In e-commerce advertising, it is crucial to jointly consider various performance metrics, e.g., user experience, advertiser utility, and platform revenue. Traditional auction mechanisms, such as GSP and VCG auctions, can be suboptimal due to their fixed allocation rules to optimize a single performance metric (e.g., revenue or social welfare). Recently, data-driven auctions, learned directly from auction outcomes to optimize multiple performance metrics, have attracted increasing research interests. However, the procedure of auction mechanisms involves various discrete calculation operations, making it challenging to be compatible with continuous optimization pipelines in machine learning. In this paper, we design Deep Neural Auctions (DNAs) to enable end-to-end auction learning by proposing a differentiable model to relax the discrete sorting operation, a key component in auctions. We optimize the performance metrics by developing deep models to efficiently extract contexts from auctions, providing rich features for auction design. We further integrate the game theoretical conditions within the model design, to guarantee the stability of the auctions. DNAs have been successfully deployed in the e-commerce advertising system at Taobao. Experimental evaluation results on both large-scale data set as well as online A/B test demonstrated that DNAs significantly outperformed other mechanisms widely adopted in industry. CCS CONCEPTS• Information systems → Computational advertising; • Theory of computation → Algorithmic mechanism design; • Computing methodologies → Neural networks.

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The non-collinear wave mixing technique was used for the quantitative evaluation of fatigue cracks. Two shear waves intersect and interact with fatigue cracks, which lead to the generation of a longitudinal wave. Non-collinear wave mixing experiments were conducted on different specimens, whereby the position at which the two incident waves intersected was scanned vertically below the notch and the measured signals were processed by filtering, time–frequency analysis and bispectral analysis. The presence of a wave packet in waveform, or wave-mixing component at the sum frequency in time–frequency domain, or bispectral peak at the sum frequency was used to characterize the fatigue cracks. The length of the fatigue cracks in two samples was estimated according to the spatial distribution of the ultrasonic nonlinear coefficient. The measured results corresponded closely with the actual lengths; therefore, the proposed method is effective for the quantitative evaluation of fatigue cracks.

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