Search arXiv⌕ Search

arXiv subjects

Simeng Wang

Publications and source records attributed to Simeng Wang.

At least 19 recordsLinked to original sources
arXiv2025

Entropy-Constrained Strategy Optimization in Urban Floods: A Multi-Agent Framework with LLM and Knowledge Graph Integration

In recent years, the increasing frequency of extreme urban rainfall events has posed significant challenges to emergency scheduling systems. Urban flooding often leads to severe traffic congestion and service disruptions, threatening public safety and mobility. However, effective decision making remains hindered by three key challenges: (1) managing trade-offs among competing goals (e.g., traffic flow, task completion, and risk mitigation) requires dynamic, context-aware strategies; (2) rapidly evolving environmental conditions render static rules inadequate; and (3) LLM-generated strategies frequently suffer from semantic instability and execution inconsistency. Existing methods fail to align perception, global optimization, and multi-agent coordination within a unified framework. To tackle these challenges, we introduce H-J, a hierarchical multi-agent framework that integrates knowledge-guided prompting, entropy-constrained generation, and feedback-driven optimization. The framework establishes a closed-loop pipeline spanning from multi-source perception to strategic execution and continuous refinement. We evaluate H-J on real-world urban topology and rainfall data under three representative conditions: extreme rainfall, intermittent bursts, and daily light rain. Experiments show that H-J outperforms rule-based and reinforcement-learning baselines in traffic smoothness, task success rate, and system robustness. These findings highlight the promise of uncertainty-aware, knowledge-constrained LLM-based approaches for enhancing resilience in urban flood response.

cs.AI↗
arXiv2025

Proper cocycles, measure equivalence and $L_p$-Fourier multipliers

We develop a new transference method for completely bounded $L_p$-Fourier multipliers via proper cocycles arising from probability measure-preserving group actions. This method extends earlier results by Haagerup and Jolissaint, which were limited to the case $p = \infty$. Based on this approach, we present a new and simple proof of the main result in [Hong-Wang-Wang, Mem. Amer. Math. Soc. 2024] regarding the pointwise convergence of noncommutative Fourier series on amenable groups, refining the associated estimate for maximal inequalities. In addition, this framework yields a transference principle for $L_p$-Fourier multipliers from lattices in linear Lie groups to their ambient groups, establishing a noncommutative analogue of Jodeit's theorem. As a further application, we construct a natural analogue of the Hilbert transform on $SL_2(\mathbb{R})$.

math.FA↗
arXiv2024

Tracial central states on compact quantum groups

Motivated by classical investigation of conjugation invariant positive-definite functions on discrete groups, we study tracial central states on universal C*-algebras associated with compact quantum groups, where centrality is understood in the sense of invariance under the adjoint action. We fully classify such states on q-deformations of compact Lie groups, on free orthogonal quantum groups, quantum permutation groups and on quantum hyperoctahedral groups.

math.OA↗
arXiv2024

Fullness of $q$-Araki-Woods factors

The $q$-Araki-Woods factor associated to a group of orthogonal transformations on a real separable Hilbert space $\mathsf{H}_{\mathbb{R}}$ is full as soon as $\dim\mathsf{H}_{\mathbb{R}}\geq 2$.

math.OA↗
arXiv2023

Enhancing Recommender Systems with Large Language Model Reasoning Graphs

Recommendation systems aim to provide users with relevant suggestions, but often lack interpretability and fail to capture higher-level semantic relationships between user behaviors and profiles. In this paper, we propose a novel approach that leverages large language models (LLMs) to construct personalized reasoning graphs. These graphs link a user's profile and behavioral sequences through causal and logical inferences, representing the user's interests in an interpretable way. Our approach, LLM reasoning graphs (LLMRG), has four components: chained graph reasoning, divergent extension, self-verification and scoring, and knowledge base self-improvement. The resulting reasoning graph is encoded using graph neural networks, which serves as additional input to improve conventional recommender systems, without requiring extra user or item information. Our approach demonstrates how LLMs can enable more logical and interpretable recommender systems through personalized reasoning graphs. LLMRG allows recommendations to benefit from both engineered recommendation systems and LLM-derived reasoning graphs. We demonstrate the effectiveness of LLMRG on benchmarks and real-world scenarios in enhancing base recommendation models.

cs.IR↗
arXiv2023

Leveraging Large Language Models for Pre-trained Recommender Systems

Recent advancements in recommendation systems have shifted towards more comprehensive and personalized recommendations by utilizing large language models (LLM). However, effectively integrating LLM's commonsense knowledge and reasoning abilities into recommendation systems remains a challenging problem. In this paper, we propose RecSysLLM, a novel pre-trained recommendation model based on LLMs. RecSysLLM retains LLM reasoning and knowledge while integrating recommendation domain knowledge through unique designs of data, training, and inference. This allows RecSysLLM to leverage LLMs' capabilities for recommendation tasks in an efficient, unified framework. We demonstrate the effectiveness of RecSysLLM on benchmarks and real-world scenarios. RecSysLLM provides a promising approach to developing unified recommendation systems by fully exploiting the power of pre-trained language models.

cs.IR↗
arXiv2023

Classical actions of quantum permutation groups

We describe explicitly all actions of the quantum permutation groups on classical compact spaces. In particular, we show that the defining action is the only non-trivial ergodic one. We then extend these results to all easy quantum groups associated to non-crossing partitions.

math.OA↗
arXiv2022

Noncommutative maximal ergodic inequalities for amenable groups

We prove a pointwise ergodic theorem and a maximal inequality for actions of amenable groups on noncommutative measure spaces. To do so, we establish a square function estimate quantifying the difference between ergodic averages and some conditional expectations. Our main technical results are the construction of a well-behaved filtration, based on the quasi-tilings of Ornstein and Weiss, and the square function bound, which we derive from non-doubling noncommutative Calder\'on-Zygmund decomposition. For actions on usual measure spaces, we obtain new variational ergodic inequalities and jump estimates.

math.OA↗
arXiv2022

On the factoriality of q-deformed Araki-Woods von Neumann algebras

The $q$-deformed Araki-Woods von Neumann algebras $\Gamma_q(\mathcal{H}_\mathbb{R}, U_t)^{\prime \prime}$ are factors for all $q\in (-1,1)$ whenever $dim(\mathcal{H}_\mathbb{R})\geq 3$. When $dim(\mathcal{H}_\mathbb{R})=2$ they are factors as well for all $q$ so long as the parameter defining $(U_t)$ is `small' or $1$ $($trivial$)$ as the case may be.

math.OA↗
arXiv2021

Tannaka-Krein reconstruction and ergodic actions of easy quantum groups

We give a new alternative version of the reconstruction procedure for ergodic actions of compact quantum groups and we refine it to include characterizations of (braided commutative) Yetter-Drinfeld C*-algebras. We then use this to construct families of ergodic actions of easy quantum groups out of combinatorial data involving partitions and study them. Eventually, we use this categorical point of view to show that the quantum permutation group cannot act ergodically on a classical connected compact space, thereby answering a question of D. Goswami and H. Huang.

math.OA↗
arXiv2020

Cutoff profiles for quantum L\'{e}vy processes and quantum random transpositions

We consider a natural analogue of Brownian motion on free orthogonal quantum groups and prove that it exhibits a cutoff at time $N\ln(N)$. Then, we study the induced classical process on the real line and compute its atoms and density. This enables us to find the cutoff profile, which involves free Poisson distributions and the semi-circle law. We prove similar results for quantum permutations and quantum random transpositions.

math.PR↗
arXiv2020

Ke Li's lemma for quantum hypothesis testing in general von Neumann algebras

A lemma stated by Ke Li in [arXiv:1208.1400] has been used in e.g. [arXiv:1510.04682,arXiv:1706.04590,arXiv:1612.01464,arXiv:1308.6503,arXiv:1602.08898] for various tasks in quantum hypothesis testing, data compression with quantum side information or quantum key distribution. This lemma was originally proven in finite dimension, with a direct extension to type I von Neumann algebras. Here we show that the use of modular theory allows to give more transparent meaning to the objects constructed by the lemma, and to prove it for general von Neumann algebras. This yields a new proof of quantum Stein's lemma with slightly weaker assumption, as well as immediate generalizations of its second order asymptotics, for example the main results in [arXiv:1510.04682] and [arXiv:1208.1400].

math-ph↗
arXiv2019

Pointwise convergence of noncommutative Fourier series

This paper is devoted to the study of pointwise convergence of Fourier series for group von Neumann algebras and quantum groups. It is well-known that a number of approximation properties of groups can be interpreted as summation methods and mean convergence of the associated noncommutative Fourier series. Based on this framework, this paper studies the refined counterpart of pointwise convergence of these Fourier series. As a key ingredient, we develop a noncommutative bootstrap method and establish a general criterion of maximal inequalities for approximate identities of noncommutative Fourier multipliers. Based on this criterion, we prove that for any countable discrete amenable group, there exists a sequence of finitely supported positive definite functions tending to $1$ pointwise, so that the associated Fourier multipliers on noncommutative $L_p$-spaces satisfy the pointwise convergence for all $p>1$. In a similar fashion, we also obtain results for a large subclass of groups (as well as quantum groups) with the Haagerup property and the weak amenability. We also consider the analogues of Fej\'{e}r and Bochner-Riesz means in the noncommutative setting. Our approach heavily relies on the noncommutative ergodic theory in conjunction with abstract constructions of Markov semigroups, inspired by quantum probability and geometric group theory. Finally, we also obtain as a byproduct the dimension free bounds of the noncommutative Hardy-Littlewood maximal inequalities associated with convex bodies.

math.OA↗
arXiv2019

Maximal ergodic inequalities for some positive operators on noncommutative $L_p$-spaces

In this paper, we establish the one-sided maximal ergodic inequalities for a large subclass of positive operators on noncommutative $L_p$-spaces for a fixed $1<p<\infty$, which particularly applies to positive isometries and general positive Lamperti contractions or power bounded doubly Lamperti operators; moreover, it is known that this subclass recovers all positive contractions on the classical Lebesgue spaces $L_p([0,1])$. Our study falls into neither the category of positive contractions considered by Junge-Xu nor the class of power bounded positive invertible operators considered by Hong-Liao-Wang. Our strategy essentially relies on various structural characterizations and dilation properties associated with Lamperti operators, which are of independent interest. More precisely, we give a structural description of Lamperti operators in the noncommutative setting, and obtain a simultaneous dilation theorem for Lamperti contractions. As a consequence we establish the maximal ergodic theorem for the strong closure of the convex hull of corresponding family of positive contractions. Moreover, in conjunction with a newly-built structural theorem, we also obtain the maximal ergodic inequalities for positive power bounded doubly Lamperti operators. We also observe that the concrete examples of positive contractions without Akcoglu's dilation, which were constructed by Junge-Le Merdy, still satisfy the maximal ergodic inequalities. We also discuss some other examples, showing sharp contrast to the classical situation.

math.OA↗
arXiv2018

Quantum symmetries on noncommutative complex spheres with partial commutation relations

We introduce the notion of noncommutative complex spheres with partial commutation relations for the coordinates. We compute the corresponding quantum symmetry groups of these spheres, and this yields new quantum unitary groups with partial commutation relations. We also discuss some geometric aspects of the quantum orthogonal groups associated with the mixture of classical and free independence discovered by Speicher and Weber. We show that these quantum groups are quantum symmetry groups on some quantum spaces of spherical vectors with partial commutation relations.

math.QA↗
arXiv2017

Noncommutative maximal ergodic inequalities associated with doubling conditions

This paper is devoted to the study of noncommutative maximal inequalities and ergodic theorems for group actions on von Neumann algebras. Consider a locally compact group $G$ of polynomial growth with a symmetric compact subset $V$. Let $\alpha $ be a continuous action of $G$ on a von Neumann algebra $\mathcal{M}$ by trace-preserving automorphisms. We then show that the operators defined by \begin{equation*} A_{n}x= \frac{1}{m(V^{n})} \int _{V^{n}}\alpha _{g}x\,dm(g),\quad x\in L_{p}( \mathcal{M}),n\in \mathbb{N},1\leq p\leq \infty , \end{equation*} are of weak type $(1,1)$ and of strong type $(p,p)$ for $1 < p<\infty $. Consequently, the sequence $(A_{n}x)_{n\geq 1}$ converges almost uniformly for $x\in L_{p}(\mathcal{M})$ for $1\leq p<\infty $. Also, we establish the noncommutative maximal and individual ergodic theorems associated with more general doubling conditions, and we prove the corresponding results for general actions on one fixed noncommutative $L_{p}$-space which are beyond the class of Dunford-Schwartz operators considered previously by Junge and Xu. As key ingredients, we also obtain the Hardy-Littlewood maximal inequality on metric spaces with doubling measures in the operator-valued setting. After the groundbreaking work of Junge and Xu on the noncommutative Dunford-Schwartz maximal ergodic inequalities, this is the first time that more general maximal inequalities are proved beyond Junge and Xu's setting. Our approach is based on quantum probabilistic methods as well as random walk theory.

math.OA↗