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Shun Xu

Publications and source records attributed to Shun Xu.

15 recordsLinked to original sources
arXiv2026

Exactness and Drinfeld-Sokolov Realization of the McRae-Yang Tensor Functors

Let $p,q\geq2$ be coprime, set $k=-2+p/q$, and let $c_{p,q}=1-6(p-q)^2/(pq)$. McRae and Yang constructed right exact braided tensor functors from the non-semisimple Kazhdan-Lusztig categories of $V^{-2+p/q}(\mathfrak{sl}_2)$ and $V^{-2+q/p}(\mathfrak{sl}_2)$ to the Virasoro category $\mathcal{O}_{c_{p,q}}$, and conjectured that these functors are exact and agree with the corresponding quantum Drinfeld-Sokolov reductions. We prove this conjecture. For the $(p,q)$ branch, we determine the images of all indecomposable projective objects without assuming exactness, using projective tensor-product recursions and exact generalized conformal-residue projections. Projective faithfulness is then combined with a one-row Virasoro extension analysis to identify the non-wall images and to prove full faithfulness on projectives. The Virasoro input is matched objectwise with Nakano's logarithmic extension theorem away from the vacuum edge; the exceptional vacuum edge is handled directly by the staggered-module theory of Kyt\"ol\"a-Ridout, including the higher prime singular-vector branch. Independently, principal Drinfeld-Sokolov reduction is shown to be exact and faithful on the whole finite-length affine category and to have the same Weyl, simple, and projective images. Compatibility with the non-standard affine twist identifies the canonical nilpotent endomorphisms on projectives and removes the remaining scalar ambiguity in the comparison of adjacent projective morphisms. Projective density for right exact functors then yields a natural isomorphism \[ F_{p,q}\cong H^0_{DS,+}\big|_{{KL}^k(\mathfrak{sl}_2)}. \] The same argument after interchanging $p$ and $q$ identifies the second McRae-Yang functor with the transposed Drinfeld-Sokolov reduction.

math.RT↗
arXiv2026

$C_2$-Cofiniteness and Rationality of the Icosahedral Orbifold $V_{L_2}^{A_5}$

Let $L_2=\mathbb{Z}\alpha$ be the rank-one root lattice with $(\alpha,\alpha)=2$, and let $A_5$ act on the lattice vertex operator algebra $V_{L_2}$ through an icosahedral subgroup of $\operatorname{Aut}(V_{L_2})\cong PSL_2(\mathbb{C})$. We prove that the fixed-point vertex operator algebra $V_{L_2}^{A_5}$ is $C_2$-cofinite and strongly rational.

math.QA↗
arXiv2026

Twisted associative algebras and intertwining operators

For a vertex algebra $V$ with a finite-order automorphism $g$ satisfying $g^T = 1$ for some $T \in \mathbb{N}$, we construct an associative algebra $\tilde{\mathbf{A}}^{g,\infty}(V)$ and prove that the category of $\frac{1}{T}\mathbb{N}$-graded $g$-twisted $\phi$-coordinated $V$-modules is isomorphic to the category of graded $\tilde{\mathbf{A}}^{g,\infty}(V)$-modules. Furthermore, when $V$ is a vertex operator algebra, we construct associative algebras $\mathbf{A}^{g,\infty}(V)$ and $A^{g,\infty}(V)$, and establish that the categories of admissible $g$-twisted $V$-modules and ordinary $g$-twisted $V$-modules are isomorphic to the categories of graded $\mathbf{A}^{g,\infty}(V)$-modules and graded $A^{g,\infty}(V)$-modules, respectively. By proving that $\tilde{\mathbf{A}}^{g,\infty}(V)$ is isomorphic to $\mathbf{A}^{g,\infty}(V)$, we obtain the equivalence between the category of $\frac{1}{T}\mathbb{N}$-graded $g$-twisted $\phi$-coordinated $V$-modules and the category of admissible $g$-twisted $V$-modules. Let $g_1, g_2, g_3$ be three commuting automorphisms of $V$ of finite order such that $g_1 g_2 = g_3$ and $g_i^T = 1$ for $i = 1, 2, 3$ and some $T \in \mathbb{N}$. Suppose that $W_i$ is a $g_i$-twisted $V$-module for each $i = 1, 2, 3$. We then construct an $A^{g_3,\infty}(V)$-$A^{g_2,\infty}(V)$-bimodule ${A}^{g_3,g_2,\infty}(W_1)$, and prove that the space of intertwining operators of type $\binom{W_3}{W_1 \; W_2}$ is isomorphic to $ \operatorname{Hom}_{A^{g_3,\infty}(V)}\!\left( {A}^{g_3,g_2,\infty}(W_1) \otimes_{A^{g_2,\infty}(V)} W_2, \, W_3 \right). $

math.QA↗
arXiv2025

Twisted bimodules and associative algebras associated to VOAs

Let $V$ be a vertex operator algebra, $g$ be an automorphism of $V$ of order $T$, and $m, n \in (1/T)\mathbb{N}$. In~\cite{HX2} and~\cite{HXX1}, it was shown respectively that the associative algebra $A_{g,n}(V)$ constructed by Dong, Li, and Mason~\cite{DLM3}, and the $A_{g,n}(V)\!-\!A_{g,m}(V)$-bimodule $A_{g,n,m}(V)$ constructed by Dong and Jiang~\cite{DJ2}, are both isomorphic to certain subquotients of $U(V[g])$, where $U(V[g])$ denotes the universal enveloping algebra of $V$ with respect to $g$. In this paper, we give a unified and concise proof of these isomorphisms.

math.QA↗
arXiv2025

Twisted $\phi$-coordinated modules for vertex algebras and Zhu's correspondence theorem

Let $V$ be a vertex algebra and $g$ be an automorphism of $V$ of order $T$. For any $n, m \in (1/T)\mathbb{N}$, we construct an $\tilde{A}_{g,n}(V)\!-\!\tilde{A}_{g,m}(V)$-bimodule $\tilde{A}_{g,n,m}(V)$, where $\tilde{A}_{g,n}(V)$ denotes the associative algebra constructed by the authors in \cite{Shun1}. We introduce the notion of $(1/T)\mathbb{N}$-graded $g$-twisted $\phi$-coordinated $V$-modules and prove that there exists a bijection between the simple $\tilde{A}_{g}(V)$-modules and the irreducible $(1/T)\mathbb{N}$-graded $g$-twisted $\phi$-coordinated $V$-modules, where $\tilde{A}_{g}(V)=\tilde{A}_{g,0}(V)$. We construct the universal enveloping algebra $U(V[g])$, showing that $\tilde{A}_{g}(V)$ is subquotient of $U(V[g])$. When $V$ is vertex operator algebra, we show that each $\tilde{A}_{g,n,m}(V)$ is isomorphic to the $A_{g,n}(V)-A_{g,m}(V)$-bimodule $A_{g,n,m}(V)$ constructed by Dong and Jiang~\cite{DJ2}. Also we prove that there exists a bijection between the irreducible admissible $g$-twisted $V$-modules and the irreducible $(1/T)\mathbb{N}$-graded $g$-twisted $\phi$-coordinated $V$-modules.

math.QA↗
arXiv2025

Single-orientation Crystalline Domains of Active Brownian Particles Lead to Collective Motions

Active Brownian particles, even without attractive and anisotropic inter-particle interactions, can form a high-density phase featuring structure-ordered domains as well as collective motion regions under thermal noise. However, the mechanism, particularly the relationship between the motion and structure, remains unclear. In this study, we show that the motion-correlation regions are spatially coincident with the single-orientation crystalline domains. Each domain translates or rotates as a whole due to the net active force or torque acting upon it, allowing relative motions between these crystalline domains. The particles at domain boundaries usually have the active forces pointing inward, which helps to stabilize these structure-ordered domains and their corresponding collective motion regions.

cond-mat.soft↗
arXiv2025

Twisted associative algebras associated to vertex algebras

Let $V$ be a vertex algebra and $g$ an automorphism of $V$ of order $T$. We construct a sequence of associative algebras $\tilde{A}_{g,n}(V )$ for any $n\in(1/T)\mathbb{N}$, which are not depend on the conformal structure of $V$. We show that for a vertex operator algebra, $g$-rationality, $g$-regularity, and twisted fusion rules are independent of the choice of the conformal vector.

math.QA↗
arXiv2025

Refining twisted bimodules associated to VOAs

Let $V$ be a vertex operator algebra and $g$ an automorphism of $V$ of finite order $T$. For any $m, n \in(1/T) \mathbb N$, an $A_{g,n}(V)\!-\!A_{g,m}(V)$ bimodule $A_{g,n, m}(V)=V/O_{g,n,m}(V)$ was defined by Dong and Jiang, where $O_{g,n,m}(V)$ is the sum of three certain subspaces $O_{g,n, m}^{\prime}(V), O_{g,n, m}^{\prime \prime}(V)$ and $O_{g,n, m}^{\prime \prime \prime}(V)$. In this paper, we show that $O_{g,n, m}(V)=O_{g,n, m}^{\prime}(V)$.

math.QA↗
arXiv2022

The coherent motions of thermal active Brownian particles

Active matter exhibits many intriguing non-equilibrium character, \emph{e.g.}, the active Brownian particles (ABP) without any attractive and aligned interactions can occur the mobility-induced phase transition to form some dense domains with both the structural ordering and dynamical coherence. Recently, the velocity correlation among the particles in the dense and ordered clusters was found in athermal ABP systems, however, seemed to disappear if including the thermal noises to describe microscopic ABPs, bringing some confusion about the generality of the consistence between structure and dynamics in ABPs. Here we demonstrate that the thermal noises imposing a large random term on the instantaneous velocity of ABPs hinder the observation of the (small) correlation in motions of ABPs. By averaging the instantaneous velocity (or equivalently, calculating the displacement) in various lag times, we show that the motions of thermal-fluctuated ABPs in the one order of magnitude smaller than the translational characteristic time are highly coherent and consistent spatially with the structural ordering of the ABPs.

cond-mat.soft↗
arXiv2021

On Recovering the Best Rank-r Approximation from Few Entries

In this note, we investigate how well we can reconstruct the best rank-$r$ approximation of a large matrix from a small number of its entries. We show that even if a data matrix is of full rank and cannot be approximated well by a low-rank matrix, its best low-rank approximations may still be reliably computed or estimated from a small number of its entries. This is especially relevant from a statistical viewpoint: the best low-rank approximations to a data matrix are often of more interest than itself because they capture the more stable and oftentimes more reproducible properties of an otherwise complicated data-generating model. In particular, we investigate two agnostic approaches: the first is based on spectral truncation; and the second is a projected gradient descent based optimization procedure. We argue that, while the first approach is intuitive and reasonably effective, the latter has far superior performance in general. We show that the error depends on how close the matrix is to being of low rank. Both theoretical and numerical evidence is presented to demonstrate the effectiveness of the proposed approaches.

stat.ME↗
arXiv2021

Automatic Identification of the End-Diastolic and End-Systolic Cardiac Frames from Invasive Coronary Angiography Videos

Automatic identification of proper image frames at the end-diastolic (ED) and end-systolic (ES) frames during the review of invasive coronary angiograms (ICA) is important to assess blood flow during a cardiac cycle, reconstruct the 3D arterial anatomy from bi-planar views, and generate the complementary fusion map with myocardial images. The current identification method primarily relies on visual interpretation, making it not only time-consuming but also less reproducible. In this paper, we propose a new method to automatically identify angiographic image frames associated with the ED and ES cardiac phases by using the trajectories of key vessel points (i.e. landmarks). More specifically, a detection algorithm is first used to detect the key points of coronary arteries, and then an optical flow method is employed to track the trajectories of the selected key points. The ED and ES frames are identified based on all these trajectories. Our method was tested with 62 ICA videos from two separate medical centers (22 and 9 patients in sites 1 and 2, respectively). Comparing consensus interpretations by two human expert readers, excellent agreement was achieved by the proposed algorithm: the agreement rates within a one-frame range were 92.99% and 92.73% for the automatic identification of the ED and ES image frames, respectively. In conclusion, the proposed automated method showed great potential for being an integral part of automated ICA image analysis.

eess.IV↗
arXiv2020

Lattice QCD package GWU-code and QUDA with HIP

The open source HIP platform for GPU computing provides an uniform framework to support both the NVIDIA and AMD GPUs, and also the possibility to porting the CUDA code to the HIP- compatible one. We present the porting progress on the Overlap fermion inverter (GWU-code) and also the general Lattice QCD inverter package - QUDA. The manual of using QUDA on HIP and also the tips of porting general CUDA code into the HIP framework are also provided.

hep-lat↗
arXiv2015

Equilibrium sampling by re-weighting non-equilibrium simulation trajectories

With the traditional equilibrium molecular simulations, it is usually difficult to efficiently visit the whole conformational space in complex systems, which are separated into some metastable conformational regions by high free energy barriers. The applied non-equilibrium process in simulations could enhance the transitions among these conformational regions, and the associated non-equilibrium effects can be removed by employing the Jarzynski equality (JE), then the global equilibrium distribution can be reproduced. However, the original JE requires the initial distribution of the non-equilibrium process is equilibrium, which largely limits the application of the non-equilibrium method in equilibrium sampling. By extending the previous method, the reweighted ensemble dynamics (RED), which re-weights many equilibrium simulation trajectories from arbitrary initial distribution to reproduce the global equilibrium, to non-equilibrium simulations, we present a method, named as re-weighted non-equilibrium ensemble dynamics (RNED), to generalize the JE in the non-equilibrium trajectories started from an arbitrary initial distribution, thus provide an efficient method to reproduce the equilibrium distribution based on multiple independent (short) non-equilibrium trajectories. We have illustrated the validity of the RNED in a one-dimensional toy model and in a Lennard-Jones system to detect the liquid-solid phase coexistence.

cond-mat.soft↗