On the bilateral preconditioning for an L2-type all-at-once system arising from time-space fractional Bloch-Torrey equations

Time-space fractional Bloch-Torrey equations (TSFBTEs) are developed by some researchers to investigate the relationship between diffusion and fractional-order dynamics. In this paper, we first propose a second-order implicit difference scheme for TSFBTEs by employing the recently proposed L2-type formula [A. A. Alikhanov, C. Huang, Appl. Math. Comput. (2021) 126545]. Then, we prove the stability and the convergence of the proposed scheme. Based on such a numerical scheme, an L2-type all-at-once system is derived. In order to solve this system in a parallel-in-time pattern, a bilateral preconditioning technique is designed to accelerate the convergence of Krylov subspace solvers according to the special structure of the coefficient matrix of the system. We theoretically show that the condition number of the preconditioned matrix is uniformly bounded by a constant for the time fractional order $\alpha \in (0,0.3624)$. Numerical results are reported to show the efficiency of our method.Comment: 24 pages, 6 tables, 4 figure

On the Generation of Medical Question-Answer Pairs

Question answering (QA) has achieved promising progress recently. However, answering a question in real-world scenarios like the medical domain is still challenging, due to the requirement of external knowledge and the insufficient quantity of high-quality training data. In the light of these challenges, we study the task of generating medical QA pairs in this paper. With the insight that each medical question can be considered as a sample from the latent distribution of questions given answers, we propose an automated medical QA pair generation framework, consisting of an unsupervised key phrase detector that explores unstructured material for validity, and a generator that involves a multi-pass decoder to integrate structural knowledge for diversity. A series of experiments have been conducted on a real-world dataset collected from the National Medical Licensing Examination of China. Both automatic evaluation and human annotation demonstrate the effectiveness of the proposed method. Further investigation shows that, by incorporating the generated QA pairs for training, significant improvement in terms of accuracy can be achieved for the examination QA system.Comment: AAAI 202

Diaqua­bis(2-methyl-1H-imidazol-3-ium-4,5-dicarboxyl­ato-κ2 O,O′)magnesium

The title compound, [Mg(C6H5N2O4)2(H2O)2], was prepared by reaction of Mg(NO3)2 and 2-methyl-1H-imidazole-4,5-dicarboxylic acid under hydro­thermal conditions. The MgII atom lies on an inversion centre and displays a distorted octa­hedral coordination geometry. An extended three-dimensional network of inter­molecular O—H⋯O and N—H⋯O hydrogen bonds stabilizes the crystal structure

Tris{2-meth­oxy-6-[(4-methyl­phenyl)­iminiometh­yl]phenolato-κ2 O,O′}tris­(thio­cyanato-κN)cerium(III)

The asymmetric unit of the title compound, [Ce(NCS)3(C15H15NO2)3], contains three Schiff base 2-methoxy-6-[(4-methyl­phenyl)iminometh­yl]­phenol (HL) ligands and three independent thio­cyanate ions that coordinate the cerium ion via their N atoms. The protonated imine N atoms are involved in an intra­molecular hydrogen bond with the respective phenoxide group. The Ce(III) ion exhibits a coordination number of nine