New monotonicity for pp-capacitary functions in 33-manifolds with nonnegative scalar curvature

In this paper, we derive general monotone quantities and geometric inequalities associated with $p$-capacitary functions in asymptotically flat $3$-manifolds with simple topology and nonnegative scalar curvature. The inequalities become equalities on the spatial Schwarzschild manifolds outside rotationally symmetric spheres. This generalizes Miao's result \cite{M} from $p=2$ to $p\in (1, 3)$. As applications, we recover mass-to-$p$-capacity and $p$-capacity-to-area inequalities due to Bray-Miao \cite{BM} and Xiao \cite{Xiao}.Comment: 30 pages. Any comments are welcome

An Analysis with Evolutionary Game of the Resource Sharing in Supply Chain Under Cloud Platform

Based on the sharing mode of supply chain resources in the environment of cloud service, this research constructed the evolutionary game model of supply chain resource-sharing to reveal the behaviors between two types of enterprise, the equilibrium in model and local stability are analyzed under the state of uniform mixed and non-uniform mixed populations. By using the method of system dynamics, the evolutionary game model is built, and a contrastive analysis of evolutionary results affected by diverse parametric variations is performed. The results of the research shows that the evolutionary trends of the game are significantly influenced by the initial sharing proportion in enterprise group, the cost and benefit of upgrading equipment, and the risk of technological loss. To facilitate the information interaction and resource sharing between enterprises, continuous improvement needed to be done in line with the above aspects

Improved Real-time Post-Processing for quantum Random Number Generators

Randomness extraction is a key problem in cryptography and theoretical computer science. With the recent rapid development of quantum cryptography, quantum-proof randomness extraction has also been widely studied, addressing the security issues in the presence of a quantum adversary. In contrast with conventional quantum-proof randomness extractors characterizing the input raw data as min-entropy sources, we find that the input raw data generated by a large class of trusted-device quantum random number generators can be characterized as the so-called reverse block source. This fact enables us to design improved extractors. Specifically, we propose two novel quantum-proof randomness extractors for reverse block sources that realize real-time block-wise extraction. In comparison with the general min-entropy randomness extractors, our designs achieve a significantly higher extraction speed and a longer output data length with the same seed length. In addition, they enjoy the property of online algorithms, which process the raw data on the fly without waiting for the entire input raw data to be available. These features make our design an adequate choice for the real-time post-processing of practical quantum random number generators. Applying our extractors to the raw data of the fastest known quantum random number generator, we achieve a simulated extraction speed as high as 374 Gbps.Comment: 11 pages, 3 figure

C2B Orders Decision-making in Multiple Supply Chains Under Cloud Manufacturing

Considering the background of cloud manufacturing and cluster supply chain, we build the basic model to assign the orders priority within each capacity. Then, considering the inter-chain horizontal cooperation, the extended model is proposed to parallel allocation of cross-chain orders as the orders exceeding one single- chain’s capacity. Lagrange algorithm is implemented, and the simulation analysis shown that the opportunity cost of rejected orders factor and cross-chain orders manufacturing cost factor have significant impacts on orders’ allocation decision, and there is a critical point in the combinations of those two factors. Through combinations, the cluster supply chain can make the acceptance decisions policy and production schedules of priority orders and cross- chain orders, so that customers’ satisfaction and the cluster supply chain’s total profits achieve the best situations

Certifying randomness in quantum state collapse

The unpredictable process of state collapse caused by quantum measurements makes the generation of quantum randomness possible. In this paper, we explore the quantitive connection between the randomness generation and the state collapse and provide a randomness verification protocol under the assumptions: (I) independence between the source and the measurement devices and (II) the L\"{u}ders' rule for collapsing state. Without involving heavy mathematical machinery, the amount of genereted quantum randomness can be directly estimated with the disturbance effect originating from the state collapse. In the protocol, we can employ general measurements that are not fully trusted. Equipped with trusted projection measurements, we can further optimize the randomness generation performance. Our protocol also shows a high efficiency and yields a higher randomness generation rate than the one based on uncertainty relation. We expect our results to provide new insights for understanding and generating quantum randomnes

Visual Prompt Tuning for Test-time Domain Adaptation

Models should have the ability to adapt to unseen data during test-time to avoid performance drop caused by inevitable distribution shifts in real-world deployment scenarios. In this work, we tackle the practical yet challenging test-time adaptation (TTA) problem, where a model adapts to the target domain without accessing the source data. We propose a simple recipe called data-efficient prompt tuning (DePT) with two key ingredients. First, DePT plugs visual prompts into the vision Transformer and only tunes these source-initialized prompts during adaptation. We find such parameter-efficient finetuning can efficiently adapt the model representation to the target domain without overfitting to the noise in the learning objective. Second, DePT bootstraps the source representation to the target domain by memory bank-based online pseudo labeling. A hierarchical self-supervised regularization specially designed for prompts is jointly optimized to alleviate error accumulation during self-training. With much fewer tunable parameters, DePT demonstrates not only state-of-the-art performance on major adaptation benchmarks, but also superior data efficiency, i.e., adaptation with only 1\% or 10\% data without much performance degradation compared to 100\% data. In addition, DePT is also versatile to be extended to online or multi-source TTA settings