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We prove matrix Li–Yau–Hamilton estimates for positive solutions to the heat equation and the backward conjugate heat equation, both coupled with the Ricci flow. We then apply these estimates to establish the monotonicity of parabolic frequencies up to correction factors. As applications, we obtain some unique continuation results under the nonnegativity of sectional or complex sectional curvature.

 

Executing actions in a correlated manner is a common strategy for human coordination that often leads to better cooperation, which is also potentially beneficial for cooperative multi-agent reinforcement learning (MARL). However, the recent success of MARL relies heavily on the convenient paradigm of purely decentralized execution, where there is no action correlation among agents for scalability considerations. In this work, we introduce a Bayesian network to inaugurate correlations between agents’ action selections in their joint policy. Theoretically, we establish a theoretical justification for why action dependencies are beneficial by deriving the multi-agent policy gradient formula under such a Bayesian network joint policy and proving its global convergence to Nash equilibria under tabular softmax policy parameterization in cooperative Markov games. Further, by equipping existing MARL algorithms with a recent method of differentiable directed acyclic graphs (DAGs), we develop practical algorithms to learn the context-aware Bayesian network policies in scenarios with partial observability and various difficulty. We also dynamically decrease the sparsity of the learned DAG throughout the training process, which leads to weakly or even purely independent policies for decentralized execution. Empirical results on a range of MARL benchmarks show the benefits of our approach. 

The recognition of dataset names is a critical task for automatic information extraction in scientific literature, enabling researchers to understand and identify research opportunities. However, existing corpora for dataset mention detection are limited in size and naming diversity. In this paper, we introduce the Dataset Mentions Detection Dataset (DMDD), the largest publicly available corpus for this task. DMDD consists of the DMDD main corpus, comprising 31,219 scientific articles with over 449,000 dataset mentions weakly annotated in the format of in-text spans, and an evaluation set, which comprises 450 scientific articles manually annotated for evaluation purposes. We use DMDD to establish baseline performance for dataset mention detection and linking. By analyzing the performance of various models on DMDD, we are able to identify open problems in dataset mention detection. We invite the community to use our dataset as a challenge to develop novel dataset mention detection models.

 

We introduce the concept of decision‐focused surrogate modeling for solving computationally challenging nonlinear optimization problems in real‐time settings. The proposed data‐driven framework seeks to learn a simpler, for example, convex, surrogate optimization model that is trained to minimize thedecision prediction error, which is defined as the difference between the optimal solutions of the original and the surrogate optimization models. The learning problem, formulated as a bilevel program, can be viewed as a data‐driven inverse optimization problem to which we apply a decomposition‐based solution algorithm from previous work. We validate our framework through numerical experiments involving the optimization of common nonlinear chemical processes such as chemical reactors, heat exchanger networks, and material blending systems. We also present a detailed comparison of decision‐focused surrogate modeling with standard data‐driven surrogate modeling methods and demonstrate that our approach is significantly more data‐efficient while producing simple surrogate models with high decision prediction accuracy.

 

Chemotherapy remains the standard treatment for triple‐negative breast cancer (TNBC); however, chemoresistance compromises its efficacy. The RNA‐binding protein Hu antigen R (HuR) could be a potential therapeutic target to enhance the chemotherapy efficacy. HuR is known to mainly stabilize its target mRNAs, and/or promote the translation of encoded proteins, which are implicated in multiple cancer hallmarks, including chemoresistance. In this study, a docetaxel‐resistant cell subline (231‐TR) was established from the human TNBC cell line MDA‐MB‐231. Both the parental and resistant cell lines exhibited similar sensitivity to the small molecule functional inhibitor of HuR, KH‐3. Docetaxel and KH‐3 combination therapy synergistically inhibited cell proliferation in TNBC cells and tumor growth in three animal models. KH‐3 downregulated the expression levels of HuR targets (e.g., β‐Catenin and BCL2) in a time‐ and dose‐dependent manner. Moreover, KH‐3 restored docetaxel's effects on activating Caspase‐3 and cleaving PARP in 231‐TR cells, induced apoptotic cell death, and caused S‐phase cell cycle arrest. Together, our findings suggest that HuR is a critical mediator of docetaxel resistance and provide a rationale for combining HuR inhibitors and chemotherapeutic agents to enhance chemotherapy efficacy.