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Dong Qiu

Publications and source records attributed to Dong Qiu.

At least 19 recordsLinked to original sources
arXiv2026

Increasing stability for the inverse potential problem of the fractional Helmholtz equation

This paper is concerned with the inverse potential scattering problem for the three-dimensional fractional Helmholtz equation. For every $0<α<1$, we establish an increasing stability of determining the potential function from multifrequency exterior measurements of the scattered field. The stability consists of a Lipschitz data discrepancy and a logarithmic remainder that decreases when the upper measured wavenumber increases. The key ingredient in the analysis is to construct appropriate geometric optics solutions, which relate the X-ray transform of the potential to the measured fields. As a consequence, the stability is derived by applying analytic continuation. Two-dimensional numerical examples with noisy near-field data illustrate the benefit of enlarging the measured frequency band for three representative fractional orders.

math.AP↗
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

Kernel retracts of co-sober spaces

Kernel retracts of co-sober spaces need not be co-sober, even when the ambient space is countably infinite and compact. We construct a co-sober $T_0$-space $Y$ and a continuous idempotent map $k\colon Y\to Y$ satisfying $k(y)\leq_Y y$ in the specialization order, whose image with the subspace topology is not co-sober. The construction starts from a countable compact $T_1$ KC anti-Hausdorff space of van Douwen type and adjoins an infinite chain. We classify the $k$-irreducible compact saturated subsets of the extension and show that each is a point saturation. The kernel operator collapses the added chain to a distinguished point while fixing the original space, thereby recovering the non-co-sober seed as its image. This answers negatively two questions of Xu and Zhao, concerning continuous kernel operators and arbitrary retracts, and contrasts with the known preservation of co-sobriety by continuous closure operators.

math.GN↗
arXiv2026

Inverse source problem for the stochastic fractional Helmholtz equation in inhomogeneous media

This paper is concerned with an inverse source problem for the stochastic fractional Helmholtz equation in a three-dimensional inhomogeneous medium. The source is modeled as real Gaussian spatial white noise with an unknown nonnegative strength function. For admissible frequencies, we establish well-posedness of the radiating solution in the distributional sense and show that it has a smooth representation outside the source region. For the inverse problem, by using two-point correlations of the field measured in an exterior open set at a single frequency, we prove a logarithmic stability estimate for recovering the source strength under an a priori Sobolev bound. As a uniform Hölder stability estimate is unavailable for the general admissible class, by assuming the difference between two source strengths has a fixed sign, we improve the stability to Hölder continuity with an optimal Hölder exponent. The analysis combines scattering theory and quantitative continuation for the fractional Laplacian using the Caffarelli-Silvestre extension.

math.AP↗
arXiv2026

An inverse moving point source problem in inhomogeneous acoustic media: uniqueness, stability and reconstruction

This paper is concerned with the simultaneous recovery of the trajectory and intensity of an unknown moving point source in an inhomogeneous acoustic medium. We prove that the whole-boundary measurements over a finite time interval uniquely determine the moving source. Furthermore, under suitable propagation and rank assumptions, Lipschitz stability of determining both the trajectory and intensity is derived using waveforms measured at four fixed receivers outside the source region. A novel Volterra--Euler reconstruction scheme is developed for solving the inverse problem, and the error estimate is derived for the proposed scheme. Numerical experiments are presented to demonstrate the effectiveness of the proposed numerical method.

math.AP↗
arXiv2026

Stationarity equations for fractional affine area measures: ellipsoid rigidity and polytopal solutions

Xi and Zhao established a first variation formula for affine inequalities involving radial mean bodies, and asked two geometric questions about the resulting stationarity equation: whether the bodies already known to satisfy it are the only ones, and whether its smooth solutions are exactly the ellipsoids. We answer both. Every strictly convex solution of the equation with $q>-1$, $q\ne0,n$ is an ellipsoid, which answers the second question affirmatively while replacing smoothness and everywhere positive Gauss curvature by strict convexity. Every full-dimensional facet-transitive polytope satisfies the equation, and so does the polar of every vertex-transitive polytope with respect to its volume centroid; the rhombic dodecahedron, the thirteen Catalan solids and the bipyramids over regular polygons other than the octahedron provide infinitely many affinely inequivalent solutions that are not affine images of regular polytopes or balls, so the answer to the first question is negative. The rigidity proof compares overlap integrals along a continuous Steiner path: stationarity forces an increase of order $o(t)$, whereas a nonaffine chord midpoint function forces an increase of order $t$. For negative parameters the required comparison rests on a minimization formula over bounded measurable auxiliary sets.

math.FA↗
arXiv2026

Uniqueness and stability for inverse potential scattering with multiple wavenumbers

This paper is concerned with the inverse scattering problem of determining a real-valued potential for the three-dimensional Schrödinger equation from multi-wavenumber data. Under suitable a priori bounds, we establish local increasing stability from near-field Dirichlet data on a fixed sphere for polynomially decaying potentials, and global increasing stability from full far-field amplitudes for exponentially decaying potentials. The stability estimates consist of a noise term and a remainder term, with the latter decreasing as the upper measured wavenumber increases. We also obtain global uniqueness from exact near-field data under weaker regularity assumptions. The analysis combines analytic continuation, weighted resolvent estimates, and half-ray identities whose differences at chord endpoints cancel the unknown exterior contribution.

math.AP↗
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

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↗