arXiv subjects

Siwei Xu

Publications and source records attributed to Siwei Xu.

4 recordsLinked to original sources

arXiv2025

On the uniqueness of Yangians

Let $\mathfrak{g}$ be a simple Lie algebra over the complex numbers, and let $\mathfrak{g}[u]$ denote its polynomial current algebra. In the mid-1980s, Drinfeld introduced the Yangian of $\mathfrak{g}$ as the unique solution to a quantization problem for a natural Lie bialgebra structure on $\mathfrak{g}[u]$. More precisely, Theorem 2 of [Dokl. Akad. Nauk SSSR 283 (1985), no. 5, 1060-1064] asserts that $\mathfrak{g}[u]$ admits a unique homogeneous quantization, the Yangian of $\mathfrak{g}$, which is described explicitly via generators and relations, starting from a copy of $\mathfrak{g}$ and its adjoint representation. Although the representation theory of Yangians has since undergone substantial development, a complete proof of Drinfeld's theorem has not appeared. In this article, we present a proof of the assertion that $\mathfrak{g}[u]$ admits at most one homogeneous quantization. Our argument combines cohomological and computational methods, and outputs a presentation of any such quantization using Drinfeld's generators and a reduced set of defining relations.

math.QA↗

arXiv2024

Single-Cell Omics Arena: A Benchmark Study for Large Language Models on Cell Type Annotation Using Single-Cell Data

Over the past decade, the revolution in single-cell sequencing has enabled the simultaneous molecular profiling of various modalities across thousands of individual cells, allowing scientists to investigate the diverse functions of complex tissues and uncover underlying disease mechanisms. Among all the analytical steps, assigning individual cells to specific types is fundamental for understanding cellular heterogeneity. However, this process is usually labor-intensive and requires extensive expert knowledge. Recent advances in large language models (LLMs) have demonstrated their ability to efficiently process and synthesize vast corpora of text to automatically extract essential biological knowledge, such as marker genes, potentially promoting more efficient and automated cell type annotations. To thoroughly evaluate the capability of modern instruction-tuned LLMs in automating the cell type identification process, we introduce SOAR, a comprehensive benchmarking study of LLMs for cell type annotation tasks in single-cell genomics. Specifically, we assess the performance of 8 instruction-tuned LLMs across 11 datasets, spanning multiple cell types and species. Our study explores the potential of LLMs to accurately classify and annotate cell types in single-cell RNA sequencing (scRNA-seq) data, while extending their application to multiomics data through cross-modality translation. Additionally, we evaluate the effectiveness of chain-of-thought (CoT) prompting techniques in generating detailed biological insights during the annotation process. The results demonstrate that LLMs can provide robust interpretations of single-cell data without requiring additional fine-tuning, advancing the automation of cell type annotation in genomics research.

cs.CL↗

arXiv2024

Accretion of the degenerate Fermi gas onto a Reissner-Nordstr\"{o}m black hole

We extend the Rioseco and Sarbach model into Reissner-Nordstr\"{o}m black hole accretes degenerate relativistic Fermi gas. The accretion theory is based on the Boyer-Lindquist coordinates and the Fermi gas follows Fermi-Dirac statistics at infinity. The expressions for the particle current density, the stress energy-momentum tensor, and three accretion rates are derived. We first investigated the impact of Risoseco and Sarbach model on the evolution of a black hole's charge. The results show that both the mass accretion rate and charge accretion rate are proportional to the particle accretion rate. We have also provided analytical results at infinity and numerical results within a finite range for these quantities. Our results indicate that the accretion rate decreases as the charge of the black hole increases, suggesting that our accretion model does not violate the cosmic censorship hypothesis. In this paper, we first point out that the accretion of Vlasov gas behaves as an anisotropic fluid containing two perfect-fluid components. One component represents the isotropic fluid of Fermi gas, while the other represents a null fluid. When using the Boyer-Lindquist coordinate system, we observed that the contribution from the null fluid persists even at infinity, which led to the radial pressure always smaller than the tangential pressure. Therefore, it's not appropriate to treat the accretion model as a perfect fluid at infinity.

gr-qc↗

arXiv2024

Analytical calculation of Kerr and Kerr-Ads black holes in $f(R)$ theory

In this paper, we extend Chandrasekhar's method of calculating rotating black holes into $f(R)$ theory. We consider the Ricci scalar is a constant and derive the Kerr and Kerr-Ads metric by using the analytical mathematical method. Suppose that the spacetime is a 4-dimensional Riemannian manifold with a general stationary axisymmetric metric, we calculate Cartan's equation of structure and derive the Einstein tensor. In order to reduce the solving difficulty, we fix the gauge freedom to transform the metric into a more symmetric form. We solve the field equations in the two cases of the Ricci scalar $R=0$ and $R\neq 0$. In the case of $R=0$, the Ernst's equations are derived. We give the elementary solution of Ernst's equations and show the way to obtain more solutions including Kerr metric. In the case of $R\neq 0$, we reasonably assume that the solution to the equations consists of two parts: the first is Kerr part and the second is introduced by the Ricci scalar. Giving solution to the second part and combining the two parts, we obtain the Kerr-Ads metric. The calculations are carried out in a general $f(R)$ theory, indicating the Kerr and Kerr-Ads black holes exist widely in general $f(R)$ models. Furthermore, the whole solving process can be treated as a standard calculation procedure to obtain rotating black holes, which can be applied to other modified gravities.

gr-qc↗