A relaxed constant positive linear dependence constraint qualification and applications

In this work we introduce a relaxed version of the constant positive linear dependence constraint qualification (CPLD) that we call RCPLD. This development is inspired by a recent generalization of the constant rank constraint qualification by Minchenko and Stakhovski that was called RCRCQ. We show that RCPLD is enough to ensure the convergence of an augmented Lagrangian algorithm and that it asserts the validity of an error bound. We also provide proofs and counter-examples that show the relations of RCRCQ and RCPLD with other known constraint qualifications. In particular, RCPLD is strictly weaker than CPLD and RCRCQ, while still stronger than Abadie's constraint qualification. We also verify that the second order necessary optimality condition holds under RCRCQ.

Seeking tools for image fusion between computed tomography, structural and functional magnetic resonance methods for applications in neurosurgery

OBJECTIVE: To evaluate tools for the fusion of images generated by tomography and structural and functional magnetic resonance imaging. METHODS: Magnetic resonance and functional magnetic resonance imaging were performed while a volunteer who had previously undergone cranial tomography performed motor and somatosensory tasks in a 3-Tesla scanner. Image data were analyzed with different programs, and the results were compared. RESULTS: We constructed a flow chart of computational processes that allowed measurement of the spatial congruence between the methods. There was no single computational tool that contained the entire set of functions necessary to achieve the goal. CONCLUSION: The fusion of the images from the three methods proved to be feasible with the use of four free-access software programs (OsiriX, Register, MRIcro and FSL). Our results may serve as a basis for building software that will be useful as a virtual tool prior to neurosurgery.