This paper considers stochastic convex optimization problems with two sets of constraints: (a) deterministic constraints on the domain variable, which are difficult to project onto; and (b) or that admit efficient projection. Problems this form arise frequently in context semidefinite programming as well when various NP-hard solved approximately via relaxation. Since projection onto first set i...

In this paper we consider distributed optimization problems over a multi-agent network, where each agent can only partially evaluate the objective function, and it is allowed to exchange messages with its immediate neighbors. Differently from all existing works on distributed optimization, our focus is given to optimizing a class of difficult non-convex problems, and under the challenging setti...

abstract. topological indices are the numerical value associated with chemical constitution purporting for correlation of chemical structure with various physical properties, chemical reactivity or biological activity. graph theory is a delightful playground for the exploration of proof techniques in discrete mathematics and its results have applications in many areas of sciences. one of the us...

This paper reports a tunable visual color filter based on a microfluidic transmission grating. The grating lines are formed by the microflows in an array of evenly spaced straight microchannels. In experimental study, the transmission of white light measures a shift of visual color from red to blue in the zeroth order diffraction in response to a change of the refractive index from 1.3290 to 1....

The equations of parallel transport for a non-linear connection on phase space are examined. It is shown that, for a free-particle Lagrangian, the connection term first-order in momentum reproduces the geodesic equation of General Relativity and the term zeroth-order in the momentum reproduces the Lorentz electromagnetic force law. Hence from one mathematical expression, a non-linear parallel t...

We show that the zeroth cohomology of effective line bundles on del Pezzo and Hirzebruch surfaces can always be computed in terms a topological index.