Classical Aspects of Higher Spin Topologically Massive Gravity

We study the classical solutions of three dimensional topologically massive gravity (TMG) and its higher spin generalization, in the first order formulation. The action of higher spin TMG has been proposed in arXiv:1110.5113 to be of a Chern-Simons-like form. The equations of motion are more complicated than the ones in pure higher spin AdS$_3$ gravity, but are still tractable. As all the solutions in higher spin gravity are automatically the solutions of higher spin TMG, we focus on other solutions. We manage to find the AdS pp-wave solutions with higher spin hair, and find that the nonvanishing higher spin fields may or may not modify the pp-wave geometry. In order to discuss the warped spacetime, we introduce the notion of special Killing vector, which is defined to be the symmetry on the frame-like fields. We reproduce various warped spacetimes of TMG in our framework, with the help of special Killing vectors.Comment: 25 pages; minor corrections, references added, published versio

Holographic R\'enyi entropy for CFT with WW symmetry

In this paper we investigate the holographic R\'enyi entropy of two disjoint intervals on complex plane with small cross ratio $x$ for conformal field theory with $W$ symmetry in the ground state, which could be dual to a higher spin AdS$_3$ gravity. We focus on the cases of $W_3$ and $W_4$ symmetries. In order to see the nontrivial contributions from the $W$ fields, we calculate the R\'enyi entropy in the expansion of $x$ to order $x^8$ in both the gravity and the CFT sides. In the gravity side the classical contributions to the entanglement entropy is still given by the Ryu-Takayanagi area formula under the reasonable assumption, while the 1-loop quantum corrections have to take into account of the contributions not only from massless gravitons, but also from massless higher spin fields. In the CFT side we still use the operator product expansion of twist operators in the small interval limit, but now we need to consider the quasiprimary fields constructed from $W$ fields, besides the ones from Virasoro Verma module. In the large central charge limit, we obtain the classical, 1-loop, 2-loop, and 3-loop parts of the R\'enyi entropy. The classical and 1-loop results in the gravity and the CFT sides are in exact match. This confirms the higher spin gravity/CFT correspondence, and also supports the holographic computation of R\'enyi entanglement entropy, including the quantum correction, in both the AdS$_3$ gravity and the higher spin AdS$_3$ gravity.Comment: 32 pages, published versio

Hidden Conformal Symmetry of Extremal Black Holes

We study the hidden conformal symmetry of the extremal black holes. We introduce a new set of conformal coordinates to write the $SL(2,R)$ generators. We find that the Laplacian of the scalar field in many extremal black holes could be written in terms of the $SL(2,R)$ quadratic Casimir. This suggests that there exist dual CFT descriptions of these black holes. From the conformal coordinates, the temperatures of the dual CFTs could be read directly. For the extremal black hole, the Hawking temperature is vanishing. Correspondingly, only the left (right) temperature of the dual CFT is non-vanishing and the excitations of the other sector are suppressed. In the probe limit, we compute the scattering amplitudes of the scalar off the extremal black holes and find perfect agreement with the CFT prediction.Comment: 16 pages; Published versio

Tensorized Self-Attention: Efficiently Modeling Pairwise and Global Dependencies Together

Neural networks equipped with self-attention have parallelizable computation, light-weight structure, and the ability to capture both long-range and local dependencies. Further, their expressive power and performance can be boosted by using a vector to measure pairwise dependency, but this requires to expand the alignment matrix to a tensor, which results in memory and computation bottlenecks. In this paper, we propose a novel attention mechanism called "Multi-mask Tensorized Self-Attention" (MTSA), which is as fast and as memory-efficient as a CNN, but significantly outperforms previous CNN-/RNN-/attention-based models. MTSA 1) captures both pairwise (token2token) and global (source2token) dependencies by a novel compatibility function composed of dot-product and additive attentions, 2) uses a tensor to represent the feature-wise alignment scores for better expressive power but only requires parallelizable matrix multiplications, and 3) combines multi-head with multi-dimensional attentions, and applies a distinct positional mask to each head (subspace), so the memory and computation can be distributed to multiple heads, each with sequential information encoded independently. The experiments show that a CNN/RNN-free model based on MTSA achieves state-of-the-art or competitive performance on nine NLP benchmarks with compelling memory- and time-efficiency

Energy Efficient User Association and Power Allocation in Millimeter Wave Based Ultra Dense Networks with Energy Harvesting Base Stations

Millimeter wave (mmWave) communication technologies have recently emerged as an attractive solution to meet the exponentially increasing demand on mobile data traffic. Moreover, ultra dense networks (UDNs) combined with mmWave technology are expected to increase both energy efficiency and spectral efficiency. In this paper, user association and power allocation in mmWave based UDNs is considered with attention to load balance constraints, energy harvesting by base stations, user quality of service requirements, energy efficiency, and cross-tier interference limits. The joint user association and power optimization problem is modeled as a mixed-integer programming problem, which is then transformed into a convex optimization problem by relaxing the user association indicator and solved by Lagrangian dual decomposition. An iterative gradient user association and power allocation algorithm is proposed and shown to converge rapidly to an optimal point. The complexity of the proposed algorithm is analyzed and the effectiveness of the proposed scheme compared with existing methods is verified by simulations.Comment: to appear, IEEE Journal on Selected Areas in Communications, 201

Optimal cloud resource auto-scaling for web applications

In the on-demand cloud environment, web application providers have the potential to scale virtual resources up or down to achieve cost-effective outcomes. True elasticity and cost-effectiveness in the pay-per-use cloud business model, however, have not yet been achieved. To address this challenge, we propose a novel cloud resource auto-scaling scheme at the virtual machine (VM) level for web application providers. The scheme automatically predicts the number of web requests and discovers an optimal cloud resource demand with cost-latency trade-off. Based on this demand, the scheme makes a resource scaling decision that is up or down or NOP (no operation) in each time-unit re-allocation. We have implemented the scheme on the Amazon cloud platform and evaluated it using three real-world web log datasets. Our experiment results demonstrate that the proposed scheme achieves resource auto-scaling with an optimal cost-latency trade-off, as well as low SLA violations. © 2013 IEEE