We show that the solution of the free-boundary incompressible ideal magnetohydrodynamic (MHD) equations with surface tension converges to that of the free-boundary incompressible ideal MHD equations without surface tension given the Rayleigh-Taylor s
ign condition holds true initially. This result is a continuation of the authors previous works [13,27,12]. Our proof is based on the combination of the techniques developed in our previous works [13,27,12], Alinhac good unknowns, and a crucial anti-symmetric structure on the boundary.
In this paper we prove the local well-posedness (LWP) for the 3D compressible Euler equations describing the motion of a liquid in an unbounded initial domain with moving boundary. The liquid is under the influence of gravity but without surface tens
ion, and it is not assumed to be irrotational. We apply the tangential smoothing method introduced in [9,10] to construct the approximation system with energy estimates uniform in the smooth parameter. It should be emphasized that, when doing the nonlinear a priori estimates, we need neither the higher order wave equation of the pressure and delicate elliptic estimates, nor the higher regularity on the flow-map or initial vorticity. Instead, we adapt the Alinhacs good unknowns to the estimates of full spatial derivatives.
The interlayer coupling in van der Waals heterostructures governs a variety of optical and electronic properties. The intrinsic dipole moment of Janus transition metal dichalcogenides (TMDs) offers a simple and versatile approach to tune the interlay
er interactions. In this work, we demonstrate how the van der Waals interlayer coupling and charge transfer of Janus MoSSe/MoS2 heterobilayers can be tuned by the twist angle and interface composition. Specifically, the Janus heterostructures with a sulfur/sulfur (S/S) interface display stronger interlayer coupling than the heterostructures with a selenium/sulfur (Se/S) interface as shown by the low-frequency Raman modes. The differences in interlayer interactions are explained by the interlayer distance computed by density-functional theory (DFT). More intriguingly, the built-in electric field contributed by the charge density redistribution and interlayer coupling also play important roles in the interfacial charge transfer. Namely, the S/S and Se/S interfaces exhibit different levels of PL quenching of MoS2 A exciton, suggesting the enhanced and reduced charge transfer at the S/S and Se/S interface, respectively. Our work demonstrates how the asymmetry of Janus TMDs can be used to tailor the interfacial interactions in van der Waals heterostructures.
Pairing symmetry which characterizes the superconducting pairing mechanism is normally determined by measuring the superconducting gap structure ($|Delta_k|$). Here, we report the measurement of a strain-induced gap modulation ($partial|Delta_k|$) in
uniaxially strained Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ utilizing angle-resolved photoemission spectroscopy and $in$-$situ$ strain-tuning. We found that the uniaxial strain drives Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ into a nematic superconducting state which breaks the four-fold rotational symmetry of the superconducting pairing. The superconducting gap increases on the $d_{yz}$ electron and hole pockets while it decreases on the $d_{xz}$ counterparts. Such orbital selectivity indicates that orbital-selective pairing exists intrinsically in non-nematic iron-based superconductors. The $d_{xz}$ and $d_{yz}$ pairing channels are balanced originally in the pristine superconducting state, but become imbalanced under uniaxial strain. Our results highlight the important role of intra-orbital scattering in mediating the superconducting pairing in iron-based superconductors. It also highlights the measurement of $partial|Delta_k|$ as an effective way to characterize the superconducting pairing from a perturbation perspective.
This paper describes a novel design of a neural network-based speech generation model for learning prosodic representation.The problem of representation learning is formulated according to the information bottleneck (IB) principle. A modified VQ-VAE
quantized layer is incorporated in the speech generation model to control the IB capacity and adjust the balance between reconstruction power and disentangle capability of the learned representation. The proposed model is able to learn word-level prosodic representations from speech data. With an optimized IB capacity, the learned representations not only are adequate to reconstruct the original speech but also can be used to transfer the prosody onto different textual content. Extensive results of the objective and subjective evaluation are presented to demonstrate the effect of IB capacity control, the effectiveness, and potential usage of the learned prosodic representation in controllable neural speech generation.
In probability theory, the independence is a very fundamental concept, but with a little mystery. People can always easily manipulate it logistically but not geometrically, especially when it comes to the independence relationships among more that tw
o variables, which may also involve conditional independence. Here I am particularly interested in visualizing Markov chains which have the well known memoryless property. I am not talking about drawing the transition graph, instead, I will draw all events of the Markov process in a single plot. Here, to simplify the question, this work will only consider dichotomous variables, but all the methods actually can be generalized to arbitrary set of discrete variables.
We consider 3D free-boundary compressible ideal magnetohydrodynamic (MHD) system under the Rayleigh-Taylor sign condition. It describes the motion of a free-surface perfect conducting fluid in an electro-magnetic field. The local well-posedness was r
ecently proved by Trakhinin and Wang [66] by using Nash-Moser iteration. In this paper, we prove the a priori estimates without loss of regularity for the free-boundary compressible MHD system in Lagrangian coordinates in anisotropic Sobolev space, with more regularity tangential to the boundary than in the normal direction. It is based on modified Alinhac good unknowns, which take into account the covariance under the change of coordinates to avoid the derivative loss; full utilization of the cancellation structures of MHD system, to turn normal derivatives into tangential ones; and delicate analysis in anisotropic Sobolev spaces. Our method is also completely applicable to compressible Euler equations and thus yields an alternative estimate for compressible Euler equations without the analysis of div-curl decomposition or the wave equation in Lindblad-Luo [42], that do not work for compressible MHD. To the best of our knowledge, we establish the first result on the energy estimates without loss of regularity for the free-boundary problem of compressible ideal MHD.
In recent years, the size of pre-trained language models (PLMs) has grown by leaps and bounds. However, efficiency issues of these large-scale PLMs limit their utilization in real-world scenarios. We present a suite of cost-effective techniques for t
he use of PLMs to deal with the efficiency issues of pre-training, fine-tuning, and inference. (1) We introduce knowledge inheritance to accelerate the pre-training process by exploiting existing PLMs instead of training models from scratch. (2) We explore the best practice of prompt tuning with large-scale PLMs. Compared with conventional fine-tuning, prompt tuning significantly reduces the number of task-specific parameters. (3) We implement a new inference toolkit, namely InfMoE, for using large-scale PLMs with limited computational resources. Based on our cost-effective pipeline, we pre-train two models: an encoder-decoder bilingual model with 11 billion parameters (CPM-2) and its corresponding MoE version with 198 billion parameters. In our experiments, we compare CPM-2 with mT5 on downstream tasks. Experimental results show that CPM-2 has excellent general language intelligence. Moreover, we validate the efficiency of InfMoE when conducting inference of large-scale models having tens of billions of parameters on a single GPU. All source code and model parameters are available at https://github.com/TsinghuaAI/CPM.
In this paper, we consider a transfer Reinforcement Learning (RL) problem in continuous state and action spaces, under unobserved contextual information. For example, the context can represent the mental view of the world that an expert agent has for
med through past interactions with this world. We assume that this context is not accessible to a learner agent who can only observe the expert data. Then, our goal is to use the context-aware expert data to learn an optimal context-unaware policy for the learner using only a few new data samples. Such problems are typically solved using imitation learning that assumes that both the expert and learner agents have access to the same information. However, if the learner does not know the expert context, using the expert data alone will result in a biased learner policy and will require many new data samples to improve. To address this challenge, in this paper, we formulate the learning problem as a causal bound-constrained Multi-Armed-Bandit (MAB) problem. The arms of this MAB correspond to a set of basis policy functions that can be initialized in an unsupervised way using the expert data and represent the different expert behaviors affected by the unobserved context. On the other hand, the MAB constraints correspond to causal bounds on the accumulated rewards of these basis policy functions that we also compute from the expert data. The solution to this MAB allows the learner agent to select the best basis policy and improve it online. And the use of causal bounds reduces the exploration variance and, therefore, improves the learning rate. We provide numerical experiments on an autonomous driving example that show that our proposed transfer RL method improves the learners policy faster compared to existing imitation learning methods and enjoys much lower variance during training.
We prove the local well-posedness of the 3D free-boundary incompressible ideal magnetohydrodynamics (MHD) equations with surface tension, which describe the motion of a perfect conducting fluid in an electromagnetic field. We adapt the ideas develope
d in the remarkable paper [11] by Coutand and Shkoller to generate an approximate problem with artificial viscosity indexed by $kappa>0$ whose solution converges to that of the MHD equations as $kappato 0$. However, the local well-posedness of the MHD equations is no easy consequence of Euler equations thanks to the strong coupling between the velocity and magnetic fields. This paper is the continuation of the second and third authors previous work [38] in which the a priori energy estimate for incompressible free-boundary MHD with surface tension is established. But the existence is not a trivial consequence of the a priori estimate as it cannot be adapted directly to the approximate problem due to the loss of the symmetric structure.
