Online Convex Optimization with Binary Constraints

We consider online optimization with binary decision variables and convex loss functions. We design a new algorithm, binary online gradient descent (bOGD) and bound its expected dynamic regret. We provide a regret bound that holds for any time horizon and a specialized bound for finite time horizons. First, we present the regret as the sum of the relaxed, continuous round optimum tracking error and the rounding error of our update in which the former asymptomatically decreases with time under certain conditions. Then, we derive a finite-time bound that is sublinear in time and linear in the cumulative variation of the relaxed, continuous round optima. We apply bOGD to demand response with thermostatically controlled loads, in which binary constraints model discrete on/off settings. We also model uncertainty and varying load availability, which depend on temperature deadbands, lockout of cooling units and manual overrides. We test the performance of bOGD in several simulations based on demand response. The simulations corroborate that the use of randomization in bOGD does not significantly degrade performance while making the problem more tractable

Optical Zener-Bloch oscillations in binary waveguide arrays

Zener tunneling in a binary array of coupled optical waveguides with transverse index gradient is shown to produce a sequence of regular or irregular beam splitting and beam recombination events superimposed to Bloch oscillations. These periodic or aperiodic Zener-Bloch oscillations provide a clear and visualizable signature in an optical system of coherent multiband dynamics encountered in solid-state or matter-wave system

Arden 2012

An amalgamation of creative student works. Items contained include, but are not limited to, art, photography, short stories, prose, poetry, and other avenues of creative composition.https://csuepress.columbusstate.edu/arden/1011/thumbnail.jp

Phase Diagrams of Bi1-xSbx Thin Films with Different Growth Orientations

A closed-form model is developed to evaluate the band-edge shift caused by quantum confinement for a two-dimensional non-parabolic carrier-pocket. Based on this model, the symmetries and the band-shifts of different carrier-pockets are evaluated for BiSb thin films that are grown along different crystalline axes. The phase diagrams for the BiSb thin film systems with different growth orientations are calculated and analyzed

Comment on "Breakdown of the Internet under Intentional Attack"

We obtain the exact position of the percolation threshold in intentionally damaged scale-free networks.Comment: 1 page, to appear in Phys. Rev. Let