Universal impurity-induced bound state in topological superfluids

We predict a universal mid-gap bound state in topological superfluids, induced by either non-magnetic or magnetic impurities in the strong scattering limit. This universal state is similar to the lowest-energy Caroli-de Gennes-Martricon bound state in a vortex core, but is bound to localized impurities. We argue that the observation of such a universal bound state can be a clear signature for identifying topological superfluids. We theoretically examine our argument for a spin-orbit coupled ultracold atomic Fermi gas trapped in a two-dimensional harmonic potential, by performing extensive self-consistent calculations within the mean-field Bogoliubov-de Gennes theory. A realistic scenario for observing universal bound state in ultracold $^{40}$K atoms is proposed.Comment: 5 pages + 4 figures; published in PRL; see the relevant study in 1D: Phys. Rev. A 87, 013622 (2013); see also the accompanying Physics Synopsis: http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.110.02040

Product Hardy spaces associated to operators with heat kernel bounds on spaces of homogeneous type

The aim of this article is to develop the theory of product Hardy spaces associated with operators which possess the weak assumption of Davies--Gaffney heat kernel estimates, in the setting of spaces of homogeneous type. We also establish a Calder\'on--Zygmund decomposition on product spaces, which is of independent interest, and use it to study the interpolation of these product Hardy spaces. We then show that under the assumption of generalized Gaussian estimates, the product Hardy spaces coincide with the Lebesgue spaces, for an appropriate range of~$p$.Comment: Accepted by Math.

室内植物表型平台及性状鉴定研究进展和展望

Plant phenomics is under rapid development in recent years, a research field that is progressing towards integration, scalability, multi-perceptivity and high-throughput analysis. Through combining remote sensing, Internet of Things (IoT), robotics, computer vision, and artificial intelligence techniques such as machine learning and deep learning, relevant research methodologies, biological applications and theoretical foundation of this research domain have been advancing speedily in recent years. This article first introduces the current trends of plant phenomics and its related progress in China and worldwide. Then, it focuses on discussing the characteristics of indoor phenotyping and phenotypic traits that are suitable for indoor experiments, including yield, quality, and stress related traits such as drought, cold and heat resistance, salt stress, heavy metals, and pests. By connecting key phenotypic traits with important biological questions in yield production, crop quality and Stress-related tolerance, we associated indoor phenotyping hardware with relevant biological applications and their plant model systems, for which a range of indoor phenotyping devices and platforms are listed and categorised according to their throughput, sensor integration, platform size, and applications. Additionally, this article introduces existing data management solutions and analysis software packages that are representative for phenotypic analysis. For example, ISA-Tab and MIAPPE ontology standards for capturing metadata in plant phenotyping experiments, PHIS and CropSight for managing complicated datasets, and Python or MATLAB programming languages for automated image analysis based on libraries such as OpenCV, Scikit-Image, MATLAB Image Processing Toolbox. Finally, due to the importance of extracting meaningful information from big phenotyping datasets, this article pays extra attention to the future development of plant phenomics in China, with suggestions and recommendations for the integration of multi-scale phenotyping data to increase confidence in research outcomes, the cultivation of cross-disciplinary researchers to lead the next-generation plant research, as well as the collaboration between academia and industry to enable world-leading research activities in the near future

Knowledge Distillation for Closed-Source Language Models

Closed-source language models such as GPT-4 have achieved remarkable performance. Many recent studies focus on enhancing the capabilities of smaller models through knowledge distillation from closed-source language models. However, due to the incapability to directly access the weights, hidden states, and output distributions of these closed-source models, the distillation can only be performed by fine-tuning smaller models with data samples generated by closed-source language models, which constrains the effectiveness of knowledge distillation. In this paper, we propose to estimate the output distributions of closed-source language models within a Bayesian estimation framework, involving both prior and posterior estimation. The prior estimation aims to derive a prior distribution by utilizing the corpus generated by closed-source language models, while the posterior estimation employs a proxy model to update the prior distribution and derive a posterior distribution. By leveraging the estimated output distribution of closed-source language models, traditional knowledge distillation can be executed. Experimental results demonstrate that our method surpasses the performance of current models directly fine-tuned on data generated by closed-source language models