arXiv subjects

Shang Xiang

Publications and source records attributed to Shang Xiang.

5 recordsLinked to original sources

arXiv2025

Charge functions for odd dimensional partitions

To construct a BPS algebra with representations furnished by n-dimensional partitions, the first step is to find the eigenvalues of the Cartan operators acting on them. The generating function of the eigenvalues is called the charge function. It has an important property that for each partition, the poles of the function correspond to the projection of the boxes which can be added to or removed from the partition legally. The charge functions of lower dimensional partitions, i.e., Young diagrams for 2D, plane partitions for 3D and solid partitions for 4D, are already given in the literature. In this paper, we propose an expression of the charge function for arbitrary odd dimensional partitions and have it proved for 5D case. Some explicit numerical tests for 7D and 9D case are also conducted to confirm our formula.

math-ph↗

arXiv2024

A high-accuracy multi-model mixing retrosynthetic method

The field of computer-aided synthesis planning (CASP) has seen rapid advancements in recent years, achieving significant progress across various algorithmic benchmarks. However, chemists often encounter numerous infeasible reactions when using CASP in practice. This article delves into common errors associated with CASP and introduces a product prediction model aimed at enhancing the accuracy of single-step models. While the product prediction model reduces the number of single-step reactions, it integrates multiple single-step models to maintain the overall reaction count and increase reaction diversity. Based on manual analysis and large-scale testing, the product prediction model, combined with the multi-model ensemble approach, has been proven to offer higher feasibility and greater diversity.

cs.LG↗

arXiv2023

Node-Aligned Graph-to-Graph (NAG2G): Elevating Template-Free Deep Learning Approaches in Single-Step Retrosynthesis

Single-step retrosynthesis (SSR) in organic chemistry is increasingly benefiting from deep learning (DL) techniques in computer-aided synthesis design. While template-free DL models are flexible and promising for retrosynthesis prediction, they often ignore vital 2D molecular information and struggle with atom alignment for node generation, resulting in lower performance compared to the template-based and semi-template-based methods. To address these issues, we introduce Node-Aligned Graph-to-Graph (NAG2G), a transformer-based template-free DL model. NAG2G combines 2D molecular graphs and 3D conformations to retain comprehensive molecular details and incorporates product-reactant atom mapping through node alignment which determines the order of the node-by-node graph outputs process in an auto-regressive manner. Through rigorous benchmarking and detailed case studies, we have demonstrated that NAG2G stands out with its remarkable predictive accuracy on the expansive datasets of USPTO-50k and USPTO-FULL. Moreover, the model's practical utility is underscored by its successful prediction of synthesis pathways for multiple drug candidate molecules. This not only proves NAG2G's robustness but also its potential to revolutionize the prediction of complex chemical synthesis processes for future synthetic route design tasks.

cs.LG↗

arXiv2022

Fast Electromagnetic Validations of Large-Scale Digital Coding Metasurfaces Accelerated by Recurrence Rebuild and Retrieval Method

The recurrence rebuild and retrieval method (R3M) is proposed in this paper to accelerate the electromagnetic (EM) validations of large-scale digital coding metasurfaces (DCMs). R3M aims to accelerate the EM validations of DCMs with varied codebooks, which involves the analysis of a group of similar but not identical structures. The method transforms general DCMs to rigorously periodic arrays by replacing each coding unit with the macro unit, which comprises all possible coding states. The system matrix corresponding to the rigorously periodic array is globally shared for DCMs with arbitrary codebooks via implicit retrieval. The discrepancy of the interactions for edge and corner units are precluded by the basis extension of periodic boundaries. Moreover, the hierarchical pattern exploitation (HPE) algorithm is leveraged to efficiently assemble the system matrix for further acceleration. Due to the fully utilization of the rigid periodicity, the computational complexity of R3M-HPE is theoretically lower than that of $\mathcal{H}$-matrix within the same paradigm. Numerical results for two types of DCMs indicate that R3M-HPE is accurate in comparison with commercial software. Besides, R3M-HPE is also compatible with the preconditioning for efficient iterative solutions. The efficiency of R3M-HPE for DCMs outperforms the conventional fast algorithms in both the storage and CPU time cost.

eess.SP↗

arXiv2018

A 36-Element Solution To Schneiders' Pyramid Hex-Meshing Problem And A Parity-Changing Template For Hex-Mesh Revision

In this paper, we present a solution that uses the least number of hexahedra to build a pyramid, which is the key block required for one type of automatic hex-meshing method to be successful. When the initial result of a hex-meshing program is not appropriate for specific applications, some templates are used for revision. The templates reported thus far are parity-preserving, which means that the parity of the number of hexahedra in a mesh is unchanged after a revision following the templates. We present a parity-changing template that makes the template set integral and more effective. These two findings are obtained by a program that we developed for this study, which is a tool for researchers to observe the characteristics of small hexahedral packings.

cs.CG↗