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Xuan Zhou

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Published work

13 published item(s)

preprint2026arXiv

GASim: A Graph-Accelerated Hybrid Framework for Social Simulation

Large-scale social simulators are essential for studying complex social patterns. Prior work explores hybrid methods to scale up simulations, combining large language models (LLM)-based agents with numerical agent-based models (ABM). However, this incurs high latency due to expensive memory retrieval and sequential ABM execution. To address this challenge, we propose GASim, a graph-accelerated hybrid multi-agent framework for large-scale social simulations. For core agents driven by LLM, GASim introduces Graph-Optimized Memory (GOM) to replace intensive LLM-based retrieval pipelines with lightweight propagation over a sparse memory graph. For the majority of ordinary agents, GASim employs Graph Message Passing (GMP), substituting sequential ABM execution with parallel updates by fine-grained feature aggregation and Graph Attention Network. We further introduce Entropy-Driven Grouping (EDG) that coordinates this hybrid partitioning, leveraging information entropy to dynamically identify emergent core agents situated in information-diverse neighborhoods. Extensive experiments show that GASim not only delivers a substantial 9.94-fold end-to-end speedup over the traditional hybrid framework but also consumes less than 20% of baseline tokens, significantly reducing costs while preserving strong alignment with real-world public opinion trends. Our code is available at https://github.com/Jasmine0201/GASim.

preprint2023arXiv

Deep Reinforcement Learning in a Monetary Model

We propose using deep reinforcement learning to solve dynamic stochastic general equilibrium models. Agents are represented by deep artificial neural networks and learn to solve their dynamic optimisation problem by interacting with the model environment, of which they have no a priori knowledge. Deep reinforcement learning offers a flexible yet principled way to model bounded rationality within this general class of models. We apply our proposed approach to a classical model from the adaptive learning literature in macroeconomics which looks at the interaction of monetary and fiscal policy. We find that, contrary to adaptive learning, the artificially intelligent household can solve the model in all policy regimes.

preprint2022arXiv

Effect of noncircularity on the dynamic behaviors of particles in a disformal rotating black-hole spacetime

A disformal rotating black-hole solution is a black-hole solution in quadratic degenerate higher-order scalar-tensor theories. It breaks the circular condition of spacetime different from the case of the usual Kerr spacetime. This study investigated the dynamic behaviors of the motion of timelike particles in such disformal black-hole spacetime with an extra deformation parameter. Results showed that the characteristics of the particle's motion depend on the sign of the deformation parameter. For the positive deformation parameter, the motion is regular and orderly. For the negative one, as the deformation parameter changes, the motion of the particles undergoes a series of transitions between the chaotic motion and the regular motion and falls into the horizon or escapes to spatial infinity. This means that the dynamic behavior of timelike particles in the disformal Kerr black-hole spacetime with noncircularity becomes richer than that in the usual Kerr black-hole case.

preprint2021arXiv

Long time asymptotics for the nonlocal mKdV equation with finite density initial data

In this paper, we consider the Cauchy problem for an integrable real nonlocal (also called reverse-space-time) mKdV equation with nonzero boundary conditions \begin{align*} &q_t(x,t)-6σq(x,t)q(-x,-t)q_{x}(x,t)+q_{xxx}(x,t)=0, &q(x,0)=q_{0}(x),\lim_{x\to \pm\infty} q_{0}(x)=q_{\pm}, \end{align*} where $|q_{\pm}|=1$ and $q_{+}=δq_{-}$, $σδ=-1$. Based on the spectral analysis of the Lax pair, we express the solution of the Cauchy problem of the nonlocal mKdV equation in terms of a Riemann-Hilbert problem. In a fixed space-time solitonic region $-6<x/t<6$, we apply $\bar{\partial}$-steepest descent method to analyze the long-time asymptotic behavior of the solution $q(x,t)$. We find that the long time asymptotic behavior of $q(x,t)$ can be characterized with an $N(Λ)$-soliton on discrete spectrum and leading order term $\mathcal{O}(t^{-1/2})$ on continuous spectrum up to an residual error order $\mathcal{O}(t^{-1})$.

preprint2016arXiv

Heisenberg double as braided commutative Yetter-Drinfel'd module algebra over Drinfel'd double in multiplier Hopf algebra case

Based on a pairing of two regular multiplier Hopf algebras $A$ and $B$, Heisenberg double $\mathscr{H}$ is the smash product $A \# B$ with respect to the left regular action of $B$ on $A$. Let $\mathscr{D}=A\bowtie B$ be the Drinfel'd double, then Heisenberg double $\mathscr{H}$ is a Yetter-Drinfel'd $\mathscr{D}$-module algebra, and it is also braided commutative by the braiding of Yetter-Drinfel'd module, which generalizes the results in [10] to some infinite dimensional cases.

preprint2015arXiv

GAIL---Guaranteed Automatic Integration Library in MATLAB: Documentation for Version 2.1

Automatic and adaptive approximation, optimization, or integration of functions in a cone with guarantee of accuracy is a relatively new paradigm. Our purpose is to create an open-source MATLAB package, Guaranteed Automatic Integration Library (GAIL), following the philosophy of reproducible research and sustainable practices of robust scientific software development. For our conviction that true scholarship in computational sciences are characterized by reliable reproducibility, we employ the best practices in mathematical research and software engineering known to us and available in MATLAB. This document describes the key features of functions in GAIL, which includes one-dimensional function approximation and minimization using linear splines, one-dimensional numerical integration using trapezoidal rule, and last but not least, mean estimation and multidimensional integration by Monte Carlo methods or Quasi Monte Carlo methods.

preprint2015arXiv

Transmutation Theory and Quantization Approach for Quantum Groupoids

Let $H$ and $L$ be quantum groupoids. If $H$ has a quasitriangular structure, then we show that $L$ induces a Hopf algebra $C_{L}(L_s)$ in the category $_{H}\mathcal{M}$, which generalizes the transmutation theory introduced by Majid. Furthermore, if $H$ is commutative, we can construct a Hopf algebra $C_H(H_s)_F$ in the category $_H\mathcal{M}_F$ for a weak invertible unit 2-cocycle $F$, which generalizes the results in \cite{D83}. Finally, we consider the relation between two Hopf algebras: $C_H(H_s)_F$ and $C_{\widetilde H}(\widetilde{H}_s)$, and obtain that they are isomorphic as objects in the category $_{\widetilde H}\mathcal{M}$, where $(\widetilde H, \widetilde{\mathcal{R}})$ is a new quasitriangular quantum groupoid induced by $(H, \mathcal{R})$.

preprint2014arXiv

Characterizing Spatial Patterns of Base Stations in Cellular Networks

The topology of base stations (BSs) in cellular networks, serving as a basis of networking performance analysis, is considered to be obviously distinctive with the traditional hexagonal grid or square lattice model, thus stimulating a fundamental rethinking. Recently, stochastic geometry based models, especially the Poisson point process (PPP), attracts an ever-increasing popularity in modeling BS deployment of cellular networks due to its merits of tractability and capability for capturing nonuniformity. In this study, a detailed comparison between common stochastic models and real BS locations is performed. Results indicate that the PPP fails to precisely characterize either urban or rural BS deployment. Furthermore, the topology of real data in both regions are examined and distinguished by statistical methods according to the point interaction trends they exhibit. By comparing the corresponding real data with aggregative point process models as well as repulsive point process models, we verify that the capacity-centric deployment in urban areas can be modeled by typical aggregative processes such as the Matern cluster process, while the coverage-centric deployment in rural areas can be modeled by representative

preprint2014arXiv

Large-scale Spatial Distribution Identification of Base Stations in Cellular Networks

The performance of cellular system significantly depends on its network topology, where the spatial deployment of base stations (BSs) plays a key role in the downlink scenario. Moreover, cellular networks are undergoing a heterogeneous evolution, which introduces unplanned deployment of smaller BSs, thus complicating the performance evaluation even further. In this paper, based on large amount of real BS locations data, we present a comprehensive analysis on the spatial modeling of cellular network structure. Unlike the related works, we divide the BSs into different subsets according to geographical factor (e.g. urban or rural) and functional type (e.g. macrocells or microcells), and perform detailed spatial analysis to each subset. After examining the accuracy of Poisson point process (PPP) in BS locations modeling, we take into account the Gibbs point processes as well as Neyman-Scott point processes and compare their accuracy in view of large-scale modeling test. Finally, we declare the inaccuracy of the PPP model, and reveal the general clustering nature of BSs deployment, which distinctly violates the traditional assumption. This paper carries out a first large-scale identification regarding available literatures, and provides more realistic and more general results to contribute to the performance analysis for the forthcoming heterogeneous cellular networks.

preprint2014arXiv

Recommendation Scheme Based on Converging Properties for Contents Broadcasting

Popular videos are often clicked by a mount of users in a short period. With content recommendation, the popular contents could be broadcast to the potential users in wireless network, to save huge transmitting resource. In this paper, the contents propagation model is analyzed due to users' historical behavior, location, and the converging properties in wireless data transmission, with the users' communication log in the Chinese commercial cellular network. And a recommendation scheme is proposed to achieve high energy efficiency.

preprint2014arXiv

Tractability of the function approximation problem in terms of the kernel's shape and scale parameters

This article studies the problem of approximating functions belonging to a Hilbert space $\mathcal H_d$ with a reproducing kernel of the form $$\tilde K_d(\boldsymbol x,\boldsymbol t):=\prod_{\ell=1}^d \left(1-α_\ell^2+α_\ell^2K_{γ_\ell}(x_\ell,t_\ell)\right)\ \ \ \mbox{for all} \ \ \ \boldsymbol x,\boldsymbol t\in\mathbb R^d.$$ The $α_\ell\in[0,1]$ are scale parameters, and the $γ_\ell>0$ are sometimes called shape parameters. The reproducing kernel $K_γ$ corresponds to some Hilbert space of functions defined on $\mathbb R$. The kernel $\tilde K_d$ generalizes the anisotropic Gaussian reproducing kernel, whose tractability properties have been established in the literature. We present sufficient conditions on $\{α_\ell γ_\ell\}_{\ell=1}^{\infty}$ under which polynomial tractability holds for function approximation problems on $\mathcal H_d$. The exponent of strong polynomial tractability arises from bounds on the eigenvalues of a positive definite linear operator.

preprint2014arXiv

Two-tier Spatial Modeling of Base Stations in Cellular Networks

Poisson Point Process (PPP) has been widely adopted as an efficient model for the spatial distribution of base stations (BSs) in cellular networks. However, real BSs deployment are rarely completely random, due to environmental impact on actual site planning. Particularly, for multi-tier heterogeneous cellular networks, operators have to place different BSs according to local coverage and capacity requirement, and the diversity of BSs' functions may result in different spatial patterns on each networking tier. In this paper, we consider a two-tier scenario that consists of macrocell and microcell BSs in cellular networks. By analyzing these two tiers separately and applying both classical statistics and network performance as evaluation metrics, we obtain accurate spatial model of BSs deployment for each tier. Basically, we verify the inaccuracy of using PPP in BS locations modeling for either macrocells or microcells. Specifically, we find that the first tier with macrocell BSs is dispersed and can be precisely modelled by Strauss point process, while Matern cluster process captures the second tier's aggregation nature very well. These statistical models coincide with the inherent properties of macrocell and microcell BSs respectively, thus providing a new perspective in understanding the relationship between spatial structure and operational functions of BSs.

preprint2013arXiv

Generalized Yetter-Drinfel'd module categories for regular multiplier Hopf algebras

For a regular multiplier Hopf algebra $A$, the Yetter-Drinfel'd module category ${}_{A}\mathcal{YD}^{A}$ is equivalent to the centre $Z({}_{A}\mathcal{M})$ of the unital left $A$-module category ${}_{A}\mathcal{M}$. Then we introduce the generalized $(α, β)$-Yetter-Drinfel'd module categories ${}_{A}\mathcal{GYD}^{A}(α, β)$, which are treated as components of a braided $T$-category. Especially when $A$ is a coFrobenius Hopf algebra, ${}_{A}\mathcal{YD}^{A}(α, β)$ is isomorphic to the unital $\hat{A} \bowtie A(α, β)$-module category ${}_{\hat{A} \bowtie A(α, β)}\mathcal{M}$. Finally for a Yetter-Drinfel'd $A$-module algebra $H$, we introduce Yetter-Drinfel'd $(H, A)$-module category, which is a monoidal.