Interacting topological phases in thin films of topological mirror Kondo insulators

We study the interaction effects on thin films of topological mirror Kondo insulators (TMKI), where the strong interaction is expected to play an important role. Our study has led to the following results: (1) We identify a rich phase diagram of non-interacting TMKI with different mirror Chern numbers in the monolayer and bilayer thin films; (2) We obtain the phase diagram with interaction and identify the regimes of interaction parameters to mimic bosonic symmetry protected topological phases with either gapless bosonic modes or spontaneous mirror symmetry breaking at the boundary; (3) For the spontaneous mirror symmetry breaking boundary, we also study various domain-wall defects between different mirror symmetry breaking order parameters at the boundary. Our results reveal that the thin film TMKI serves as an intriguing platform for the experimental studies of interacting topological phases.Comment: 11 pages, 4 figure

Performance Enhancement for High-order Gas-kinetic Scheme Based on WENO-adaptive-order Reconstruction

High-order gas-kinetic scheme (HGKS) has been well-developed in the past years. Abundant numerical tests including hypersonic flow, turbulence, and aeroacoustic problems, have been used to validate its accuracy, efficiency, and robustness. However, there are still rooms for its further improvement. Firstly, the reconstruction in the previous scheme mainly achieves a third-order accuracy for the initial non-equilibrium states. At the same time, the equilibrium state in space and time in HGKS has to be reconstructed separately. Secondly, it is complicated to get reconstructed data at Gaussian points from the WENO-type method in high dimensions. For HGKS, besides the point-wise values at the Gaussian points it also requires the slopes in both normal and tangential directions of a cell interface. Thirdly, there exists visible spurious overshoot/undershoot at weak discontinuities from the previous HGKS with the standard WENO reconstruction. In order to overcome these difficulties, in this paper we use an improved reconstruction for HGKS. The WENO with adaptive order (WENO-AO) method is implemented for reconstruction.A whole polynomial inside each cell is provided in WENO-AO reconstruction. The HGKS becomes simpler than the previous one with the direct implementation of cell interface values and their slopes from WENO-AO. The additional reconstruction of equilibrium state at the beginning of each time step can be avoided as well by dynamically merging the reconstructed non-equilibrium slopes. The new HGKS essentially releases or totally removes the above existing problems in previous HGKS. The accuracy of the scheme from 1D to 3D from the new HGKS can recover the theoretical order of accuracy of the WENO reconstruction.In the two- and three-dimensional simulations, the new HGKS shows better robustness and efficiency than the previous scheme in all test cases

A Hopf algebra on subgraphs of a graph

In this paper, we construct a bialgebraic and further a Hopf algebraic structure on top of subgraphs of a given graph. Further, we give the dual structure of this Hopf algebraic structure. We study the algebra morphisms induced by graph homomorphisms, and obtain a covariant functor from a graph category to an algebra category.Comment: 16 page

Q factor in numerical simulations of DPSK with optical delay demodulation

A simple model is used to estimate the Q factor in numerical simulations of differential phase shift keying (DPSK) with optical delay demodulation and balanced detection. It is found that an alternative definition of Q is needed for DPSK in order to have a more accurate prediction of the bit error ratio (BER).Comment: This is a manuscript that was rejected by IEEE Photonics Technology Letters in 2002 (Manucript #9527

Optimal Resource Allocation for Wireless Powered Mobile Edge Computing with Dynamic Task Arrivals

This paper considers a wireless powered multiuser mobile edge computing (MEC) system, where a multi-antenna access point (AP) employs the radio-frequency (RF) signal based wireless power transfer (WPT) to charge a number of distributed users, and each user utilizes the harvested energy to execute computation tasks via local computing and task offloading. We consider the frequency division multiple access (FDMA) protocol to support simultaneous task offloading from multiple users to the AP. Different from previous works that considered one-shot optimization with static task models, we study the joint computation and wireless resource allocation optimization with dynamic task arrivals over a finite time horizon consisting of multiple slots. Under this setup, our objective is to minimize the system energy consumption including the AP's transmission energy and the MEC server's computing energy over the whole horizon, by jointly optimizing the transmit energy beamforming at the AP, and the local computing and task offloading strategies at the users over different time slots. To characterize the fundamental performance limit of such systems, we focus on the offline optimization by assuming the task and channel information are known a-priori at the AP. In this case, the energy minimization problem corresponds to a convex optimization problem. Leveraging the Lagrange duality method, we obtain the optimal solution to this problem in a well structure. It is shown that in order to maximize the system energy efficiency, the optimal number of task input-bits at each user and the AP are monotonically increasing over time, and the offloading strategies at different users depend on both the wireless channel conditions and the task load at the AP. Numerical results demonstrate the benefit of the proposed joint-WPT-MEC design over alternative benchmark schemes without such joint design.Comment: 7 pages, 3 figures, and Accepted by IEEE ICC 2019, Shanghai, Chin

A Multi-scale Monte Carlo Method for Electrolytes

Artifacts arise in the simulations of electrolytes using periodic boundary conditions (PBC). We show the origin of these artifacts are the periodic image charges and the constraint of charge neutrality inside the simulation box, both of which are unphysical from the view point of real systems. To cure these problems, we introduce a multi-scale Monte Carlo method, where ions inside a spherical cavity are simulated explicitly, whilst ions outside are treated implicitly using continuum theory. Using the method of Debye charging, we explicitly derive the effective interactions between ions inside the cavity, arising due to the fluctuations of ions outside. We find that these effective interactions consist of two types: 1) a constant cavity potential due to the asymmetry of the electrolyte, and 2) a reaction potential that depends on the positions of all ions inside. Combining the Grand Canonical Monte Carlo (GCMC) with a recently developed fast algorithm based of image charge method, we perform a multi-scale Monte Carlo simulation of symmetric electrolytes, and compare it with other simulation methods, including PBC+GCMC method, as well as large scale Monte Carlo simulation. We demonstrate that our multi-scale MC method is capable of capturing the correct physics of a large system using a small scale simulation.Comment: 14 pages, 11 figure

Bi-Directional Differentiable Input Reconstruction for Low-Resource Neural Machine Translation

We aim to better exploit the limited amounts of parallel text available in low-resource settings by introducing a differentiable reconstruction loss for neural machine translation (NMT). This loss compares original inputs to reconstructed inputs, obtained by back-translating translation hypotheses into the input language. We leverage differentiable sampling and bi-directional NMT to train models end-to-end, without introducing additional parameters. This approach achieves small but consistent BLEU improvements on four language pairs in both translation directions, and outperforms an alternative differentiable reconstruction strategy based on hidden states.Comment: Accepted at NAACL 201

Solve Traveling Salesman Problem by Monte Carlo Tree Search and Deep Neural Network

We present a self-learning approach that combines deep reinforcement learning and Monte Carlo tree search to solve the traveling salesman problem. The proposed approach has two advantages. First, it adopts deep reinforcement learning to compute the value functions for decision, which removes the need of hand-crafted features and labelled data. Second, it uses Monte Carlo tree search to select the best policy by comparing different value functions, which increases its generalization ability. Experimental results show that the proposed method performs favorably against other methods in small-to-medium problem settings. And it shows comparable performance as state-of-the-art in large problem setting.Comment: Was previously submitted to ICAPS201

Modeling aggressive market order placements with Hawkes factor models

Price changes are induced by aggressive market orders in stock market. We introduce a bivariate marked Hawkes process to model aggressive market order arrivals at the microstructural level. The order arrival intensity is marked by an exogenous part and two endogenous processes reflecting the self-excitation and cross-excitation respectively. We calibrate the model for an SSE stock. We find that the exponential kernel with a smooth cut-off (i.e. the subtraction of two exponentials) produces much better calibration than the monotonous exponential kernel (i.e. the sum of two exponentials). The exogenous baseline intensity explains the $U$-shaped intraday pattern. Our empirical results show that the endogenous submission clustering is mainly caused by self-excitation rather than cross-excitation.Comment: 9 pages, 7 figure

Mellin Transform and Image Charge Method for Dielectric Sphere in an Electrolyte

We revisit the image charge method for the Green's function problem of the Poisson-Boltzmann equation for a dielectric sphere immersed in ionic solutions. Using finite Mellin transformation, we represent the reaction potential due to a source charge inside the sphere in terms of one dimensional distribution of image charges. The image charges are generically composed of a point image at the Kelvin point and a line image extending from the Kelvin point to infinity with an oscillatory line charge strength. We further develop an efficient and accurate algorithm for discretization of the line image using Pad\'e approximation and finite fraction expansion. Finally we illustrate the power of our method by applying it in a multiscale reaction-field Monte Carlo simulation of monovalent electrolytes.Comment: 20 pages, 7 figures, version to be published in SIAM J. Appl. Mat