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In this paper, we study a mean curvature type flow with capillary boundary in a horoball in hyperbolic space. Our flow preserves the volume of the bounded domain enclosed by the hypersurface and monotonically decreases the energy functional. We show that it has the long time existence and converges to a truncated umbilical hypersurface in hyperbolic space. As an application, we solve an isoperimetric type problem for hypersurfaces with capillary boundary in a horoball., Comment: 18 pages, 1 figure

In this paper, we propose a new definition of stable $(r+1)$-th capillary hypersurfaces from variational perspective for any $1\leq r\leq n-1$. More precisely, we define stable $(r+1)$-th capillary hypersurfaces to be smooth local minimizers of a new energy functional under volume-preserving and contact angle-preserving variations. Using the new concept of the stable $(r+1)$-th capillary hypersurfaces, we generalize the stability results of Souam \cite{Souam} in an Euclidean half-space and Guo-Wang-Xia \cite{GWX} in a horoball in hyperbolic space for capillary hypersurface to $(r+1)$-th capillary hypersurface case., Comment: 31 pages,2 figures

Satellite-collected nighttime light provides a unique perspective on human activities, including urbanization, population growth, and epidemics. Yet, long-term and fine-grained nighttime light observations are lacking, leaving the analysis and applications of decades of light changes in urban facilities undeveloped. To fill this gap, we developed an innovative framework and used it to design a new super-resolution model that reconstructs low-resolution nighttime light data into high resolution. The validation of one billion data points shows that the correlation coefficient of our model at the global scale reaches 0.873, which is significantly higher than that of other existing models (maximum = 0.713). Our model also outperforms existing models at the national and urban scales. Furthermore, through an inspection of airports and roads, only our model's image details can reveal the historical development of these facilities. We provide the long-term and fine-grained nighttime light observations to promote research on human activities. The dataset is available at \url{https://doi.org/10.5281/zenodo.7859205}.

In this paper, we study stability problem of anisotropic capillary hypersurfaces in an Euclidean half-space. We prove that any compact immersed anisotropic capillary constant anisotropic mean curvature hypersurface in the half-space is weakly stable if and only if it is a truncated Wulff shape. On the other hand, we prove a Bernstein-type theorem for stable anisotropic capillary minimal surfaces in the three dimensional half-space under Euclidean area growth assumption., Comment: 20 pages,final version,to appear in Indiana U. Math. J

In dialogue state tracking, dialogue history is a crucial material, and its utilization varies between different models. However, no matter how the dialogue history is used, each existing model uses its own consistent dialogue history during the entire state tracking process, regardless of which slot is updated. Apparently, it requires different dialogue history to update different slots in different turns. Therefore, using consistent dialogue contents may lead to insufficient or redundant information for different slots, which affects the overall performance. To address this problem, we devise DiCoS-DST to dynamically select the relevant dialogue contents corresponding to each slot for state updating. Specifically, it first retrieves turn-level utterances of dialogue history and evaluates their relevance to the slot from a combination of three perspectives: (1) its explicit connection to the slot name; (2) its relevance to the current turn dialogue; (3) Implicit Mention Oriented Reasoning. Then these perspectives are combined to yield a decision, and only the selected dialogue contents are fed into State Generator, which explicitly minimizes the distracting information passed to the downstream state prediction. Experimental results show that our approach achieves new state-of-the-art performance on MultiWOZ 2.1 and MultiWOZ 2.2, and achieves superior performance on multiple mainstream benchmark datasets (including Sim-M, Sim-R, and DSTC2)., Comment: Accepted by ACL 2022 main conference (long paper)

In this paper, we consider a Minkowski inequality for a domain supported on any umbilical hypersurface with free boundary in space forms. We generalize the main result in \cite{Xia} into free boundary case and obtain a free boundary version of optimal weighted Minkowski inequality in space forms., Comment: 12 pages

In this paper, we study a stability problem of free boundary hypersurfaces, and also capillary ones whose boundary supported on a horosphere in hyperbolic space. We prove that umbilical hypersurfaces are only stable immersed capillary hypersurfaces whose boundary supported on a horosphere. Using the same method, we show that a totally geodesic hyperplane is only stable immersed type-II hypersurface whose boundary supported on a horosphere., Comment: 16 pages,1 figure

The goal of dialogue state tracking (DST) is to predict the current dialogue state given all previous dialogue contexts. Existing approaches generally predict the dialogue state at every turn from scratch. However, the overwhelming majority of the slots in each turn should simply inherit the slot values from the previous turn. Therefore, the mechanism of treating slots equally in each turn not only is inefficient but also may lead to additional errors because of the redundant slot value generation. To address this problem, we devise the two-stage DSS-DST which consists of the Dual Slot Selector based on the current turn dialogue, and the Slot Value Generator based on the dialogue history. The Dual Slot Selector determines each slot whether to update slot value or to inherit the slot value from the previous turn from two aspects: (1) if there is a strong relationship between it and the current turn dialogue utterances; (2) if a slot value with high reliability can be obtained for it through the current turn dialogue. The slots selected to be updated are permitted to enter the Slot Value Generator to update values by a hybrid method, while the other slots directly inherit the values from the previous turn. Empirical results show that our method achieves 56.93%, 60.73%, and 58.04% joint accuracy on MultiWOZ 2.0, MultiWOZ 2.1, and MultiWOZ 2.2 datasets respectively and achieves a new state-of-the-art performance with significant improvements., Comment: Accepted by ACL-IJCNLP 2021 main conference (long paper)

In the first part of this paper, we consider a partially overdetermined mixed boundary value problem in space forms and generalize the main result in \cite{GX} into the case of general domains with partial umbilical boundary in space forms. Precisely, we prove that a partially overdetermined problem in a domain with partial umbilical boundary admits a solution if and only if the rest part of the boundary is also part of an umbilical hypersurface. In the second part of this paper, we prove a Heintze-Karcher-Ros type inequality for embedded hypersurfaces with free boundary lying on a horosphere or an equidistant hypersurface in the hyperbolic space. As an application, we show Alexandrov type theorem for constant mean curvature hypersurfaces with free boundary in these settings., Comment: 22 pages,4 figures,final version,to appear in Adv.Calc.Var

In this paper, we study stability and instability problem for type-II partitioning problem. First, we make a complete classification of stable type-II stationary hypersurfaces in a ball in a space form as totally geodesic $n$-balls. Second, for general ambient spaces and convex domains, we give some topological restriction for type-II stable stationary immersed surfaces in two dimension. Third, we give a lower bound for the Morse index for type-II stationary hypersurfaces in terms of their topology., Comment: Final version, J. Geom. Anal., to appear

In this paper, we study a partially overdetermined mixed boundary value problem in a half ball. We prove that a domain in which this partially overdetermined problem admits a solution if and only if the domain is a spherical cap intersecting $\ss^{n-1}$ orthogonally. As an application, we show a stationary point for a partially torsional rigidity under a volume constraint must be a spherical cap., Comment: Final version, to appear in Calc. Var. PDEs