Network of Recurrent Neural Networks

We describe a class of systems theory based neural networks called "Network Of Recurrent neural networks" (NOR), which introduces a new structure level to RNN related models. In NOR, RNNs are viewed as the high-level neurons and are used to build the high-level layers. More specifically, we propose several methodologies to design different NOR topologies according to the theory of system evolution. Then we carry experiments on three different tasks to evaluate our implementations. Experimental results show our models outperform simple RNN remarkably under the same number of parameters, and sometimes achieve even better results than GRU and LSTM.Comment: Under review as a conference paper at AAAI 201

Water waves problem with surface tension in a corner domain II: the local well-posednes

Based on the a priori estimates in our previous work \cite{MW}, we continue to investigate the water-waves problem in a bounded two dimensional corner domain in this paper. We prove the local well-posedness of the solution to the water-waves system when the contact angles are less than $\frac{\pi}{16}$.Comment: 38 page

Water waves problem with surface tension in a corner domain I: A priori estimates with constrained contact angle

We study the two dimensional water waves problem with surface tension in the case when there is a non-zero contact angle between the free surface and the bottom. In the presence of surface tension, dissipations take place at the contact point. Moreover, when the contact angle is less than $\pi/6$, no singularity appears in our settings. Using elliptic estimates in corner domains and a geometric approach, we prove an a priori estimate for the water waves problem.Comment: 37 pages, 1 figure

Elliptic estimates for Dirichlet-Neumann operator on a corner domain

We consider the elliptic estimates for Dirichlet-Neumann operator related to the water-wave problem on a two-dimensional corner domain in this paper. Due to the singularity of the boundary, there will be singular parts in the solution of the elliptic problem for D-N operator. To begin with, we study elliptic problems with mixed boundary condition to derive singularity decompositions and estimates. Based on the analysis, we present the estimates for both D-N operator and its shape derivative with the existence of singular parts.Comment: 54 pages, 1 figure

The Existence of Featureless Paramagnets on the Square and the Honeycomb Lattices in 2+1D

The peculiar features of quantum magnetism sometimes forbid the existence of gapped `featureless' paramagnets which are fully symmetric and unfractionalized. The Lieb-Schultz-Mattis theorem is an example of such a constraint, but it is not known what the most general restriction might be. We focus on the existence of featureless paramagnets on the spin-1 square lattice and the spin-1 and spin-1/2 honeycomb lattice with spin rotation and space group symmetries in 2+1D. Although featureless paramagnet phases are not ruled out by any existing theorem, field theoretic arguments disfavor their existence. Nevertheless, by generalizing the construction of Affleck, Kennedy, Lieb and Tasaki to a class we call `slave-spin' states, we propose featureless wave functions for these models. The featureless-ness of the spin-1 slave-spin states on the square and honeycomb lattice are verified both analytically and numerically, but the status of the spin-1/2 honeycomb state remains unclear.Comment: 11 pages, 16 figures, Added additional reference

Moire Insulators viewed as the Surface of three dimensional Symmetry Protected Topological Phases

Recently, correlated physics such as superconductivity and insulator at commensurate fractional electron fillings has been discovered in several different systems with Moire superlattice and narrow electron bands near charge neutrality. Before we learn more experimental details and the accurate microscopic models describing the insulators, some general conclusions can already be made about these systems, simply based on their symmetries and electron fillings. The insulator in the Moire superlattice is described by an effective spin-orbital model with approximate higher symmetries than ordinary spin systems. We demonstrate that both the insulators observed at the 1/2 and 1/4 fillings away from the charge neutrality can be viewed as the boundary of a three-dimensional bosonic symmetry protected topological phase, and hence have the 't Hooft anomaly once the spatial symmetries are viewed as internal symmetries.Comment: 9 pages, 2 figure

Paired Superfluidity and Fractionalized Vortices in Spin-orbit Coupled Bosons

In this letter we study finite temperature properties of spin-1/2 interacting bosons with spin-orbit coupling in two dimensions. When the ground state has stripe order, we show that thermal fluctuations will first melt the stripe order and lead to a superfluid of boson pairs if the spin-orbit coupling is isotropic or nearly isotropic. Such a phase supports fractionalized quantum vortices. The Kosterlize-Thouless transition from superfluid to normal state is driven by proliferation of half vortices. When the ground state is a plane wave state, the transition to normal state is driven by conventional Kosterlize-Thouless transition. However, the critical temperature will drop to zero for isotropic spin-orbit coupling.Comment: 4+2 pages, 4 figure

Opportunistic Jamming for Enhancing Security: Stochastic Geometry Modeling and Analysis

This correspondence studies the secrecy communication of the single-input single-output multi-eavesdropper (SISOME) channel with multiple single-antenna jammers, where the jammers and eavesdroppers are distributed according to the independent two-dimensional homogeneous Poisson point process (PPP). For enhancing the physical layer security, we propose an opportunistic multiple jammer selection scheme, where the jammers whose channel gains to the legitimate receiver less than a threshold, are selected to transmit independent and identically distributed (\emph{i.i.d.}) Gaussian jamming signals to confound the eavesdroppers. We characterize the secrecy throughput achieved by our proposed jammer selection scheme, and show that the secrecy throughput is a quasi-concave function of the selection threshold.Comment: IEEE Transactions on Vehicular Technology, to appea

Spin-Orbit Coupled Spinor Bose-Einstein Condensates

An effective spin-orbit coupling can be generated in cold atom system by engineering atom-light interactions. In this letter we study spin-1/2 and spin-1 Bose-Einstein condensates with Rashba spin-orbit coupling, and find that the condensate wave function will develop non-trivial structures. From numerical simulation we have identified two different phases. In one phase the ground state is a single plane wave, and often we find the system splits into domains and an array of vortices plays the role as domain wall. In this phase, time-reversal symmetry is broken. In the other phase the condensate wave function is a standing wave and it forms spin stripe. The transition between them is driven by interactions between bosons. We also provide an analytical understanding of these results and determines the transition point between the two phases.Comment: 5 pages, 4 figure

Physical Layer Security in Millimeter Wave Cellular Networks

Recent researches show that millimeter wave (mmWave) communications can offer orders of magnitude increases in the cellular capacity. However, the secrecy performance of a mmWave cellular network has not been investigated so far. Leveraging the new path-loss and blockage models for mmWave channels, which are significantly different from the conventional microwave channel, this paper comprehensively studies the network-wide physical layer security performance of the downlink transmission in a mmWave cellular network under a stochastic geometry framework. We first study the secure connectivity probability and the average number of perfect communication links per unit area in a noise-limited mmWave network for both non-colluding and colluding eavesdroppers scenarios, respectively. Then, we evaluate the effect of the artificial noise (AN) on the secrecy performance, and derive the analysis result of average number of perfect communication links per unit area in an interference-limited mmWave network. Numerical results are demonstrated to show the network-wide secrecy performance, and provide interesting insights into how the secrecy performance is influenced by various network parameters: antenna array pattern, base station (BS) intensity, and AN power allocation, etc