Fast Non-Parametric Learning to Accelerate Mixed-Integer Programming for Online Hybrid Model Predictive Control

Today's fast linear algebra and numerical optimization tools have pushed the frontier of model predictive control (MPC) forward, to the efficient control of highly nonlinear and hybrid systems. The field of hybrid MPC has demonstrated that exact optimal control law can be computed, e.g., by mixed-integer programming (MIP) under piecewise-affine (PWA) system models. Despite the elegant theory, online solving hybrid MPC is still out of reach for many applications. We aim to speed up MIP by combining geometric insights from hybrid MPC, a simple-yet-effective learning algorithm, and MIP warm start techniques. Following a line of work in approximate explicit MPC, the proposed learning-control algorithm, LNMS, gains computational advantage over MIP at little cost and is straightforward for practitioners to implement

Effective tuning of exciton polarization splitting in coupled quantum dots

The polarization splitting of the exciton ground state in two laterally coupled quantum dots under an in-plane electric field is investigated and its effective tuning is designed. It is found that there are significant Stark effect and anticrossing in energy levels. Due to coupling between inter- and intra-dot states, the absolute value of polarization splitting is significantly reduced, and it could be tuned to zero by the electric field for proper inter-dot separations. Our scheme is interesting for the research on the quantum dots-based entangled-photon source.Comment: 4 pages, 2 figures, to appear in Appl. Phys. Let

Macroscopic quantum coherence in antiferromagnetic molecular magnets

The macroscopic quantum coherence in a biaxial antiferromagnetic molecular magnet in the presence of magnetic field acting parallel to its hard anisotropy axis is studied within the two-sublattice model. On the basis of instanton technique in the spin-coherent-state path-integral representation, both the rigorous Wentzel-Kramers-Brillouin exponent and preexponential factor for the ground-state tunnel splitting are obtained. We find that the quantum fluctuations around the classical paths can not only induce a new quantum phase previously reported by Chiolero and Loss (Phys. Rev. Lett. 80, 169 (1998)), but also have great influnence on the intensity of the ground-state tunnel splitting. Those features clearly have no analogue in the ferromagnetic molecular magnets. We suggest that they may be the universal behaviors in all antiferromagnetic molecular magnets. The analytical results are complemented by exact diagonalization calculation.Comment: 6 pages, 1 figur

Effects of arbitrarily directed field on spin phase oscillations in biaxial molecular magnets

Quantum phase interference and spin-parity effects are studied in biaxial molecular magnets in a magnetic field at an arbitrarily directed angle. The calculations of the ground-state tunnel splitting are performed on the basis of the instanton technique in the spin-coherent-state path-integral representation, and complemented by exactly numerical diagonalization. Both the Wentzel-Kramers-Brillouin exponent and the preexponential factor are obtained for the entire region of the direction of the field. Our results show that the tunnel splitting oscillates with the field for the small field angle, while for the large field angle the oscillation is completely suppressed. This distinct angular dependence, together with the dependence of the tunnel splitting on the field strengh, provide an independent test for spin-parity effects in biaxial molecular magnets. The analytical results for the molecular Fe$_{8}$ magnet, are found to be in good areement with the numerical simulations, which suggests that even the molecular magnet with total spin S=10 is large enough to be treated as a giant spin system.Comment: 19 pages, 5 figure

Energy Efficiency of Network Cooperation for Cellular Uplink Transmissions

There is a growing interest in energy efficient or so-called "green" wireless communication to reduce the energy consumption in cellular networks. Since today's wireless terminals are typically equipped with multiple network access interfaces such as Bluetooth, Wi-Fi, and cellular networks, this paper investigates user terminals cooperating with each other in transmitting their data packets to a base station (BS) by exploiting the multiple network access interfaces, referred to as inter-network cooperation, to improve the energy efficiency in cellular uplink transmission. Given target outage probability and data rate requirements, we develop a closed-form expression of energy efficiency in Bits-per-Joule for the inter-network cooperation by taking into account the path loss, fading, and thermal noise effects. Numerical results show that when the cooperating users move towards to each other, the proposed inter-network cooperation significantly improves the energy efficiency as compared with the traditional non-cooperation and intra-network cooperation. This implies that given a certain amount of bits to be transmitted, the inter-network cooperation requires less energy than the traditional non-cooperation and intra-network cooperation, showing the energy saving benefit of inter-network cooperation.Comment: in Proceedings of the 2013 IEEE International Conference on Communications (IEEE ICC 2013), Budapest, Hungary, June 201