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Pu Zhang

Publications and source records attributed to Pu Zhang.

At least 37 records · Page 2Linked to original sources
arXiv2025

Chains of model structures arising from modules of finite Gorenstein dimension

For any integer $n\ge 0$ and any ring $R$, \ $(\mathcal {PGF}_n, \ \mathcal P_n^\perp \cap \mathcal {PGF}^{\perp})$ proves to be a complete hereditary cotorsion pair in $R$-Mod, where $\mathcal {PGF}$ is the class of PGF modules, introduced by J. Šaroch and J. Štovíček, and \ $\mathcal {PGF}_n$ is the class of $R$-modules of PGF dimension $\le n$. For any Artin algebra $R$, \ $(\mathcal {GP}_n, \ \mathcal P_n^\perp \cap \mathcal {GP}^{\perp})$ proves to be a complete and hereditary cotorsion pair in $R$-Mod, where $\mathcal {GP}_n$ is the class of modules of Gorenstein projective dimension $\le n$. These cotorsion pairs induce two chains of hereditary Hovey triples \ $(\mathcal {PGF}_n, \ \mathcal P_n^\perp, \ \mathcal {PGF}^{\perp})$ and \ $(\mathcal {GP}_n, \ \mathcal P_n^\perp, \ \mathcal {GP}^{\perp})$, and the corresponding homotopy categories in the same chain are the same. It is observed that some complete cotorsion pairs in $R$-Mod can induce complete cotorsion pairs in some special extension closed subcategories of $R$-Mod. Then corresponding results in exact categories $\mathcal {PGF}_n$, \ $\mathcal {GP}_n$, \ $\mathcal {GF}_n$, \ $\mathcal {PGF}^{<\infty}$, \ $\mathcal {GP}^{<\infty}$ and $\mathcal {GF}^{<\infty}$, are also obtained. As a byproduct, $\mathcal{PGF} = \mathcal {GP}$ for a ring $R$ if and only if $\mathcal{PGF}^\perp\cap\mathcal{GP}_n=\mathcal P_n$ for some $n$.

math.RT↗
arXiv2025

Claus Michael Ringel's main contributions to Gorenstein-projective modules

In this article we try to recall Claus Michael Ringel's works on the Gorenstein-projective modules. This will involve but not limited to his fundamental contributions, such as in, the solution to the independence problem of totally reflexivity conditions; the technique of $\mho$-quivers; a fast algorithm to obtain the Gorenstein-projective modules over the Nakayama algebras; the one to one correspondence between the indecomposable non-projective perfect differential modules of a quiver and the indecomposable representations of this quiver; the description of the module category of the preprojective algebras of type $\mathbb A_n$ via submodule category; semi-Gorenstein-projective modules, reflexive modules, Koszul modules, as well as the $Ω$-growth of modules, over short local algebras; and his negative answer to the question whether an algebra has to be self-injective in case all the simple modules are reflexive.

math.RT↗
arXiv2025

Automating Security Audit Using Large Language Model based Agent: An Exploration Experiment

In the current rapidly changing digital environment, businesses are under constant stress to ensure that their systems are secured. Security audits help to maintain a strong security posture by ensuring that policies are in place, controls are implemented, gaps are identified for cybersecurity risks mitigation. However, audits are usually manual, requiring much time and costs. This paper looks at the possibility of developing a framework to leverage Large Language Models (LLMs) as an autonomous agent to execute part of the security audit, namely with the field audit. password policy compliance for Windows operating system. Through the conduct of an exploration experiment of using GPT-4 with Langchain, the agent executed the audit tasks by accurately flagging password policy violations and appeared to be more efficient than traditional manual audits. Despite its potential limitations in operational consistency in complex and dynamic environment, the framework suggests possibilities to extend further to real-time threat monitoring and compliance checks.

cs.CR↗
arXiv2025

Roadmap on Nonlocality in Photonic Materials and Metamaterials

Photonic technologies continue to drive the quest for new optical materials with unprecedented responses. A major frontier in this field is the exploration of nonlocal (spatially dispersive) materials, going beyond the local, wavevector-independent assumption traditionally made in optical material modeling. On one end, the growing interest in plasmonic, polaritonic and quantum materials has revealed naturally occurring nonlocalities, emphasizing the need for more accurate models to predict and design their optical responses. This has major implications also for topological, nonreciprocal, and time-varying systems based on these material platforms. Beyond natural materials, artificially structured materials--metamaterials and metasurfaces--can provide even stronger and engineered nonlocal effects, emerging from long-range interactions or multipolar effects. This is a rapidly expanding area in the field of photonic metamaterials, with open frontiers yet to be explored. In the case of metasurfaces, in particular, nonlocality engineering has become a powerful tool for designing strongly wavevector-dependent responses, enabling enhanced wavefront control, spatial compression, multifunctional devices, and wave-based computing. Furthermore, nonlocality and related concepts play a critical role in defining the ultimate limits of what is possible in optics, photonics, and wave physics. This Roadmap aims to survey the most exciting developments in nonlocal photonic materials, highlight new opportunities and open challenges, and chart new pathways that will drive this emerging field forward--toward new scientific discoveries and technological advancements.

cond-mat.mes-hall↗
arXiv2025

Model structures on triangulated categories with proper class of triangles

In contrast with the Hovey correspondence of abelian model structures from two compatible complete cotorsion pairs, Beligiannis and Reiten give a construction of model structures on abelian categories from one hereditary complete cotorsion pair. The aim of this paper is to extend this result to triangulated categories together with a proper class $ξ$ of triangles. There indeed exist non-trivial proper classes of triangles, and a proper class of triangles is not closed under rotations, in general. This is quite different from the class of all triangles. Thus one needs to develop a theory of triangles in $ξ$ and hereditary complete cotorsion pairs in a triangulated category $\T$ with respect to $ξ$. The Beligiannis - Reiten correspondence between weakly $ξ$-projective model structures on $\T$ and hereditary complete cotorsion pairs $(\X, \Y)$ with respect to $ξ$ such that the core $ω= \X \cap \Y$ is contravariantly finite in $\T$ is also obtained. To study the homotopy category of a model structure on a triangulated category, the condition in Quillen's Fundamental theorem of model categories needs to be weakened, by replacing the existence of pull-backs and push-outs by homotopy cartesian squares.

math.CT↗
arXiv2025

Model structure from one hereditary complete cortorsion pair

In contrast with the Hovey correspondence of abelian model structures from two complete cotorsion pairs, Beligiannis and Reiten give a construction of model structures on abelian categories from only one complete cotorsion pair. The aim of this paper is to extend this result to weakly idempotent complete exact categories, by adding the condition of heredity of the complete cotorsion pair. In fact, even for abelian categories, this condition of heredity should be added. This construction really gives model structures which are not necessarily exact in the sense of Gillespie. The correspondence of Beligiannis and Reiten of weakly projective model structures also holds for weakly idempotent complete exact categories.

math.RT↗
arXiv2025

Bi-Frobenius quantum complete intersections with permutation antipodes

Quantum complete intersections $A= A({\bf q, a})$ are Frobenius algebras, but in the most cases they can not become Hopf algebras. This paper aims to find bi-Frobenius algebra structures on $A$. A key step is the construction of comultiplication, such that $A$ becomes a bi-Frobenius algebra. By introducing compatible permutation and permutation antipode, a necessary and sufficient condition is found, such that $A$ admits a bi-Frobenius algebra structure with permutation antipode; and if this is the case, then a concrete construction is explicitly given. Using this, intrinsic conditions only involving the structure coefficients $({\bf q, a})$ of $A$ are obtained, for $A$ admitting a bi-Frobenius algebra structure with permutation antipode. When $A$ is symmetric, $A$ admits a bi-Frobenius algebra structure with permutation antipode if and only if there exists a compatible permutation $π$ with $A$ such that $π^2 = {\rm Id}$.

math.RA↗
arXiv2025

Homotopy categories and fibrant model structures

The homotopy category of a model structure on a weakly idempotent complete additive category is proved to be equivalent to the additive quotient of the category of cofibrant-fibrant objects with respect to the subcategory of cofibrant-fibrant-trivial objects. A model structure on pointed category is fibrant, if every object is a fibrant object. Fibrant model structures is explicitly described by trivial cofibrations, and also by fibrations. Fibrantly weak factorization systems are introduced, fibrant model structures are constructed via fibrantly weak factorization systems, and a one-one correspondence between fibrantly weak factorization systems and fibrant model structures is given. Applications are given to rediscover the $ω$-model structures and the $\mathcal W$-model structures, and their relations with exact model structures are discussed.

math.RT↗
arXiv2024

Quantum-hydrodynamic modal perspective on plasmonic gap structures

Plasmonic gap structures are among the few configurations capable of generating extreme light confinement, finding applications in surface-enhanced spectroscopy, ultrasensitive detection, photocatalysis and more. Their plasmonic response undergoes a dramatic, quantum effect-driven transition as the gap size approaches zero. Modal analysis can reveal insights into the mechanisms governing this process, which are otherwise obscured by nonlocal damping effects. Here, we offer a fresh modal perspective on the transition of the plasmonic response using quantum hydrodynamic theory (QHT)-based quasinormal mode (QNM) analysis. Focusing on the bonding dipolar and charge-transfer plasmons of a nanosphere dimer, we examine the detailed mode transition through the touching regime as well as the asymptotic behavior compared with the classical results as the constituent nanoparticles either separate or overlap. The complex eigenfrequency particularly provides accurate information on the linewidth and quality factor of the plasmon modes. We introduce an index to characterize charge-transfer efficiency, especially for the charge-transfer plasmon. The significant role of nonlocal damping in the mode evolution is elucidated by our mode-resolved QHT-QNM analysis. The insights from our theoretical study provide an integrated understanding of mode evolution in plasmonic gap structures, which can further advance gap structure-based applications.

cond-mat.mes-hall↗
arXiv2024

Ultra-wideband integrated microwave photonic multi-parameter measurement system on thin-film lithium niobate

Research on microwave signal measurement techniques is risen, driven by the expanding urgent demands of wireless communication, global positioning systems, remote sensing and 6G networks. In stark contrast with traditional electronic-based realization, the implementations of microwave signal measurement systems based on integrated compact photonic chip have exhibited distinct advantages in high operation bandwidth, light weight, and strong immunity to electromagnetic interference. However, although numerous integrated microwave photonic signal measurement systems have been reported, measurement bandwidth of the majority of them is still below 30 GHz due to the bandwidth limitation of electro-optical modulators (EOMs). Furthermore, previous studies often are more focused on the measurement of one single parameter (typically the frequency) of microwave signals, which has hindered their practical application in complex situations. Here, an integrated photonic microwave multi-parameter measurement system composed of microwave frequency measurement module and microwave phase amplitude measurement module based on thin-film lithium niobate (TFLN) platform is reported. Utilizing this system, not only the ultra-high bandwidth (up to 60GHz) of microwave frequency, phase and amplitude measurement with low root-mean-squares errors (450MHz, 3.43° and 1.64% of the measurement for frequency, phase and amplitude, respectively), but also the time-domain reconstruction of sinusoidal microwave signals is achieved. This demonstration further broadens the application of integrated TFLN photonic devices in microwave signal measurement technology to address the bandwidth bottleneck of the ever-growing microwave networks in the future information society.

physics.optics↗
arXiv2024

Enabling Intelligent Interactions between an Agent and an LLM: A Reinforcement Learning Approach

Large language models (LLMs) encode a vast amount of world knowledge acquired from massive text datasets. Recent studies have demonstrated that LLMs can assist an embodied agent in solving complex sequential decision making tasks by providing high-level instructions. However, interactions with LLMs can be time-consuming. In many practical scenarios, it requires a significant amount of storage space that can only be deployed on remote cloud servers. Additionally, using commercial LLMs can be costly since they may charge based on usage frequency. In this paper, we explore how to enable intelligent cost-effective interactions between a down stream task oriented agent and an LLM. We find that this problem can be naturally formulated by a Markov decision process (MDP), and propose When2Ask, a reinforcement learning based approach that learns when it is necessary to query LLMs for high-level instructions to accomplish a target task. On one side, When2Ask discourages unnecessary redundant interactions, while on the other side, it enables the agent to identify and follow useful instructions from the LLM. This enables the agent to halt an ongoing plan and transition to a more suitable one based on new environmental observations. Experiments on MiniGrid and Habitat environments that entail planning sub-goals demonstrate that When2Ask learns to solve target tasks with only a few necessary interactions with the LLM, significantly reducing interaction costs in testing environments compared with baseline methods. Our code is available at: https://github.com/ZJLAB-AMMI/LLM4RL.

cs.AI↗
arXiv2024

Large Language Model as a Policy Teacher for Training Reinforcement Learning Agents

Recent studies have uncovered the potential of Large Language Models (LLMs) in addressing complex sequential decision-making tasks through the provision of high-level instructions. However, LLM-based agents lack specialization in tackling specific target problems, particularly in real-time dynamic environments. Additionally, deploying an LLM-based agent in practical scenarios can be both costly and time-consuming. On the other hand, reinforcement learning (RL) approaches train agents that specialize in the target task but often suffer from low sampling efficiency and high exploration costs. In this paper, we introduce a novel framework that addresses these challenges by training a smaller, specialized student RL agent using instructions from an LLM-based teacher agent. By incorporating the guidance from the teacher agent, the student agent can distill the prior knowledge of the LLM into its own model. Consequently, the student agent can be trained with significantly less data. Moreover, through further training with environment feedback, the student agent surpasses the capabilities of its teacher for completing the target task. We conducted experiments on challenging MiniGrid and Habitat environments, specifically designed for embodied AI research, to evaluate the effectiveness of our framework. The results clearly demonstrate that our approach achieves superior performance compared to strong baseline methods. Our code is available at https://github.com/ZJLAB-AMMI/LLM4Teach.

cs.AI↗
arXiv2024

Towards Commonsense Knowledge based Fuzzy Systems for Supporting Size-Related Fine-Grained Object Detection

Deep learning has become the dominating approach for object detection. To achieve accurate fine-grained detection, one needs to employ a large enough model and a vast amount of data annotations. In this paper, we propose a commonsense knowledge inference module (CKIM) which leverages commonsense knowledge to assist a lightweight deep neural network base coarse-grained object detector to achieve accurate fine-grained detection. Specifically, we focus on a scenario where a single image contains objects of similar categories but varying sizes, and we establish a size-related commonsense knowledge inference module (CKIM) that maps the coarse-grained labels produced by the DL detector to size-related fine-grained labels. Considering that rule-based systems are one of the popular methods of knowledge representation and reasoning, our experiments explored two types of rule-based CKIMs, implemented using crisp-rule and fuzzy-rule approaches, respectively. Experimental results demonstrate that compared with baseline methods, our approach achieves accurate fine-grained detection with a reduced amount of annotated data and smaller model size. Our code is available at: https://github.com/ZJLAB-AMMI/CKIM.

cs.CV↗
arXiv2024

Commutators of the maximal and sharp functions with weighted Lipschitz functions

Let $M$ be the Hardy-Littlewood maximal function. Denote by $M_b$ and $[b,M]$ the maximal and the nonlinear commutators of $M$ with a function $b$. The boundedness of $M_b$ and $[b,M]$ on weighted Lebesgue spaces are characterized when the symbols $b$ belong to weighted Lipschitz (weighted Morrey-Campanato) spaces. Some new characterizations for weighted Lipschitz spaces are obtained. Similar results are also established for the nonlinear commutator of the sharp function.

math.CA↗
arXiv2023

SwinLSTM:Improving Spatiotemporal Prediction Accuracy using Swin Transformer and LSTM

Integrating CNNs and RNNs to capture spatiotemporal dependencies is a prevalent strategy for spatiotemporal prediction tasks. However, the property of CNNs to learn local spatial information decreases their efficiency in capturing spatiotemporal dependencies, thereby limiting their prediction accuracy. In this paper, we propose a new recurrent cell, SwinLSTM, which integrates Swin Transformer blocks and the simplified LSTM, an extension that replaces the convolutional structure in ConvLSTM with the self-attention mechanism. Furthermore, we construct a network with SwinLSTM cell as the core for spatiotemporal prediction. Without using unique tricks, SwinLSTM outperforms state-of-the-art methods on Moving MNIST, Human3.6m, TaxiBJ, and KTH datasets. In particular, it exhibits a significant improvement in prediction accuracy compared to ConvLSTM. Our competitive experimental results demonstrate that learning global spatial dependencies is more advantageous for models to capture spatiotemporal dependencies. We hope that SwinLSTM can serve as a solid baseline to promote the advancement of spatiotemporal prediction accuracy. The codes are publicly available at https://github.com/SongTang-x/SwinLSTM.

cs.CV↗
arXiv2023

Cotorsion pairs and model structures on Morita rings

This paper is to study cotorsion pairs and abelian model structures on some Morita rings \ $Λ=\left(\begin{smallmatrix} A & {}_AN_B {}_BM_A & B\end{smallmatrix}\right)$. From cotorsion pairs $(\mathcal U, \mathcal X)$ and $(\mathcal V, \mathcal Y)$, respectively in $A$-Mod and $B$-Mod, one constructs 4 kinds of cotorsion pairs in $Λ$-Mod. There even exists an algebra $Λ$ such that the four cotorsion pairs above are pairwise different. The heredity and completeness of these cotorsion pairs are studied. The problem of identifications, namely, when the first two cotorsion pairs are the same, and when the second two cotorsion pairs are the same, is investigated. Various model structures on $Λ$\mbox{-}{\rm Mod} are obtained, by explicitly giving the corresponding Hovey triples and Quillen's homotopy categories. In particular, cofibrantly generated Hovey triples, and the Gillespie-Hovey triples induced by compatible generalized projective (respectively, injective) cotorsion pairs, are explicitly contructed.

math.RT↗
arXiv2023

Bi-Frobenius algebra structure on quantum complete intersections

This paper is to look for bi-Frobenius algebra structures on quantum complete intersections. We find a class of comultiplications, such that if $\sqrt{-1}\in k$, then a quantum complete intersection becomes a bi-Frobenius algebra with comultiplication of this form if and only if all the parameters $q_{ij} = \pm 1$. Also, it is proved that if $\sqrt{-1}\in k$ then a quantum exterior algebra in two variables admits a bi-Frobenius algebra structure if and only if the parameter $q = \pm 1$. While if $\sqrt{-1}\notin k$, then the exterior algebra with two variables admits no bi-Frobenius algebra structures. Since a quantum complete intersection over a field of characteristic zero admits no bialgebra structures, this gives a class of examples of bi-Frobenius algebras which are not bialgebras (and hence not Hopf algebras). On the other hand, a quantum exterior algebra admits a bialgebra structure if and only if ${\rm char} \ k = 2$. In commutative case, other two comultiplications on complete intersection rings are given, such that they admit non-isomorphic bi-Frobenius algebra structures.

math.RT↗