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

MCP: Self-supervised Pre-training for Personalized Chatbots with Multi-level Contrastive Sampling

Personalized chatbots focus on endowing the chatbots with a consistent personality to behave like real users and further act as personal assistants. Previous studies have explored generating implicit user profiles from the user's dialogue history for building personalized chatbots. However, these studies only use the response generation loss to train the entire model, thus it is prone to suffer from the problem of data sparsity. Besides, they overemphasize the final generated response's quality while ignoring the correlations and fusions between the user's dialogue history, leading to rough data representations and performance degradation. To tackle these problems, we propose a self-supervised learning framework MCP for capturing better representations from users' dialogue history for personalized chatbots. Specifically, we apply contrastive sampling methods to leverage the supervised signals hidden in user dialog history, and generate the pre-training samples for enhancing the model. We design three pre-training tasks based on three types of contrastive pairs from user dialogue history, namely response pairs, sequence augmentation pairs, and user pairs. We pre-train the utterance encoder and the history encoder towards the contrastive objectives and use these pre-trained encoders for generating user profiles while personalized response generation. Experimental results on two real-world datasets show a significant improvement in our proposed model MCP compared with the existing methods

An immunocompetent adult patient with hepatitis and guillain-barré syndrome after cytomegalovirus infection

<p>Abstract</p> <p>Objectives</p> <p>It is to describe an immunocompetent adult patient with hepatitis and Guillain-Barré syndrome (GBS) after Cytomegalovirus (CMV) infection. In the initial course of the diagnosis and treatment, CMV infection was ignored.</p> <p>Case report</p> <p>A 19-year-old Chinese girl complained of fatigue with pain and numbness of the limbs, with abnormal liver function. She was diagnosed as a case of GBS based on history, clinical findings and auxiliary examinations. On day 13 of admission, her liver function was still abnormal. So CMV was recommended to examine. CMV hepatitis was diagnosed on positive serum anti-CMV IgG and IgM antibodies. The case was improved only with intravenous immunoglobulin therapy, without the use of antiviral therapy.</p> <p>Conclusions</p> <p>This case showed an immunocompetent adult patient with hepatitis and GBS induced by CMV. The physicians should take into account multi-system involvement of severe CMV infection.</p

To Answer or Not to Answer? Improving Machine Reading Comprehension Model with Span-based Contrastive Learning

Machine Reading Comprehension with Unanswerable Questions is a difficult NLP task, challenged by the questions which can not be answered from passages. It is observed that subtle literal changes often make an answerable question unanswerable, however, most MRC models fail to recognize such changes. To address this problem, in this paper, we propose a span-based method of Contrastive Learning (spanCL) which explicitly contrast answerable questions with their answerable and unanswerable counterparts at the answer span level. With spanCL, MRC models are forced to perceive crucial semantic changes from slight literal differences. Experiments on SQuAD 2.0 dataset show that spanCL can improve baselines significantly, yielding 0.86-2.14 absolute EM improvements. Additional experiments also show that spanCL is an effective way to utilize generated questions

Energy trading and pricing in microgrids with uncertain energy supply:A three-stage hierarchical game approach

This paper studies an energy trading and pricing problem for microgrids with uncertain energy supply. The energy provider with the renewable energy (RE) generation (wind power) determines the energy purchase from the electricity markets and the pricing strategy for consumers to maximize its profit, and then the consumers determine their energy demands to maximize their payoffs. The hierarchical game is established between the energy provider and the consumers. The energy provider is the leader and the consumers are the followers in the hierarchical game. We consider two types of consumers according to their response to the price, i.e., the price-taking consumers and the price-anticipating consumers. We derive the equilibrium point of the hierarchical game through the backward induction method. Comparing the two types of consumers, we study the influence of the types of consumers on the equilibrium point. In particular, the uncertainty of the energy supply from the energy provider is considered. Simulation results show that the energy provider can obtain more profit using the proposed decision-making scheme

Biomechanical analysis of the Maxillary Sinus Floor Membrane During internal Sinus Floor Elevation With Implants at Different angles of the Maxillary Sinus angles

OBJECTIVE: This study analyzed and compared the biomechanical properties of maxillary sinus floor mucosa with implants at three different maxillary sinus angles during a modified internal sinus floor elevation procedure. METHODS: 3D reconstruction of the implant, maxillary sinus bone, and membrane were performed. The maxillary sinus model was set at three different angles. Two internal maxillary sinus elevation models were established, and finite element analysis was used to simulate the modified maxillary sinus elevation process. The implant was elevated to 10 mm at three maxillary sinus angles when the maxillary sinus floor membrane was separated by 0 and 4 mm. The stress of the maxillary sinus floor membrane was analyzed and compared. RESULTS: When the maxillary sinus floor membrane was separated by 0 mm and elevated to 10 mm, the peak stress values of the implant on the maxillary sinus floor membrane at three different angles were as follows: maxillary sinus I: 5.14-78.32 MPa; maxillary sinus II: 2.81-73.89 MPa; and maxillary sinus III: 2.82-51.87 MPa. When the maxillary sinus floor membrane was separated by 4 mm and elevated to 10 mm, the corresponding values were as follows: maxillary sinus I: 0.50-7.25 MPa; maxillary sinus II: 0.81-16.55 MPa; and maxillary sinus III: 0.49-22.74 MPa. CONCLUSION: The risk of sinus floor membrane rupture is greatly reduced after adequate dissection of the maxillary sinus floor membrane when performing modified internal sinus elevation in a narrow maxillary sinus. In a wide maxillary sinus, the risk of rupture or perforation of the wider maxillary sinus floor is reduced, regardless of whether traditional or modified internal sinus elevation is performed at the same height