Conditional Log-Laplace Functionals of Immigration Superprocesses with Dependent Spatial Motion

A non-critical branching immigration superprocess with dependent spatial motion is constructed and characterized as the solution of a stochastic equation driven by a time-space white noise and an orthogonal martingale measure. A representation of its conditional log-Laplace functionals is established, which gives the uniqueness of the solution and hence its Markov property. Some properties of the superprocess including an ergodic theorem are also obtained

RKKY interaction in three-dimensional electron gases with linear spin-orbit coupling

We theoretically study the impacts of linear spin-orbit coupling (SOC) on the Ruderman-Kittel-Kasuya-Yosida interaction between magnetic impurities in two kinds of three-dimensional noncentrosymmetric systems. It has been found that linear SOCs lead to the Dzyaloshinskii-Moriya interaction and the Ising interaction, in addition to the conventional Heisenberg interaction. These interactions possess distinct range functions from three dimensional electron gases and Dirac/Weyl semimetals. In the weak SOC limit, the Heisenberg interaction dominates over the other two interactions in a moderately large region of parameters. Sufficiently strong Rashba SOC makes the Dzyaloshinskii-Moriya interaction or the Ising interaction dominate over the Heisenberg interaction in some regions. The change in topology of the Fermi surface leads to some quantitative changes in periods of oscillations of range functions. The anisotropy of Ruderman-Kittel-Kasuya-Yosida interaction in bismuth tellurohalides family BiTe$X$ ($X$ = Br, Cl, and I) originates from both the specific form of Rashba SOC and the anisotropic effective mass. Our work provides some insights into understanding observed spin textures and the application of these materials in spintronics.Comment: 11 pages, 4 figures, Final Version in PR

Multi-channel Encoder for Neural Machine Translation

Attention-based Encoder-Decoder has the effective architecture for neural machine translation (NMT), which typically relies on recurrent neural networks (RNN) to build the blocks that will be lately called by attentive reader during the decoding process. This design of encoder yields relatively uniform composition on source sentence, despite the gating mechanism employed in encoding RNN. On the other hand, we often hope the decoder to take pieces of source sentence at varying levels suiting its own linguistic structure: for example, we may want to take the entity name in its raw form while taking an idiom as a perfectly composed unit. Motivated by this demand, we propose Multi-channel Encoder (MCE), which enhances encoding components with different levels of composition. More specifically, in addition to the hidden state of encoding RNN, MCE takes 1) the original word embedding for raw encoding with no composition, and 2) a particular design of external memory in Neural Turing Machine (NTM) for more complex composition, while all three encoding strategies are properly blended during decoding. Empirical study on Chinese-English translation shows that our model can improve by 6.52 BLEU points upon a strong open source NMT system: DL4MT1. On the WMT14 English- French task, our single shallow system achieves BLEU=38.8, comparable with the state-of-the-art deep models.Comment: Accepted by AAAI-201

The Large Deviation Principle and Steady-state Fluctuation Theorem for the Entropy Production Rate of a Stochastic Process in Magnetic Fields

Fluctuation theorem is one of the major achievements in the field of nonequilibrium statistical mechanics during the past two decades. Steady-state fluctuation theorem of sample entropy production rate in terms of large deviation principle for diffusion processes have not been rigorously proved yet due to technical difficulties. Here we give a proof for the steady-state fluctuation theorem of a diffusion process in magnetic fields, with explicit expressions of the free energy function and rate function. The proof is based on the Karhunen-Lo\'{e}ve expansion of complex-valued Ornstein-Uhlenbeck process