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We investigate group actions on the category of coherent sheaves over weighted projective lines. We show that the equivariant category with respect to certain finite group action is equivalent to the category of coherent sheaves over a weighted projective curve, where the genus of the underlying smooth projective curve and the weight data are given by explicit formulas. Moreover, we obtain a trichotomy result for all such equivariant relations. This equivariant approach provides an effective way to investigate smooth projective curves via weighted projective lines. As an application, we give a description for the category of coherent sheaves over a hyperelliptic curve of arbitrary genus. Links to smooth projective curves of genus 2 and also to Arnold's exceptional unimodal singularities are also established.

Link prediction is a fundamental challenge in network science. Among various methods, similarity-based algorithms are popular for their simplicity, interpretability, high efficiency and good performance. In this paper, we show that the most elementary local similarity index Common Neighbor (CN) can be linearly decomposed by eigenvectors of the adjacency matrix of the target network, with each eigenvector's contribution being proportional to the square of the corresponding eigenvalue. As in many real networks, there is a huge gap between the largest eigenvalue and the second largest eigenvalue, the CN index is thus dominated by the leading eigenvector and much useful information contained in other eigenvectors may be overlooked. Accordingly, we propose a parameter-free algorithm that ensures the contributions of the leading eigenvector and the secondary eigenvector the same. Extensive experiments on real networks demonstrate that the prediction performance of the proposed algorithm is remarkably better than well-performed local similarity indices in the literature. A further proposed algorithm that can adjust the contribution of leading eigenvector shows the superiority over state-of-the-art algorithms with tunable parameters for its competitive accuracy and lower computational complexity., Comment: 22 pages, 4 figures, 4 tables

As we all know, users and item-providers are two main parties of participants in recommender systems. However, most existing research efforts on recommendation were focused on better serving users and overlooked the purpose of item-providers. This paper is devoted to improve the item exposure fairness for item-providers' objective, and keep the recommendation accuracy not decreased or even improved for users' objective. We propose to set stock volume constraints on items, to be specific, limit the maximally allowable recommended times of an item to be proportional to the frequency of its being interacted in the past, which is validated to achieve superior item exposure fairness to common recommenders and thus mitigates the Matthew Effect on item popularity. With the two constraints of pre-existing recommendation length of users and our stock volumes of items, a heuristic strategy based on normalized scores and a Minimum Cost Maximum Flow (MCMF) based model are proposed to solve the optimal user-item matching problem, whose accuracy performances are even better than that of baseline algorithm in regular recommendation context, and in line with state-of-the-art enhancement of the baseline. What's more, our MCMF based strategy is parameter-free, while those counterpart algorithms have to resort to parameter traversal process to achieve their best performance.

Ischemic stroke lesion segmentation from Computed Tomography Perfusion (CTP) images is important for accurate diagnosis of stroke in acute care units. However, it is challenged by low image contrast and resolution of the perfusion parameter maps, in addition to the complex appearance of the lesion. To deal with this problem, we propose a novel framework based on synthesized pseudo Diffusion-Weighted Imaging (DWI) from perfusion parameter maps to obtain better image quality for more accurate segmentation. Our framework consists of three components based on Convolutional Neural Networks (CNNs) and is trained end-to-end. First, a feature extractor is used to obtain both a low-level and high-level compact representation of the raw spatiotemporal Computed Tomography Angiography (CTA) images. Second, a pseudo DWI generator takes as input the concatenation of CTP perfusion parameter maps and our extracted features to obtain the synthesized pseudo DWI. To achieve better synthesis quality, we propose a hybrid loss function that pays more attention to lesion regions and encourages high-level contextual consistency. Finally, we segment the lesion region from the synthesized pseudo DWI, where the segmentation network is based on switchable normalization and channel calibration for better performance. Experimental results showed that our framework achieved the top performance on ISLES 2018 challenge and: 1) our method using synthesized pseudo DWI outperformed methods segmenting the lesion from perfusion parameter maps directly; 2) the feature extractor exploiting additional spatiotemporal CTA images led to better synthesized pseudo DWI quality and higher segmentation accuracy; and 3) the proposed loss functions and network structure improved the pseudo DWI synthesis and lesion segmentation performance., Comment: 14 pages, 10 figures

Nowadays, recommender systems (RSes) are becoming increasingly important to individual users and business marketing, especially in the online e-commerce scenarios. However, while the majority of recommendation algorithms proposed in the literature have focused their efforts on improving prediction accuracy, other important aspects of recommendation quality, such as diversity of recommendations, have been more or less overlooked. In the latest decade, recommendation diversity has drawn more research attention, especially in the models based on user-item bipartite networks. In this paper, we introduce a family of approaches to extract fabricated experts from users in RSes, named as the Expert Tracking Approaches (ExTrA for short), and explore the capability of these fabricated experts in improving the recommendation diversity, by highlighting them in a well-known bipartite network-based method, called the Mass Diffusion (MD for short) model. These ExTrA-based models are compared with two state-of-the-art MD-improved models HHP and BHC, with respect to recommendation accuracy and diversity. Comprehensive empirical results on three real-world datasets MovieLens, Netflix and RYM show that, our proposed ExTrA-based models can achieve significant diversity gain while maintain comparable level of recommendation accuracy.

The primary goal of a recommender system is often known as "helping users find relevant items", and a lot of recommendation algorithms are proposed accordingly. However, these accuracy-oriented methods usually suffer the problem of recommendation bias on popular items, which is not welcome to not only users but also item providers. To alleviate the recommendation bias problem, we propose a generic rank aggregation framework for the recommendation results of an existing algorithm, in which the user- and item-oriented ranking results are linearly aggregated together, with a parameter controlling the weight of the latter ranking process. Experiment results of a typical algorithm on two real-world data sets show that, this framework is effective to improve the recommendation fairness of any existing accuracy-oriented algorithms, while avoiding significant accuracy loss., Comment: published on Physica A: Statistical Mechanics and its Applications, 2019, volume 534, article ID: 122073