Hardy-Littlewood-Sobolev inequalities with partial variable weight on the upper half space and related inequalities

In this paper, we establish a class of Hardy-Littlewood-Sobolev inequality with partial variable weight functions on the upper half space using a weighted Hardy type inequality. Overcoming the impact of weighted functions, the existence of extremal functions is proved via the concentration compactness principle, whereas Riesz rearrangement inequality is not available. Moreover, the cylindrical symmetry with respect to $t$-axis and the explicit forms on the boundary of all nonnegative extremal functions are discussed via the method of moving planes and method of moving spheres, as well as, regularity results are obtained by the regularity lift lemma and bootstrap technique. As applications, we obtain some weighted Sobolev inequalities with partial variable weight function for Laplacian and fractional Laplacian

Reversed Hardy-Littewood-Sobolev inequality

Abstract In this paper, we obtain a reversed Hardy-Littlewood-Sobolev inequality: for 0 < p, t < 1 and λ = n − α < 0 with 1/p + 1/t + λ/n = 2, there is a best constant N (n, λ, p) > 0, such that For p = t, we prove the existence of extremal functions, classify all extremal functions via the method of moving sphere, and compute the best constant

Structure-aware Protein Self-supervised Learning

Protein representation learning methods have shown great potential to yield useful representation for many downstream tasks, especially on protein classification. Moreover, a few recent studies have shown great promise in addressing insufficient labels of proteins with self-supervised learning methods. However, existing protein language models are usually pretrained on protein sequences without considering the important protein structural information. To this end, we propose a novel structure-aware protein self-supervised learning method to effectively capture structural information of proteins. In particular, a well-designed graph neural network (GNN) model is pretrained to preserve the protein structural information with self-supervised tasks from a pairwise residue distance perspective and a dihedral angle perspective, respectively. Furthermore, we propose to leverage the available protein language model pretrained on protein sequences to enhance the self-supervised learning. Specifically, we identify the relation between the sequential information in the protein language model and the structural information in the specially designed GNN model via a novel pseudo bi-level optimization scheme. Experiments on several supervised downstream tasks verify the effectiveness of our proposed method.Comment: 7 pages and 4 figure

C-Watcher: A Framework for Early Detection of High-Risk Neighborhoods Ahead of COVID-19 Outbreak

The novel coronavirus disease (COVID-19) has crushed daily routines and is still rampaging through the world. Existing solution for nonpharmaceutical interventions usually needs to timely and precisely select a subset of residential urban areas for containment or even quarantine, where the spatial distribution of confirmed cases has been considered as a key criterion for the subset selection. While such containment measure has successfully stopped or slowed down the spread of COVID-19 in some countries, it is criticized for being inefficient or ineffective, as the statistics of confirmed cases are usually time-delayed and coarse-grained. To tackle the issues, we propose C-Watcher, a novel data-driven framework that aims at screening every neighborhood in a target city and predicting infection risks, prior to the spread of COVID-19 from epicenters to the city. In terms of design, C-Watcher collects large-scale long-term human mobility data from Baidu Maps, then characterizes every residential neighborhood in the city using a set of features based on urban mobility patterns. Furthermore, to transfer the firsthand knowledge (witted in epicenters) to the target city before local outbreaks, we adopt a novel adversarial encoder framework to learn "city-invariant" representations from the mobility-related features for precise early detection of high-risk neighborhoods, even before any confirmed cases known, in the target city. We carried out extensive experiments on C-Watcher using the real-data records in the early stage of COVID-19 outbreaks, where the results demonstrate the efficiency and effectiveness of C-Watcher for early detection of high-risk neighborhoods from a large number of cities.Comment: 11 pages, accepted by AAAI 2021, appendix is include

Multi-Job Intelligent Scheduling with Cross-Device Federated Learning

Recent years have witnessed a large amount of decentralized data in various (edge) devices of end-users, while the decentralized data aggregation remains complicated for machine learning jobs because of regulations and laws. As a practical approach to handling decentralized data, Federated Learning (FL) enables collaborative global machine learning model training without sharing sensitive raw data. The servers schedule devices to jobs within the training process of FL. In contrast, device scheduling with multiple jobs in FL remains a critical and open problem. In this paper, we propose a novel multi-job FL framework, which enables the training process of multiple jobs in parallel. The multi-job FL framework is composed of a system model and a scheduling method. The system model enables a parallel training process of multiple jobs, with a cost model based on the data fairness and the training time of diverse devices during the parallel training process. We propose a novel intelligent scheduling approach based on multiple scheduling methods, including an original reinforcement learning-based scheduling method and an original Bayesian optimization-based scheduling method, which corresponds to a small cost while scheduling devices to multiple jobs. We conduct extensive experimentation with diverse jobs and datasets. The experimental results reveal that our proposed approaches significantly outperform baseline approaches in terms of training time (up to 12.73 times faster) and accuracy (up to 46.4% higher).Comment: To appear in TPDS; 22 pages, 17 figures, 8 tables. arXiv admin note: substantial text overlap with arXiv:2112.0592