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Dong Qiu

Publications and source records attributed to Dong Qiu.

At least 19 recordsLinked to original sources
arXiv2026

Stability for the inverse source problem of the stochastic fractional Helmholtz equation

This paper is concerned with the inverse source problem for the stochastic fractional Helmholtz equation driven by white noise. For every fractional order $0<α<1$, we prove the existence and uniqueness of the outgoing distributional solution to the direct problem with resolvent estimates at high frequencies, and establish its stochastic representation. For the inverse problem, we demonstrate that the variance of the source can be uniquely determined by the correlated random exterior data at a single frequency. We further establish an increasing stability estimate for the inverse problem by using the multifrequency correlated exterior data. Our stability result shows that as the upper bound of the bandwidth of the utilized frequency increases, the stability will also improve. The analysis employs the construction of geometric optics solutions, which connects the correlated data to the X-ray transform of the variance.

math.AP↗
arXiv2026

Stable determination of coefficients for the nonlinear third-order acoustic equations

In this paper, we study an inverse boundary value problem for a generalized Jordan-Moore-Gibson-Thompson equation with Westervelt-type nonlinearity and space-dependent coefficients. This third-order (in time) hyperbolic equation models nonlinear ultrasound propagation in viscous and thermally relaxing media. Assuming that the diffusivity and the sound speed are known a priori, we investigate the simultaneous stable determination of the friction coefficient, the weak damping coefficient, the potential, and the nonlinear coefficient from the associated Dirichlet-to-Neumann map. The proof combines the finite-difference linearization method with the construction of Gaussian beam and geometric optics solutions. These arguments reduce the inverse problem to stability estimates for (attenuated) geodesic ray transforms under the foliation condition. As a consequence, we obtain Hölder-type stability estimates of recovering the linear and nonlinear coefficients.

math.AP↗
arXiv2026

From $\log 2$ to $π/2$: the sharp asymptotic inradius of polynomial lemniscates

Let $R_n$ be the infimum of the inradii of $\{z:|p(z)|<1\}$ over monic degree-$n$ polynomials whose zeros lie in the closed unit disk. We prove $nR_n\toπ/2$, matching the asymptotic obstruction supplied by $z^n-1$. We first establish the exact universal radius $2^{1/n}-1$ for disks centered at zeros, which recovers the $(\log2)/n$ bound. Small inradius then forces radial concentration of the zeros and decay of their low reciprocal moments. These estimates give an entire limit with a modulus reflection identity; a second rescaling produces an exponential tangent and strict sublevel disks of every radius below $π/2$. The proof is accompanied by a Lean~4 formalization and a step-by-step source index.

math.CV↗
arXiv2026

On fuzzy contractions in fuzzy metric spaces

The classical Banach principle relies on contractive sequences being Cauchy. Gregori and Sapena (2002) established a fuzzy analogue but required this as an extra hypothesis, leaving it as an open problem. Gregori et al. (2020) later asked whether strictly fuzzy $ψ$-contractive sequences are necessarily Cauchy. We settle both problems negatively via a single counterexample: in a constructed GV-fuzzy metric space, there exists a sequence which is both GS-contractive and strictly fuzzy $ψ$-contractive, yet not Cauchy. This shows that contractivity never implies Cauchyness in general GV-fuzzy metric spaces, and additional structural conditions in fuzzy fixed point theorems are indispensable.

math.GN↗
arXiv2026

A note on definable endomorphisms of ordered abelian groups

We answer Kourovka Notebook Problem~18.16 affirmatively in the pure language of ordered abelian groups, with parameters allowed. The piecewise-affine description of definable functions reduces the question to an algebraic rigidity theorem: an additive endomorphism of a torsion-free abelian group that is covered by finitely many rational-affine laws has one global rational slope. The parameter-free pure-language case is included, whereas the unrestricted expansion-language variant admits a simple counterexample.

math.LO↗
arXiv2026

Agentic Software Engineering: Foundational Pillars and a Research Roadmap

Agentic Software Engineering (SE 3.0) represents a new era where intelligent agents are tasked not with simple code generation, but with achieving complex, goal-oriented SE objectives. To harness these new capabilities while ensuring trustworthiness, we must recognize a fundamental duality within the SE field in the Agentic SE era, comprising two symbiotic modalities: SE for Humans and SE for Agents. This duality demands a radical reimagining of the foundational pillars of SE (actors, processes, tools, and artifacts) which manifest differently across each modality. We propose two purpose-built workbenches to support this vision. The Agent Command Environment (ACE) serves as a command center where humans orchestrate and mentor agent teams, handling outputs such as Merge-Readiness Packs (MRPs) and Consultation Request Packs (CRPs). The Agent Execution Environment (AEE) is a digital workspace where agents perform tasks while invoking human expertise when facing ambiguity or complex trade-offs. This bi-directional partnership, which supports agent-initiated human callbacks and handovers, gives rise to new, structured engineering activities (i.e., processes) that redefine human-AI collaboration, elevating the practice from agentic coding to true agentic software engineering. This paper presents the Structured Agentic Software Engineering (SASE) vision, outlining several of the foundational pillars for the future of SE. The paper culminates in a research roadmap that identifies a few key challenges and opportunities while briefly discussing the resulting impact of this future on SE education. Our goal is not to offer a definitive solution, but to provide a conceptual scaffold with structured vocabulary to catalyze a community-wide dialogue, pushing the SE community to think beyond its classic, human-centric tenets toward a disciplined, scalable, and trustworthy agentic future.

cs.SE↗
arXiv2026

Gauge symmetry and uniqueness in inverse problems for the JMGT equation

In this paper, we study an inverse boundary value problem for the Jordan--Moore--Gibson--Thompson equation on a simple Riemannian manifold. We consider an all boundary measurement map that maps Dirichlet boundary data and initial data to the corresponding Neumann-type boundary data and final-time data. Our main result shows that the nonlinear acoustic coefficient $β$ is uniquely determined by this measurement map, and the linear damping coefficients $α$ and $q$, along with the internal source term $F$, can be recovered up to a gauge symmetry. As a corollary, we also establish a specific case in which all coefficients are uniquely recovered. The proof relies on the method of first-order and second-order linearization and on the construction of geometric optics solutions. In the intermediate step, we establish the unique recovery of the lower-order coefficients in the linearized MGT equation.

math.AP↗
arXiv2026

Inverse boundary value problems of determining nonlinear coefficients for the JMGT equation

We consider inverse boundary value problems for the Jordan-Moore-Gibson-Thompson (JMGT) equation in nonlinear acoustics with quadratic nonlinearities of Kuznetsov-type and Westervelt-type. We show that the associated boundary Dirichlet-to-Neumann map uniquely determines the nonlinear coefficients $β$ in the Westervelt-type model, and the pair $(β,κ)$ in the Kuznetsov-type model, provided that the observation time is greater than the maximal boundary-to-boundary geodesic travel time. The results are obtained in both the Euclidean setting and on compact Riemannian manifolds with proper geometric assumptions. The proof is based on the idea of second order linearization combined with the construction of geometric optics and Gaussian beam solutions, reducing the inverse problem of uniqueness to the injectivity of associated geodesic ray transforms.

math.AP↗
arXiv2026

Graph Neural Network Prediction of Infrared Spectra of Interstellar Polycyclic Aromatic Hydrocarbons

Polycyclic aromatic hydrocarbons (PAHs) are recognized as the primary contributors to the aromatic infrared bands (AIBs) widely observed in space. However, analyzing these AIBs remains challenging because of the immense structural diversity within the PAH family, which makes the computation of reliable reference spectra difficult. To address this, we developed an efficient graph neural network (GNN) framework that can predict PAH absorption spectra up to 10,000 times faster than traditional quantum chemical methods. We evaluated four representative GNN architectures, including graph convolutional network (GCN), graph attention network (GAT), message passing neural network (MPNN), and attentive fingerprint (AFP). The AFP model is found to deliver the best overall performance and is further trained using five different spectral distance metrics as loss functions, among which the Jensen-Shannon divergence yields the most accurate and stable results. The model performs best for PAHs containing 20-40 carbon atoms, while accuracy decreases for larger molecules, reflecting the limited availability of training data. Overall, this framework offers a fast method to generate approximate reference spectra for small- to medium-sized PAHs, supporting future AIB analysis.

astro-ph.GA↗
arXiv2025

Reinforcement Learning-Augmented LLM Agents for Collaborative Decision Making and Performance Optimization

Large Language Models (LLMs) perform well in language tasks but often lack collaborative awareness and struggle to optimize global performance in multi-agent settings. We present a reinforcement learning-augmented LLM agent framework that formulates cooperation as a decentralized partially observable Markov decision process (Dec-POMDP) and adopts centralized training with decentralized execution (CTDE). We introduce Group Relative Policy Optimization (GRPO) to jointly optimize agent policies with access to global signals during training, together with a simplified joint reward that balances task quality, speed, and coordination cost. On collaborative writing and coding benchmarks, our framework delivers a 3x increase in task processing speed over single-agent baselines, 98.7% structural/style consistency in writing, and a 74.6% test pass rate in coding. The approach consistently outperforms strong multi-agent LLM baselines and provides a practical path toward reliable collaboration in complex workflows.

cs.AI↗
arXiv2025

Group Deliberation Oriented Multi-Agent Conversational Model for Complex Reasoning

This paper proposes a group deliberation oriented multi-agent conversational model to address the limitations of single large language models in complex reasoning tasks. The model adopts a three-level role division architecture consisting of generation, verification, and integration. An opinion generation agent produces diverse reasoning perspectives, an evidence verification agent retrieves external knowledge and quantifies factual support, and a consistency arbitration agent integrates logically coherent conclusions. A self-game mechanism is introduced to expand multi-path reasoning trajectories, while a retrieval enhancement module dynamically supplements external knowledge. A composite reward function combining factual consistency and logical coherence is designed, and an improved proximal policy optimization strategy is applied for collaborative training. Experimental results show that the proposed model improves multi-hop reasoning accuracy by 16.8 percent on HotpotQA, 14.3 percent on 2WikiMultihopQA, and 19.2 percent on MeetingBank, while improving consistency by 21.5 percent. The model achieves higher reasoning efficiency than mainstream multi-agent approaches, providing an effective and stable solution for complex reasoning tasks.

cs.AI↗
arXiv2025

Uniqueness Result For Semi-linear Wave Equations With Sources

This paper addresses the inverse problem of simultaneously recovering multiple unknown parameters for semilinear wave equations from boundary measurements. We consider an initial-boundary value problem for a wave equation with a general semilinear term and an internal source. The inverse problem is to determine the nonlinear coefficients (potentials), the source term, and the initial data from the Dirichlet-to-Neumann (DtN) map. Our approach combines higher-order linearization and the construction of complex geometrical optics (CGO) solutions. The main results establish that while unique recovery is not always possible, we can precisely characterize the gauge equivalence classes in the solutions to this inverse problem. For a wave equation with a polynomial nonlinearity of degree $n$, we prove that only the highest-order coefficient can be uniquely determined from the DtN map; the lower-order coefficients and the source can only be recovered up to a specific gauge transformation involving a function $ψ$. Furthermore, we provide sufficient conditions under which unique determination of all parameters is guaranteed. We also extend these results to various specific non-polynomial nonlinearities, demonstrating that the nature of the nonlinearity critically influences whether unique recovery or a gauge symmetry is obtained.

math.AP↗
arXiv2025

Superconductivity Favored Anisotropic Phase Stiffness in Infinite-Layer Nickelates

In unconventional superconductors such as cuprates and iron pnictides and chalcogenides, phase stiffness - a measure of the energy cost associated with superconducting phase variations - is on the same order of magnitude as the strength of Cooper pairing, translating to superconductivity governed by phase fluctuations. However, due to a lack of a direct experimental probe, there remains a fundamental gap in establishing microscopic picture between unconventional superconductivity and phase fluctuations. Here we show a vector current technique that allows for in-situ angle-resolved transport measurements, providing exclusive evidence suggesting an anisotropic nature of phase stiffness in infinite-layer nickelate superconductors. Pronounced anisotropy of in-plane resistance manifests itself in both normal and superconducting transition states, indicating crystal symmetry breaking. Remarkably, the electric conductivity of Nd0.8Sr0.2NiO2 peaks at 125° between the direction of the current and crystal principal axis, but this angle evolves to 160° near zero-resistance temperature. Further measurements reveal that the superconductivity is favored along a direction with minimized phase fluctuations, an orientation strikingly deviating from the symmetric direction imposed by both electronic anisotropy and the underlying crystal lattice. Identical measurements conducted on a prototypical cuprate superconductor yield consistent results, suggesting that this previously unknown behavior could be ubiquitous. By shielding insight into the contrasting anisotropy between electron fluid and superfluid, our findings provide clues for a unified framework for understanding unconventional superconductors

cond-mat.supr-con↗
arXiv2025

Quantum fluctuations-driven Melting Transitions in Two-dimensional Superconductors

Quantum fluctuations are pivotal in driving quantum phase transitions, exemplified by the quantum melting of Wigner crystals into Fermi liquids in electron systems. However, their impact on superconducting systems near zero temperature, particularly in the superconductor-insulator/metal transition, remains poorly understood. In this study, through electric transport measurements on the two-dimensional (2D) superconductor (SnS)1.17NbS2, we demonstrate that quantum fluctuations induce vortex displacement from their mean position, leading to the quantum melting of vortex solid near zero temperature. Quantitative analysis reveals the magnetic field-induced anomalous metal originates from this quantum melting transition, with energy dissipation governed by quantum fluctuations-driven vortex displacements. Remarkably, further extending this analysis to various 2D superconductors yields the same results, and many properties of anomalous metal can be qualitatively understood within the framework of quantum melting. The connection between the quantum melting of vortex solids and dissipative anomalous metal opens a novel pathway towards understanding quantum phase transitions through vortex dynamics, providing new insights on both fields.

cond-mat.supr-con↗
arXiv2024

On the Amplitude of Vortex Entropy: A Semiclassical Treatment

Despite a long history of Nernst effect in superconductors, a satisfactory theory on its amplitude in vortex liquid phase is still absent. The central quantity of vortex Nernst signals is the entropy $s_ϕ$ carried by each vortex. Here we show a semiclassical treatment based on London equation and Pippard nonlocal generalization. The derived $s_ϕ$ is a function of both temperatures and magnetic fields. Its magnitude $s_ϕ^{amp}$ scales with normal-state conductivity $σ_n$. Estimations based on our formula show good consistency with experimentally determined values. In dirty limit, the relation is further simplified into a Wiedemann-Franz-like ratio $s_ϕ^{amp}/σ_n \propto k_B \ln 2/σ_Q$ if taking parameter values deduced from Homes' law, where $σ_Q=4e^2/h$ is two-dimensional quantum conductivity. We also address related issues, including bounds to $s_ϕ$, the Nernst signal and viscosity-entropy density ratio, which are all expressed in fundamental physical constants.

cond-mat.supr-con↗
arXiv2023

Software Architecture Recovery with Information Fusion

Understanding the architecture is vital for effectively maintaining and managing large software systems. However, as software systems evolve over time, their architectures inevitably change. To keep up with the change, architects need to track the implementation-level changes and update the architectural documentation accordingly, which is time-consuming and error-prone. Therefore, many automatic architecture recovery techniques have been proposed to ease this process. Despite efforts have been made to improve the accuracy of architecture recovery, existing solutions still suffer from two limitations. First, most of them only use one or two type of information for the recovery, ignoring the potential usefulness of other sources. Second, they tend to use the information in a coarse-grained manner, overlooking important details within it. To address these limitations, we propose SARIF, a fully automated architecture recovery technique, which incorporates three types of comprehensive information, including dependencies, code text and folder structure. SARIF can recover architecture more accurately by thoroughly analyzing the details of each type of information and adaptively fusing them based on their relevance and quality. To evaluate SARIF, we collected six projects with published ground-truth architectures and three open-source projects labeled by our industrial collaborators. We compared SARIF with nine state-of-the-art techniques using three commonly-used architecture similarity metrics and two new metrics. The experimental results show that SARIF is 36.1% more accurate than the best of the previous techniques on average. By providing comprehensive architecture, SARIF can help users understand systems effectively and reduce the manual effort of obtaining ground-truth architectures.

cs.SE↗
arXiv2019

Supercontinuum generation without residual pump peak through multiple coherent pump seeds

Residual pump peak in fiber-based supercontinuum, as a general phenomenon, limits its practical application. We report a novel supercontinuum generation (SCG) in a conventional highly nonlinear fiber (HNLF) through multiple coherent pump technique, which eliminates the residual pump peak existed in conventional SCG. The multiple coherent pump technique is realized by double bound-state solitons achieved from a homemade modelocked fiber laser. We further compare the SCGs pumped by conventional bound-state soliton and single soliton. It confirms that the effective elimination of the residual pump peak in supercontinuum owes to higher transferring efficiency of the pump energy to new generated frequencies in the multiple coherent pump scheme. The use of multiple coherent pump scheme, i.e., double bound-state solitons, provides a new, simple and promising method to obtain flat supercontinuum source.

physics.optics↗