Least Squares Regression Estimations Based on Censored Data with Measurement Errors

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Setup Cost Reduction in the Lumpy Demand Production Quantity Model with Discounting

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Strong solutions of the compressible nematic liquid crystal flow

We study strong solutions of the simplified Ericksen-Leslie system modeling compressible nematic liquid crystal flows in a domain $\Omega \subset\mathbb R^3$. We first prove the local existence of unique strong solutions provided that the initial data $\rho_0, u_0, d_0$are sufficiently regular and satisfy a natural compatibility condition. The initial density function $\rho_0$ may vanish on an open subset (i.e., an initial vacuum may exist). We then prove a criterion for possible breakdown of such a local strong solution at finite time in terms of blow up of the quantities $\|\rho\|_{L^\infty_tL^\infty_x}$ and $\|\nabla d\|_{L^3_tL^\infty_x}$

Sequential Prediction of Social Media Popularity with Deep Temporal Context Networks

Prediction of popularity has profound impact for social media, since it offers opportunities to reveal individual preference and public attention from evolutionary social systems. Previous research, although achieves promising results, neglects one distinctive characteristic of social data, i.e., sequentiality. For example, the popularity of online content is generated over time with sequential post streams of social media. To investigate the sequential prediction of popularity, we propose a novel prediction framework called Deep Temporal Context Networks (DTCN) by incorporating both temporal context and temporal attention into account. Our DTCN contains three main components, from embedding, learning to predicting. With a joint embedding network, we obtain a unified deep representation of multi-modal user-post data in a common embedding space. Then, based on the embedded data sequence over time, temporal context learning attempts to recurrently learn two adaptive temporal contexts for sequential popularity. Finally, a novel temporal attention is designed to predict new popularity (the popularity of a new user-post pair) with temporal coherence across multiple time-scales. Experiments on our released image dataset with about 600K Flickr photos demonstrate that DTCN outperforms state-of-the-art deep prediction algorithms, with an average of 21.51% relative performance improvement in the popularity prediction (Spearman Ranking Correlation).Comment: accepted in IJCAI-1

Strong solutions of the compressible nematic liquid crystal flow

AbstractWe study strong solutions of the simplified Ericksen–Leslie system modeling compressible nematic liquid crystal flows in a domain Ω⊂R3. We first prove the local existence of a unique strong solution provided that the initial data ρ0,u0,d0 are sufficiently regular and satisfy a natural compatibility condition. The initial density function ρ0 may vanish on an open subset (i.e., an initial vacuum may exist). We then prove a criterion for possible breakdown of such a local strong solution at finite time in terms of blow up of the quantities ‖ρ‖Lt∞Lx∞ and ‖∇d‖Lt3Lx∞