Quantum resource studied from the perspective of quantum state superposition

Quantum resources,such as discord and entanglement, are crucial in quantum information processing. In this paper, quantum resources are studied from the aspect of quantum state superposition. We define the local superposition (LS) as the superposition between basis of single part, and nonlocal superposition (NLS) as the superposition between product basis of multiple parts. For quantum resource with nonzero LS, quantum operation must be introduced to prepare it, and for quantum resource with nonzero NLS, nonlocal quantum operation must be introduced to prepare it. We prove that LS vanishes if and only if the state is classical and NLS vanishes if and only if the state is separable. From this superposition aspect, quantum resources are categorized as superpositions existing in different parts. These results are helpful to study quantum resources from a unified frame.Comment: 9 pages, 4 figure

No-Service Rail Surface Defect Segmentation via Normalized Attention and Dual-scale Interaction

No-service rail surface defect (NRSD) segmentation is an essential way for perceiving the quality of no-service rails. However, due to the complex and diverse outlines and low-contrast textures of no-service rails, existing natural image segmentation methods cannot achieve promising performance in NRSD images, especially in some unique and challenging NRSD scenes. To this end, in this paper, we propose a novel segmentation network for NRSDs based on Normalized Attention and Dual-scale Interaction, named NaDiNet. Specifically, NaDiNet follows the enhancement-interaction paradigm. The Normalized Channel-wise Self-Attention Module (NAM) and the Dual-scale Interaction Block (DIB) are two key components of NaDiNet. NAM is a specific extension of the channel-wise self-attention mechanism (CAM) to enhance features extracted from low-contrast NRSD images. The softmax layer in CAM will produce very small correlation coefficients which are not conducive to low-contrast feature enhancement. Instead, in NAM, we directly calculate the normalized correlation coefficient between channels to enlarge the feature differentiation. DIB is specifically designed for the feature interaction of the enhanced features. It has two interaction branches with dual scales, one for fine-grained clues and the other for coarse-grained clues. With both branches working together, DIB can perceive defect regions of different granularities. With these modules working together, our NaDiNet can generate accurate segmentation map. Extensive experiments on the public NRSD-MN dataset with man-made and natural NRSDs demonstrate that our proposed NaDiNet with various backbones (i.e., VGG, ResNet, and DenseNet) consistently outperforms 10 state-of-the-art methods. The code and results of our method are available at https://github.com/monxxcn/NaDiNet.Comment: 10 pages, 6 figures, Accepted by IEEE Transactions on Instrumentation and Measurement 202

Applications of Schauder’s Fixed Point Theorem to Semipositone Singular Differential Equations

We study the existence of positive periodic solutions of second-order singular differential equations. The proof relies on Schauder’s fixed point theorem. Our results generalized and extended those results contained in the studies by Chu and Torres (2007) and Torres (2007) . In some suitable weak singularities, the existence of periodic solutions may help

FAN: Fatigue-Aware Network for Click-Through Rate Prediction in E-commerce Recommendation

Since clicks usually contain heavy noise, increasing research efforts have been devoted to modeling implicit negative user behaviors (i.e., non-clicks). However, they either rely on explicit negative user behaviors (e.g., dislikes) or simply treat non-clicks as negative feedback, failing to learn negative user interests comprehensively. In such situations, users may experience fatigue because of seeing too many similar recommendations. In this paper, we propose Fatigue-Aware Network (FAN), a novel CTR model that directly perceives user fatigue from non-clicks. Specifically, we first apply Fourier Transformation to the time series generated from non-clicks, obtaining its frequency spectrum which contains comprehensive information about user fatigue. Then the frequency spectrum is modulated by category information of the target item to model the bias that both the upper bound of fatigue and users' patience is different for different categories. Moreover, a gating network is adopted to model the confidence of user fatigue and an auxiliary task is designed to guide the learning of user fatigue, so we can obtain a well-learned fatigue representation and combine it with user interests for the final CTR prediction. Experimental results on real-world datasets validate the superiority of FAN and online A/B tests also show FAN outperforms representative CTR models significantly