Non-local control in the conduction coefficients: well posedness and convergence to the local limit

We consider a problem of optimal distribution of conductivities in a system governed by a non-local diffusion law. The problem stems from applications in optimal design and more specifically topology optimization. We propose a novel parametrization of non-local material properties. With this parametrization the non-local diffusion law in the limit of vanishing non-local interaction horizons converges to the famous and ubiquitously used generalized Laplacian with SIMP (Solid Isotropic Material with Penalization) material model. The optimal control problem for the limiting local model is typically ill-posed and does not attain its infimum without additional regularization. Surprisingly, its non-local counterpart attains its global minima in many practical situations, as we demonstrate in this work. In spite of this qualitatively different behaviour, we are able to partially characterize the relationship between the non-local and the local optimal control problems. We also complement our theoretical findings with numerical examples, which illustrate the viability of our approach to optimal design practitioners

Inversible Max-Plus Algebras and Integrable systems

We present an extended version of max-plus algebra which includes the inverse operator of "max". This algebra enables us to ultra-discretize the system including subtractions and obtain new ultra-discrete equations. The known ultra-discrete equations can also be recovered by this construction.Comment: 21 page

The Story of the Puerto Rican-Chicano Committee

The concept or idea for The Puerto Rican-Chicano Committee (PRCC) came from UB student Alberto O. Cappas, who also was the original founder of PODER, at the time known as the Puerto Rican Organization for Dignity, Elevation, and Responsibility