Online advertising is a primary source of income for e-commerce platforms. In the current advertising pattern, the oriented targets are the online store owners who are willing to pay extra fees to enhance the position of their stores. On the other hand, brand suppliers are also desirable to advertise their products in stores to boost brand sales. However, the currently used advertising mode cannot satisfy the demand of both stores and brand suppliers simultaneously. To address this, we innovatively propose a joint advertising model termed ''Joint Auction'', allowing brand suppliers and stores to collaboratively bid for advertising slots, catering to both their needs. However, conventional advertising auction mechanisms are not suitable for this novel scenario. In this paper, we propose JRegNet, a neural network architecture for the optimal joint auction design, to generate mechanisms that can achieve the optimal revenue and guarantee (near-)dominant strategy incentive compatibility and individual rationality. Finally, multiple experiments are conducted on synthetic and real data to demonstrate that our proposed joint auction significantly improves platform's revenue compared to the known baselines.

Inferring gene regulatory networks (GRNs) allows us to obtain a deeper understanding of cellular function and disease pathogenesis. Recent advances in single-cell RNA sequencing (scRNA-seq) technology have improved the accuracy of GRN inference. However, many methods for inferring individual GRNs from scRNA-seq data are limited because they overlook intercellular heterogeneity and similarities between different cell subpopulations, which are often present in the data. Here, we propose a deep learning-based framework, DeepGRNCS, for jointly inferring GRNs across cell subpopulations. We follow the commonly accepted hypothesis that the expression of a target gene can be predicted based on the expression of transcription factors (TFs) due to underlying regulatory relationships. We initially processed scRNA-seq data by discretizing data scattering using the equal-width method. Then, we trained deep learning models to predict target gene expression from TFs. By individually removing each TF from the expression matrix, we used pre-trained deep model predictions to infer regulatory relationships between TFs and genes, thereby constructing the GRN. Our method outperforms existing GRN inference methods for various simulated and real scRNA-seq datasets. Finally, we applied DeepGRNCS to non-small cell lung cancer scRNA-seq data to identify key genes in each cell subpopulation and analyzed their biological relevance. In conclusion, DeepGRNCS effectively predicts cell subpopulation-specific GRNs. The source code is available at https://github.com/Nastume777/DeepGRNCS.

In various applications, ads are displayed together with prices, so as to provide a direct comparison among similar products or services. The price-displaying feature not only influences the consumers’ decision, but also affects the bidding behavior of advertisers. In this paper, we study ad auctions with display prices from the perspective of mechanism design, in which advertisers are asked to submit both the product costs and the display prices of their commodities. We first provide a characterization for all individually rational and incentive-compatible mechanisms in the presence of display prices, then use it to design ad auctions in two scenarios. In the former scenario, the display prices are assumed to be exogenously determined. For this scenario, we derive the welfare-maximizing and revenue-maximizing auctions for any given display price profile. In the latter, advertisers are allowed to strategize their display prices freely. We investigate two families of allocation policies within the scenario and identify the equilibrium display prices accordingly. Our findings demonstrate the impact of display prices on the design of ad auctions, and highlight how platforms can utilize display price information to optimize the performance of ad delivery.