Poly[bis­[μ2-2-(1H-1,2,4-triazol-1-yl)acetato]zinc(II)]

In the title compound, [Zn(C4H4N3O2)2]n, the ZnII atom is coordinated by two O atoms [Zn—O = 1.969 (2) and 1.997 (2) Å] and two N atoms [Zn—N = 2.046 (2) and 2.001 (2) Å] in a distorted tetra­hedral geometry. Non-classical inter­molecular C—H⋯O hydrogen bonds link the complex into a three-dimensional supra­molecular framework

Two classes of minimal generic fundamental invariants for tensors

Motivated by the problems raised by B\"{u}rgisser and Ikenmeyer, we discuss two classes of minimal generic fundamental invariants for tensors of order 3. The first one is defined on $\otimes^3 \mathbb{C}^m$, where $m=n^2-1$. We study its construction by obstruction design introduced by B\"{u}rgisser and Ikenmeyer, which partially answers one problem raised by them. The second one is defined on $\mathbb{C}^{\ell m}\otimes \mathbb{C}^{mn}\otimes \mathbb{C}^{n\ell}$. We study its evaluation on the matrix multiplication tensor $\langle\ell,m,n\rangle$ and unit tensor $\langle n^2 \rangle$ when $\ell=m=n$. The evaluation on the unit tensor leads to the definition of Latin cube and 3-dimensional Alon-Tarsi problem. We generalize some results on Latin square to Latin cube, which enrich the understanding of 3-dimensional Alon-Tarsi problem. It is also natural to generalize the constructions to tensors of other orders. We illustrate the distinction between even and odd dimensional generalizations by concrete examples. Finally, some open problems in related fields are raised.Comment: Some typos were changed.New publication information has been update

Simplifying Deep-Learning-Based Model for Code Search

To accelerate software development, developers frequently search and reuse existing code snippets from a large-scale codebase, e.g., GitHub. Over the years, researchers proposed many information retrieval (IR) based models for code search, which match keywords in query with code text. But they fail to connect the semantic gap between query and code. To conquer this challenge, Gu et al. proposed a deep-learning-based model named DeepCS. It jointly embeds method code and natural language description into a shared vector space, where methods related to a natural language query are retrieved according to their vector similarities. However, DeepCS' working process is complicated and time-consuming. To overcome this issue, we proposed a simplified model CodeMatcher that leverages the IR technique but maintains many features in DeepCS. Generally, CodeMatcher combines query keywords with the original order, performs a fuzzy search on name and body strings of methods, and returned the best-matched methods with the longer sequence of used keywords. We verified its effectiveness on a large-scale codebase with about 41k repositories. Experimental results showed the simplified model CodeMatcher outperforms DeepCS by 97% in terms of MRR (a widely used accuracy measure for code search), and it is over 66 times faster than DeepCS. Besides, comparing with the state-of-the-art IR-based model CodeHow, CodeMatcher also improves the MRR by 73%. We also observed that: fusing the advantages of IR-based and deep-learning-based models is promising because they compensate with each other by nature; improving the quality of method naming helps code search, since method name plays an important role in connecting query and code

Large-step neural network for learning the symplectic evolution from partitioned data

In this study, we focus on learning Hamiltonian systems, which involves predicting the coordinate (q) and momentum (p) variables generated by a symplectic mapping. Based on Chen & Tao (2021), the symplectic mapping is represented by a generating function. To extend the prediction time period, we develop a new learning scheme by splitting the time series (q_i, p_i) into several partitions. We then train a large-step neural network (LSNN) to approximate the generating function between the first partition (i.e. the initial condition) and each one of the remaining partitions. This partition approach makes our LSNN effectively suppress the accumulative error when predicting the system evolution. Then we train the LSNN to learn the motions of the 2:3 resonant Kuiper belt objects for a long time period of 25000 yr. The results show that there are two significant improvements over the neural network constructed in our previous work (Li et al. 2022): (1) the conservation of the Jacobi integral, and (2) the highly accurate predictions of the orbital evolution. Overall, we propose that the designed LSNN has the potential to considerably improve predictions of the long-term evolution of more general Hamiltonian systems.Comment: 13 pages, 7 figures, accepted for publication in MNRA

A study of particles looseness in screening process of a linear vibrating screen

We investigated the movement of particles in screening process over the sieve plate of a linear vibrating screen using the Discrete Element Method (DEM). The behavior of particles which is affected by a series of vibrational parameters including amplitude, frequency and vibration direction angle determining screening performance. This paper centers on particles looseness by analyzing the looseness coefficient and looseness rate. The relationships between the looseness coefficient, looseness rate and vibration parameters were profoundly discussed. Mathematical models relating looseness coefficient to time were established using the least squares method. An experimental platform which combines high-speed camera system with experimental prototype of vibrating screen was designed. The research made a more in-depth investigation of particles’ movements and analysis of particle looseness. Physical experiments were used to verify the reliability of simulation results. Finally, we would come into the following conclusions: high frequency and large amplitude make particles obtain more energy to be active and the average distances among particles get larger slowly. On the contrary, at low frequency and amplitude, the looseness coefficient and looseness rate were relatively low. When the amplitude approaches 2.7 mm, the frequency is about 34 Hz and the vibration angle is around 42 degrees, the looseness ratio produces better performance. The paper offered insights to the design and manufacturing of vibrating screen