arXiv subjects

Juan Li

Publications and source records attributed to Juan Li.

At least 19 recordsLinked to original sources

arXiv2026

Degenerate McKean--Vlasov SDE with Yamada--Osgood Coefficients and Arbitrary Modulus of Continuity in Wasserstein Distance

We establish the well-posedness of strong solutions for a class of degenerate mean-field stochastic differential equations with coefficients satisfying non-Lipschitz conditions. The diffusion coefficient is not required to be non-degenerate. Both the diffusion and the drift coefficients may depend on the law through the Kantorovich-Rubinstein metric with an arbitrary modulus of continuity. The drift and the diffusion satisfy a dimension-dependent Osgood-type condition, that becomes particularly sharp in dimension one. The proof combines the classical Yamada--Watanabe argument with Schauder's fixed-point theorem and does not rely on Gaussian estimates, allowing us to cover degenerate diffusions where such estimates are not available. This fills a gap in the existing literature.

math.PR↗

arXiv2026

Profile-Driven User Simulation via Reinforcement Learning with Hierarchical Rewards for Task-Oriented Dialogues

Building Task-Oriented Dialogue (TOD) systems for high-value scenarios such as financial marketing requires large volumes of domain-specific dialogue data, which privacy regulations, annotation costs, and the need for expert labor make hard to obtain. User simulation offers a remedy, but existing methods target general-domain dialogue and exhibit two key limitations: insufficient modeling of domain-specific business processes and compliance constraints, and inadequate capture of the colloquial, spoken-language character of voice interactions. We propose ProfileSim, a profile-driven user simulation framework for financial marketing outbound calls. It jointly models user profiles---demographics and Big Five personality traits---and business profiles---intents reverse-engineered from real call logs---enabling fine-grained control over simulated behavior. The base model is fine-tuned on real voice dialogue data and refined by Group Relative Policy Optimization (GRPO) with hierarchical rewards at the dialogue and utterance levels. Paired with a customer service agent integrating Standard Operating Procedure (SOP) constraints and Retrieval-Augmented Generation (RAG), ProfileSim achieves the highest colloquial naturalness, the strongest user profile adherence and the lowest agent score on long-tail intents among all evaluated user generators, while producing substantially shorter user utterances at comparable business compliance. The generated dialogue data is designed to support intent recognition training, agent evaluation, and rapid cold-start deployment.

cs.CL↗

arXiv2026

Stochastic differential games with random coefficients and state constraints: associated stochastic Hamilton-Jacobi-Bellman-Isaacs equations with Neumann boundary conditions

We study a stochastic differential game in which the state process is governed by a reflected stochastic differential equation (RSDE) and the recursive payoff is defined by a generalized backward stochastic differential equation (GBSDE). Unlike the Markovian models in \cite{Li08sicon,Fan}, all coefficients may depend directly on $ω$, so the value functions are random fields. We show that the lower and upper value functions are viscosity solutions of stochastic Hamilton--Jacobi--Bellman--Isaacs (HJBI) equations with nonlinear Neumann boundary conditions, thereby extending the framework of \cite{Qiu22AAP} to reflected state constraints. Under weak boundary regularity, we derive estimates for RSDEs and GBSDEs, prove regularity of the value functions, and establish the dynamic programming principle (DPP) as well as the existence of viscosity solutions. Finally, under additional assumptions in a one-dimensional linear setting, we prove a comparison theorem and the uniqueness of bounded $(L_y,0)$-viscosity solutions, where $L_y$ is the constant coefficient of $y$ in the running generator. To prove the comparison theorem, we homogenize the boundary condition and construct smooth adapted comparison fields by solving deterministic uniformly parabolic Neumann problems in finite dimensions.

math.PR↗

arXiv2026

Backward stochastic porous media equation with polynomial growth

We investigate the well-posedness of a backward stochastic porous media equation whose nonlinear term is a polynomial operator corresponding to the slow diffusion regime. The main challenge stems from the structure of this nonlinear operator, which causes the operator to lose maximal monotonicity and prevents the use of standard weak-strong convergence techniques to identify the limit. Moreover, since the Laplace operator makes it difficult to separate the operators and discuss them individually, we attempt to obtain the of limit by investigating the global properties of the operator.

math.PR↗

arXiv2026

Stochastic Porous Media Equations With Nonhomogeneous Dirichlet Boundary Conditions

We aim at studying the well-posedness of stochastic porous media equation problems under nonhomogeneous Dirichlet boundary. We obtain an unconventional homogeneous Dirichlet boundary stochastic porous medium equation by transformation under an additional assumption, and then use approximation problems to obtain the well-posedness properties of the equation with homogeneous Dirichlet boundary conditions under different initial conditions. Consequently, we obtain the corresponding solution to the original equation.

math.PR↗

arXiv2026

Codimension Reduction of Minimal Submanifolds with Flat Normal Bundle in Spheres

Let $x:M^n\to\mathbb{S}^{n+q}$ be a minimal immersion of a complete connected manifold with flat normal bundle, where $n\ge3$ and $q\ge2$. We prove that if the squared norm of the second fundamental form $S$ satisfies $S<2n$, then $M^n$ lies in $\mathbb{S}^{n+1}$. The standard minimal products of three spheres show that the upper bound $2n$ is optimal. We also prove a codimension reduction theorem under the condition $S+λ_2\le 2n+\frac{2n}{3n-2}$, where $λ_2$ is the second largest eigenvalue of the Gram matrix of the shape operators, implying that $M^n$ lies in $\mathbb{S}^{n+1}$.

math.DG↗

arXiv2026

Metallic-Phase-Fe$_3$GaTe$_2$ Enabled Interface Engineering for Self-Powered and High-Gain WS$_2$ Photodetectors

Two-dimensional transition-metal dichalcogenides offer strong light-matter interaction but suffer from inefficient carrier separation and contact-related losses in photodetectors. Here, we demonstrate a high-gain WS$_2$/Fe$_3$GaTe$_2$ van der Waals heterostructure photodetector, where metallic Fe$_3$GaTe$_2$ serves as an active interfacial contact. The work-function mismatch, together with interfacial charge redistribution and asymmetric contact geometry, contributes to a built-in field that supports self-powered photodetection at zero bias. Under 450 nm illumination, the device delivers a zero-bias responsivity of 23.5 A/W and an apparent external quantum efficiency of 6.4 x 10$^3$%. At -1 V biasing, the heterostructure exhibits photoresponse at 450, 520 and 633 nm, achieving a responsivity of 9.7 x 10$^3$ A/W and a noise derived specific detectivity of 2.3 x 10$^13$ Jones at 100 Hz under 450 nm illumination. The high photoresponse is attributed to interfacial carrier separation, efficient extraction, and a likely contribution from trap-assisted photogating in multilayer WS$_2$. These results establish Fe$_3$GaTe$_2$-enabled interface engineering as an effective route for self-powered, highly sensitive 2D photodetectors.

cond-mat.mtrl-sci↗

arXiv2026

Rigidity of Ricci-Pinched Complete Self-Shrinkers in Arbitrary Codimension

Let $M$ be an $n$-dimensional complete connected self-shrinker in $\mathbb{R}^{n+p}$. Denote by $\operatorname{Ric}$ and $\mathbf{H}$ the Ricci curvature tensor and the mean curvature vector of $M$, respectively. We prove that if the self-shrinker $M$ satisfies $\operatorname{Ric}\ge(\frac{n-2}{n^2}+\varepsilon_n)|\mathbf{H}|^2g$, then $M$ is either a linear subspace or a round shrinking sphere, where $\varepsilon_n$ is an explicit positive constant equal to $\frac{1}{3n^2}+O\left(\frac{1}{n^5}\right)$. Moreover, we obtain a rigidity theorem that is sharp in codimension two for the self-shrinker satisfying $\operatorname{Ric}\ge\frac{n-2}{n^2}|\mathbf{H}|^2g$.

math.DG↗

arXiv2026

VATO: A Vortex-Force-Aware Transformer Operator for Unsteady Separated Aerofoil Flows

Accurate prediction of unsteady separated flows is challenging because the aerodynamic loads depend on nonlinear separation and vortex-shedding dynamics. Although high-fidelity CFD resolves these mechanisms, its cost limits repeated use in design and control. Standard field-level surrogate training, however, does not distinguish the flow regions that contribute most strongly to the aerodynamic loads. We introduce VATO (Vortex-Force-Aware Transformer Operator), which couples the Vortex Force Map (VFM) method to a geometry-aware neural operator through two complementary mechanisms. VATO-S adds training-only supervision of the local VFM force-contribution field, with no increase in model size or inference cost. VATO-A uses VFM contribution and sensitivity fields to prioritise force-relevant source locations for residual cross attention. The methods are evaluated on unsteady CFD data for double-edged-plate aerofoils over 54 trajectories from nine geometries. Over lead times of 1-20~ms, VATO-S reduces velocity, pressure, and vorticity errors by 10.4\%, 1.0\%, and 15.6\%, respectively, while VATO-A achieves reductions of 15.8\%, 7.5\%, and 31.2\%. VATO-S gives the lowest VFM-derived drag error, whereas VATO-A gives the lowest pressure-derived lift and drag errors. Over lead times extending 50\% beyond the training range, VATO-A retains a 26.9\% reduction in vorticity error and larger improvements in all four force readouts, despite reduced gains in velocity and pressure. These results show that force-aware operator learning can improve both flow-field prediction and aerodynamic functional accuracy in unsteady separated flows.

cs.LG↗

arXiv2026

Deforming Vortex Force Mapping for Undulating Swimmers

Undulatory propulsion is commonly interpreted through reactive added-mass loading associated with body kinematics and vortex-induced loading, but their relative contributions to the streamwise force have not been systematically quantified across swimming kinematics. Moreover, existing vortex-based descriptions do not resolve the signed spatial contribution of vortical flow to the streamwise force. We extend vortex force map (VFM) attribution to deforming bodies, demonstrated for prescribed two-dimensional undulating swimmers at $Re=5000$ across a range of Strouhal numbers and dimensionless wavelengths. The deforming-body VFM organises the streamwise force as a positive reactive added-mass scale with a signed vortex-pressure modification. Across the 80 cases, vortex pressure opposes the reactive contribution in 76 cases. Reference-configuration maps show that the near-body vortex-pressure contribution is consistently adverse, whereas the wake contribution changes sign across regimes and becomes favourable at high thrust. Net vortex-pressure assistance occurs only for the high-thrust anguilliform swimmer. A matched high-thrust pair further shows that the case with the higher peak downstream velocity has the smaller signed wake contribution, demonstrating that wake intensity alone does not determine its force effect.

physics.flu-dyn↗

arXiv2026

STCO: Conditional Neural Operators for Time-Dependent PDEs

Neural operators have emerged as efficient surrogates for time-dependent physical systems governed by partial differential equations (PDEs), but their future-state predictions are often conditioned only on observed states and static problem descriptors. For control or optimization, however, body motion, inflow, or forcing are prescribed for the query without being determined solely by the observed state. We introduce the Spatiotemporal Conditional Operator (STCO) for prescribed-condition operator learning (PCOL), a common interface that supplies prescribed target-time condition fields to heterogeneous backbone architectures while retaining their architecture-specific core computation and context pathways. Its condition interface combines Flow-Aware Graph Leaf (FAGL) with Dual-Site Feature-wise Linear Modulation (DSFiLM). Non-learned FAGL uses vorticity from the final observed frame to construct a fixed-cardinality adaptive partition, then co-locates the observed history and target-time condition fields at its regional coordinates. DSFiLM injects separate motion, inflow, and force routes before and after operator computation through current-feature-driven slot- and channel-wise gates. We evaluate twelve matched backbone architectures with different existing physical and temporal inputs. The immersed-boundary computational fluid dynamics (CFD) benchmark spans prescribed motion, inflow disturbances, body-force actuation, and morphology. Across twelve matched backbones, three regimes, and two lead ranges, STCO yields mean paired reductions of 31.1% in relative-L2 field error and 24.7% in normalized pressure-derived load error. It also lowers longer-lead field error for 11 backbones, while interventions on individual condition groups produce measurable prediction changes for every group evaluated.

cs.AI↗

arXiv2026

Neuro-Symbolic Participation Governance for Verifiable AI Agents in Open Digital Twin Ecosystems

Autonomous AI agents, increasingly empowered by large language models, are becoming important components of human-machine systems for high-stakes decision support in digital twin ecosystems. However, existing multi-agent systems often lack robust verification for identity, capability, and policy compliance, especially in decentralized environments spanning multiple institutions. This paper proposes a neuro-symbolic decentralized governance framework for verifiable agents in collaborative digital twin environments. By representing agents through multi-layer semantic profiles, the framework bridges probabilistic neural reasoning with deterministic institutional governance, thereby supporting trustworthy human-AI collaboration and meaningful human oversight. Capabilities are grounded in formal domain ontologies to enable machine-interpretable, policy-aware, and context-sensitive participation. These credentials, issued by organizational authorities, are validated via blockchain-based smart contracts, ensuring auditable participation without exposing sensitive data. We demonstrate the framework using a decision-support prototype with clinic, digital twin, and wearable provider agents effectively prevents unauthorized interaction and enforces institutional policies with manageable overhead. Our findings suggest that neuro-symbolic decentralized governance provides a scalable and trustworthy pathway for safe human-machine collaboration across institutional boundaries.

cs.CR↗

arXiv2026

Stochastic Control of Addiction with State-Dependent Jump Relapse

We study a continuous-time rational addiction model where addiction capital follows a piecewise deterministic Markov process with state-dependent jumps capturing relapse and recovery. The instantaneous utility combines consumption and addiction capital via a power specification, leading to Hamilton-Jacobi-Bellman (HJB) equations with nonlocal jump terms. In the capped, bounded-control case we obtain a unique bounded viscosity solution and prove that optimal policies are bang-bang, switching between minimal and maximal consumption, while in the uncapped case we derive explicit linear feedback controls and closed-form value functions in several parameter regimes.

math.OC↗

arXiv2026

Stackelberg Games with a Robust Leader

In this paper we study a Stackelberg game with one leader and multiple followers. Given the leader's control, the followers solve a Nash game with possibly multiple equilibria. We consider a robust leader who considers the worst scenario, namely the followers would select the equilibrium worst for the leader. By using the weak formulation, the problem induces a zero sum game problem with open loop controls, which is time inconsistent. We shall characterize the last problem through an HJB equation on the Wasserstein space of probability measures. The principal-agent problem with one principal and multiple agents can be viewed as a special case of our problem, but with certain constraints.

math.OC↗

arXiv2026

Molecule-dependent Abundance Behavior of Oxygen-bearing Complex Organics in High-Mass Star-Forming Regions: A Uniform 50-source Survey

We present a uniform IRAM-30\,m survey analysis of four oxygen-bearing complex organic molecules (COMs), methanol (CH$_3$OH), acetaldehyde (CH$_3$CHO), methyl formate (CH$_3$OCHO), and dimethyl ether (CH$_3$OCH$_3$), toward 50 high-mass star-forming regions (HMSFRs) associated with 6.7\,GHz methanol masers. Column densities were derived through a homogeneous rotation-diagram approach, with CH$_3$CN used as a proxy excitation-temperature reference when needed. In CH$_3$OH-normalized abundance-ratio space, CH$_3$OCHO/CH$_3$OH and CH$_3$OCH$_3$/CH$_3$OH show the strongest pairwise correlation, whereas the correlations involving CH$_3$CHO are weaker. No clear monotonic trends are found with Galactocentric distance or beam-averaged H$_2$ column density. Comparison with previous observations places the CH$_3$OCHO--CH$_3$OCH$_3$ behavior within the range of earlier abundance-ratio measurements, while CH$_3$CHO shows larger inter-study variation. A representative warm-up chemical model is used only for qualitative comparison with the observed abundance ranges, which are most closely matched during the decline from the post-desorption abundance peaks in the model. These results provide homogeneous beam-averaged abundance-ratio constraints for common O-bearing COMs in high-mass star-forming regions and show that their source-to-source behavior is molecule-dependent rather than fully described by a single common abundance pattern.

astro-ph.GA↗

arXiv2026

Forensic Schema for Psychological Manipulation in Cyber Fraud: LLM-Driven Victim Reports Analysis

Existing cybercrime classification schemas capture contact metadata and financial transactions but omit the psychological manipulation techniques perpetrators employ. We present a forensic schema (four categories, 35 questions) adding 11 manipulation indicators and cryptocurrency evidence fields to established forensic foundations. Applied to 10,994 victim reports via large language model (LLM)-driven annotation and validated against two human annotators (mean LLM-human $κ= 0.69$, matching inter-annotator $κ= 0.68$), the schema revealed a statistically distinct manipulation profile for each major fraud type (Cramer's $V$ up to $0.790$). A rationale-based evidence audit nonetheless exposed a forensic detail gap: detection of manipulation techniques was reliable, but victim narratives varied widely in the actionable detail supporting each Yes answer, and blockchain-specific identifiers were nearly absent. These findings point to AI-assisted victim intake with schema-informed follow-up questions as the most direct way to close the gap. The tiered annotation strategy also provides a reusable template for LLM-based extraction from other forensic text domains.

cs.CR↗

arXiv2026

The evolution of C4H and c-C3H2 in molecular cores

Linear C4H and cyclic c-C3H2, as small unsaturated hydrocarbons, are the key precursors to complex organic molecules and are critical components of the interstellar medium. We present on-the-fly mapping observations of C4H 9-8 lines, c-C3H2 2-1, H13CO+ 1-0, and H42 toward a sample of 22 massive star-forming regions using the IRAM 30m telescope. Our aim is to further explore the evolution of these carbon-chain molecules by combining observational results obtained in cold cores. We employed H13CO+ 1-0 and H42 as tracers to probe the positions of molecular cloud cores and ionised hydrogen regions (HII regions), respectively. One chemical model in particular, which includes gas, dust grain surface, and icy mantle phases for C4H and c-C3H2 molecules, was used to make comparisons with observed abundances. From mapping observations targeting 31 regions across 22 sources, C4H 9-8 (J = 19/2-17/2) and C4H 9-8 (J = 17/2-15/2) were detected in only 17 regions, while H13CO+ 1-0 and c-C3H2 2-1 were successfully detected in all 31 regions. We find that the emission of C4H 9-8 and c-C3H2 2-1 is concentrated at the edges of H42 emission regions. The C4H/H13CO+ and c-C3H2/H13CO+ relative abundance ratios range from 0.17 to 1.77 and 1.42 to 6.69, respectively, with a median C4H/c-C3H2 ratio of 0.13. By combining the observational results of cold cores, we find that C4H/H13CO+ and c-C3H2/H13CO+ ratios show a strong decreasing trend as molecular cores evolve. The decreasing trends in C4H/H13CO+ and c-C3H2/H13CO+ ratios imply that small unsaturated hydrocarbons can be consumed and converted into other organic molecules during the evolution of molecular cores. The spatial concentration of C4H and c-C3H2 emission at the edges of H42 regions further supports their role as precursors in the chemical pathways that lead to complex organic molecules in the interstellar medium.

astro-ph.GA↗

arXiv2026

MiMIC: Mitigating Visual Modality Collapse in Universal Multimodal Retrieval While Avoiding Semantic Misalignment

Universal Multimodal Retrieval (UMR) aims to map different modalities (e.g., visual and textual) into a shared embedding space for multi-modal retrieval. Existing UMR methods can be broadly divided into two categories: early-fusion approaches, such as Marvel, which projects visual features into the language model (LM) space for integrating with text modality, and late-fusion approaches, such as UniVL-DR, which encode visual and textual inputs using separate encoders and obtain fused embeddings through addition. Our pilot study reveals that Marvel exhibits visual modality collapse, which is characterized by the model's tendency to disregard visual features while depending excessively on textual cues. In contrast, although UniVL-DR is less affected by this issue, it is more susceptible to semantic misalignment, where semantically related content is positioned far apart in the embedding space. To address these challenges, we propose MiMIC, which introduces two key innovations: (1) a fusion-in-decoder architecture for effective multimodal integration, and (2) robust training through single modality mixin and random caption dropout. Experiments on the WebQA+ and EVQA+ datasets, where image in documents or queries might lack captions, indicate that MiMIC consistently outperforms both early- and late-fusion baselines.

cs.CV↗