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Real-Time Bidding (RTB) is an important paradigm in display advertising, where advertisers utilize extended information and algorithms served by Demand Side Platforms (DSPs) to improve advertising performance. A common problem for DSPs is to help advertisers gain as much value as possible with budget constraints. However, advertisers would routinely add certain key performance indicator (KPI) constraints that the advertising campaign must meet due to practical reasons. In this paper, we study the common case where advertisers aim to maximize the quantity of conversions, and set cost-per-click (CPC) as a KPI constraint. We convert such a problem into a linear programming problem and leverage the primal-dual method to derive the optimal bidding strategy. To address the applicability issue, we propose a feedback control-based solution and devise the multivariable control system. The empirical study based on real-word data from Taobao.com verifies the effectiveness and superiority of our approach compared with the state of the art in the industry practices.

Hefan He,1 Weifeng Liu,1 Yingying Zhou,1 Yibin Liu,1 Peiqing Weng,1 Yasong Li,2 Huangde Fu3 1Department of Anesthesia, the Second Affiliated Hospital, Fujian Medical University, Quanzhou, Fujian, China; 2Department of Neurosurgery, the Second Affiliated Hospital, Fujian Medical University, Quanzhou, Fujian, China; 3Department of Neurosurgery, Affiliated Hospital of Youjiang Medical University for Nationalities, Baise, Guangxi, China Background: Sevoflurane post-conditioning exerts nerve-protective effects through inhibiting caspase-dependent neuronal apoptosis after a traumatic brain injury (TBI). Autophagy that is induced by the endoplasmic reticulum stress plays an important role in the secondary neurological dysfunction after a TBI. However, the relationship between autophagy and caspase-dependent apoptosis as well as the underlying nerve protection mechanism that occurs with sevoflurane post-conditioning following a TBI remains unclear. Methods: The Feeney TBI model was used to induce brain injury in rats. Evaluation of the modified neurological severity scores, measurement of brain water content, Nissl staining, and terminal deoxynucleotidyl transferase dUTP nick end labeling assay were used to determine the neuroprotective effects of the sevoflurane post-conditioning. Both immunofluorescence and Western blot analyses were used to detect the expression of autophagy-related proteins microtubule-associated protein 1 light chain 3-II and Beclin-1, pro-apoptotic factors, as well as the activation of the phosphatidylinositide 3-kinase/protein kinase B (PI3K/AKT) signaling pathway within the lesioned cortex. Results: Autophagy and neuronal apoptosis were activated in the lesioned cortex following the TBI. Sevoflurane post-conditioning enhanced early autophagy, suppressed neuronal apoptosis, and alleviated brain edema, which improved nerve function after a TBI (all P < 0.05). Sevoflurane post-conditioning induced the activation of PI3K/AKT sig