Entropy/Area spectra of the charged black hole from quasinormal modes

With the new physical interpretation of quasinormal modes proposed by Maggiore, the quantum area spectra of black holes have been investigated recently. Adopting the modified Hod's treatment, results show that the area spectra for black holes are equally spaced and the spacings are in a unified form, $\triangle A=8\pi \hbar$, in Einstein gravity. On the other hand, following Kunstatter's method, the studies show that the area spectrum for a nonrotating black hole with no charge is equidistant. And for a rotating (or charged) black hole, it is also equidistant and independent of the angular momentum $J$ (or charge $q$) when the black hole is far from the extremal case. In this paper, we mainly deal with the area spectrum of the stringy charged Garfinkle-Horowitz-Strominger black hole, originating from effective action that emerges in the low-energy string theory. We find that both methods give the same results-that the area spectrum is equally spaced and does not depend on the charge $q$. Our study may provide new insights into understanding the area spectrum and entropy spectrum for stringy black holes.Comment: 13 pages, no figure

Existence of optimal delay-dependent control for finite-horizon continuous-time Markov decision process

This paper intends to study the optimal control problem for the continuous-time Markov decision process with denumerable states and compact action space. The admissible controls depend not only on the current state of the jumping process but also on its history. By the compactification method, we show the existence of an optimal delay-dependent control under some explicit conditions, and further establish the dynamic programming principle. Moreover, we show that the value function is the unique viscosity solution of certain Hamilton-Jacobi-Bellman equation which does not depend on the delay-dependent control policies. Consequently, under our explicit conditions, there is no impact on the value function to make decision depending on or not on the history of the jumping process.Comment: 22 page

Practical Block-wise Neural Network Architecture Generation

Convolutional neural networks have gained a remarkable success in computer vision. However, most usable network architectures are hand-crafted and usually require expertise and elaborate design. In this paper, we provide a block-wise network generation pipeline called BlockQNN which automatically builds high-performance networks using the Q-Learning paradigm with epsilon-greedy exploration strategy. The optimal network block is constructed by the learning agent which is trained sequentially to choose component layers. We stack the block to construct the whole auto-generated network. To accelerate the generation process, we also propose a distributed asynchronous framework and an early stop strategy. The block-wise generation brings unique advantages: (1) it performs competitive results in comparison to the hand-crafted state-of-the-art networks on image classification, additionally, the best network generated by BlockQNN achieves 3.54% top-1 error rate on CIFAR-10 which beats all existing auto-generate networks. (2) in the meanwhile, it offers tremendous reduction of the search space in designing networks which only spends 3 days with 32 GPUs, and (3) moreover, it has strong generalizability that the network built on CIFAR also performs well on a larger-scale ImageNet dataset.Comment: Accepted to CVPR 201

Time-Dependent Scalar Fields in Modified Gravities in a Stationary Spacetime

Most no-hair theorems involve the assumption that the scalar field is independent of time. Recently in [Phys. Rev. D90 (2014) 041501(R)] the existence of time-dependent scalar hair outside a stationary black hole in general relativity was ruled out. We generalize this work to modified gravities and non-minimally coupled scalar field with an additional assumption that the spacetime is axisymmetric. It is shown that in higher-order gravity such as metric $f(R)$ gravity the time-dependent scalar hair doesn't exist. While in Palatini $f(R)$ gravity and non-minimally coupled case the time-dependent scalar hair may exist.Comment: 6 pages, no figure