III activity was pharmacologically inhibited. Metabolic labeling in mouse cells revealed that complex I was assembled, although its stability was severely hampered. Conversely, complex III stability was not influenced by the absence of complex I. This structural dependence among complexes I and III was confirmed in a muscle biopsy of a patient harboring a nonsense cytochrome b mutation