We consider a class of 4D supersymmetric black hole solutions, arising from string theory compactifications, which classically have vanishing horizon area and singular spacetime geometry. String theory motivates the inclusion of higher derivative terms, which convert these singular classical solutions into regular black holes with finite horizon area. In particular, the supersymmetric attractor...

We consider an infinite horizon production planning problem with non-stationary, convex production and inventory costs. Backlogging is allowed unlike related previous work and inventory cost is interpreted as backlogging cost when inventory is negative. We create finite horizon truncations of the infinite horizon problem and employ classic results on convex production planning to derive a close...

A method is presented to obtain an inner-approximation of the backward reachable set a given target tube, along with admissible controller that maintains trajectories inside this tube. The proposed optimization algorithms are formulated as nonlinear problems, which decoupled into tractable subproblems and solved by iterative algorithm using polynomial S-procedure sum-of-squares techniques. This...

Aspects of d = 4,N = 4 superconformal U(N) gauge theory are studied at finite temperature. Utilizing the dual descriptions of the large N and strong coupling limit via Type IIB string theory compactification on Schwarzschild anti-de Sitter spacetime, we study correlations of Wilson-Polyakov loops and the static quark anti-quark potential thereof. We find two branches of macroscopic string repre...

We consider the problem of minimum energy steering of a linear stochastic system to a final prescribed distribution over a finite horizon and the problem to maintain a stationary distribution over an infinite horizon. For both problems the control and noise channels are allowed to be distinct, thereby, placing the results of this paper outside of the scope of previous work both in probability a...