arXiv subjects

Qin Li

Publications and source records attributed to Qin Li.

At least 19 recordsLinked to original sources

arXiv2026

Two Adjoint Perspectives on Fokker-Planck Optimization: A Microscopic-Macroscopic Correspondence

The Fokker-Planck equation admits both a macroscopic Eulerian description through probability densities and a microscopic Lagrangian description through stochastic trajectories. Consequently, optimization problems constrained by the Fokker-Planck equation can be formulated from either perspective. Surprisingly, the corresponding adjoint equations appear to be fundamentally different: the macroscopic adjoint is governed by the backward Kolmogorov equation, whereas the microscopic adjoint evolves pathwise along stochastic trajectories. In this note, we reconcile these two formulations by establishing their correspondence in the continuum setting. We further show that, although their discrete gradients no longer coincide after discretization, both provide consistent numerical approximations of the continuum gradient. Explicit convergence rates are established for both discretization strategies.

math.NA↗

arXiv2026

Relativistic Modeling for Solid Earth Tide Estimation via Space-to-Ground Clock Comparison

With the rapid development of modern atomic clock technology, their unprecedented precision elevates them from timekeeping tools to gravitational potential sensors, thereby fostering the highly interdisciplinary field of Relativistic Geodesy. Given the potential for high-precision clock networks to detect periodic gravitational variations, it is imperative to assess their capability to invert solid Earth tide parameters via space-to-ground links in the presence of complex observational noise. To this end, we incorporate Earth's gravitational potential, direct lunisolar tidal potentials, and solid Earth tide effects into a high-precision relativistic framework for space-to-ground clock comparisons. By employing a three-link Doppler cancellation configuration to isolate the target signal, we perform numerical simulations for an inclined geosynchronous orbit satellite to analyze the effects of clock instability and colored precise orbit determination errors on parameter extraction. Our findings reveal that while high orbital altitudes cause severe collinearity between individual Love numbers, an effective parameter combining the $h_2$ and $k_2$ Love numbers successfully converges to a stable estimate within a 30-day continuous observation window. Furthermore, sensitivity analysis demonstrates that extraction accuracy is currently limited by clock stability rather than radial precise orbit determination errors.

gr-qc↗

arXiv2026

Toward Operational Solar Flare Peak Flux Nowcasting: A Strategy Combining Real-Time Data, Machine Learning, and NOAA Flare Detection Criteria

We present the RMN strategy (Real-time data, machine learning, and NOAA flare detection criteria) for nowcasting the peak soft X-ray flux of ongoing solar flares under operationally realistic conditions. The strategy combines real-time GOES 0.1-0.8 nm X-ray observations with an attention-based sequence-to-sequence Long Short-Term Memory model. Under the NOAA flare detection criteria, predictions are evaluated at one-minute intervals from three minutes after the cataloged onset to the observed peak using the preceding 60 minutes of X-ray observations. We apply the RMN strategy to C-, M-, and X-class flares observed by GOES-8-18 from 1997 to 2024 using four-fold cross-validation. The major results of this study are as follows. First, the model nowcasts peak soft X-ray flux with RMSE and PE values of 0.26 and 3.11\% for the $\geq$C-class group, 0.45 and 5.59\% for the $\geq$M-class group, and 0.87 and 12.76\% for the X-class group. The higher discrepancy toward stronger flare groups indicates that peak-flux prediction is more challenging for higher-intensity flares. Second, the model performance depends on flare rise time and prediction time, with larger errors for longer rise time events and improved performance as the prediction time approaches the flare peak. Shorter rise time events approach their final peak more rapidly, providing a clearer indication of the eventual peak, whereas the larger difference for longer rise time events may partly reflect more complex temporal evolution. Third, empirical coverage based on total uncertainty remains high but decreases for stronger flares, with noise uncertainty contributing more than model uncertainty.

astro-ph.SR↗

arXiv2026

Statistical Analysis of Minifilament Eruptions Using Full-disk H$\alpha$ Blue-wing Observations at Big Bear Solar Observatory

This paper presents a comprehensive statistical analysis of minifilament eruptions (MFEs) using high-cadence full-disk H$\alpha$ blue-wing observations from Big Bear Solar Observatory. Despite the recognized importance of MFEs for coronal dynamics and solar wind structuring, previous efforts were often limited by small sample sizes or restricted fields of view, leaving open questions about their global occurrence and characteristic properties. We developed an algorithm incorporating intensity thresholding and temporal tracking to detect sudden enhancements in H$\alpha$ blue-wing images. A total of 1986 such events were identified during a 4 hr period on 2020 June 9. These detections were cross-validated using H$\alpha$ line-center observations to confirm the presence of associated filament structures. The analysis yields an occurrence rate of $\sim$6.6$\times 10^4$ per day, an average length of $\sim$17 Mm, and a typical lifetime of $\sim$21 minutes. A power-law distribution in eruption lengths (with slope $\sim$-4.8) and a sublinear scaling between duration and length suggest that larger eruptions tend to last longer. The length distribution of MFEs was further analyzed relative to active region proximity, revealing that eruptions occurring nearby a sunspot region were, on average, larger than the global mean eruption length. Additionally, an eruption density map was used to analyze the spatial distribution of MFEs relative to coronal hole boundaries. The results indicate a mild suppression of activity inside coronal holes and intermediate eruption frequency in the boundary regions. We briefly discuss their potential role in structuring the small-scale solar wind features such as magnetic switchbacks and small-scale magnetic flux ropes.

astro-ph.SR↗

arXiv2026

Coordinated incentives in AI-generated misinformation governance

With the rapid diffusion of AI-generated content, AI-driven misinformation is becoming increasingly pervasive and difficult to govern, undermining information credibility and social trust. This study models the strategic interdependence among a government regulator, an AI enterprise, and users through a three-party evolutionary game that incorporates heterogeneous rewards and punishments. From the resulting replicator equations, we characterize the evolutionary stability of competing governance and production strategies. The analysis indicates that neither unilateral regulation nor market incentives alone can effectively curb misinformation. Instead, an evolutionarily stable regime of real-information production arises only when regulatory rewards and punishment intensity, enterprise reputation loss, and user adoption incentives collectively surpass critical thresholds. The findings highlight the need for coordinated and adaptive policy mixes that align regulatory instruments with enterprise behavior and user uptake while managing governance costs.

physics.soc-ph↗

arXiv2026

Performance appraisal promotes cooperation in spatial public goods games

In real organizations, performance appraisal serves as an important means of evaluating employees' work outcomes and behaviors, while performance pay directly links compensation to the evaluation results. However, in traditional spatial public goods games, the total payoff of a group is equally distributed among all participants without considering individual differences in contributions, an approach that ignores the heterogeneity of individual efforts. To overcome this limitation, we propose a spatial public goods game model based on performance appraisal, in which individual payoffs are divided into two parts: an equally distributed component and a performance-weighted component. Specifically, each individual receives scores from its neighboring groups, and the individual's reputation is dynamically updated by accumulating these scores, which further modulates the fitness function during strategy imitation. Extensive numerical simulation results demonstrate that the performance appraisal mechanism significantly promotes the emergence of cooperative behavior. The reputation reinforcement mechanism amplifies this positive effect by creating fitness advantages for high-reputation individuals. These findings suggest that incorporating performance appraisal into payoff allocation helps mitigate social dilemmas and promote collective cooperation.

physics.soc-ph↗

arXiv2026

Kinetic Optimization of Magnetic Mirror Confinement: Beyond Classical Loss-Cone Theory

Magnetic mirrors are among the conceptually simplest plasma confinement configurations and remain promising candidates for thermonuclear fusion. Their design requires shaping an externally applied magnetic field to confine plasma within an open-ended cylindrical device. In contrast to toroidally closed devices such as tokamaks and stellarators, confinement in magnetic mirrors depends intrinsically on kinetic mechanisms, particularly velocity-space trapping and particle loss through the open ends. We formulate magnetic mirror design as a PDE-constrained optimization problem governed by a reduced multispecies drift-kinetic-Poisson model. The resulting optimization reveals two physical effects not captured by the classical loss-cone argument. First, the self-consistent electric field generated through Poisson coupling acts as a secondary confinement barrier and substantially alters particle retention in the nonlinear regime. Second, the optimized magnetic-field configuration depends qualitatively on the underlying kinetic model: an electron-only model favors an unconventional centrally peaked field, whereas the fully coupled electron-ion model recovers the classical boundary-peaked mirror configuration. These results demonstrate that optimal magnetic mirror design cannot be determined solely from loss-cone considerations, but must account for the self-consistent nonlinear kinetic dynamics of the plasma.

physics.plasm-ph↗

arXiv2026

Nesterov acceleration in optimizing over probability measures

Optimization over probability measures has become an increasingly important paradigm in modern machine learning, scientific computing, and uncertainty quantification. Motivated by Nesterov's accelerated gradient method in Euclidean space, we develop Heavy-ball and Nesterov acceleration methods over the probability measure space $\mathcal{P}_2$ and establish non-asymptotic convergence guarantees that match their Euclidean counterparts. In particular, we derive convergence rates with respect to both the number of iterations and the number of particles used to represent the underlying probability distributions. Extending accelerated optimization from Euclidean space to probability measures is challenging. The natural notion of momentum requires concepts such as tangent bundles of the set of probability space and they are hard to operate numerically. To overcome these difficulties, we introduce two complementary lifting procedures. The first lifts probability measures to phase space through a Hamiltonian formulation, introducing momentum variables into the dynamics. The second lifts probability measures to a common Hilbert space, restoring the linear structure required for convergence analysis while simultaneously yielding executable particle dynamics. Together, these two complementary lifting procedures provide a systematic methodology for designing, analyzing, and implementing momentum-based accelerated optimization methods over probability measure spaces.

math.OC↗

arXiv2026

Adaptive Epidemic Dynamics on Hypergraphs with Group-Level Immunization and Rewiring

Understanding how higher-order social structures shape epidemic spreading requires models that couple group interactions with adaptive behavior. We introduce an adaptive simplicial susceptible-infected-susceptible (s-SIS) model on d-uniform hypergraphs, where both node states and hyperedge activity co-evolve in response to local infection pressure. Hyperedges represent group interactions of fixed size and dynamically reduce their activity through a feedback mechanism in highly infected environments. Within this framework, we design two classes of hyperedge-level interventions: (i) risk-driven immunization, combining spontaneous, activity-based isolation with targeted deactivation guided by hyperedge infection pressure, and (ii) structural rewiring, which reconstructs group structures either randomly or via degree-preferential attachment. By extending the microscopic Markov chain approximation to higher-order interactions, we derive analytical conditions for the existence and stability of both endemic and disease-free stationary states. Our analysis shows that adaptive hyperedge feedback can induce discontinuous phase transitions, nonlinear epidemic thresholds, and bistable regimes in which sufficiently high initial prevalence drives the system to a disease-free equilibrium. Extensive Monte Carlo simulations support the theory and confirm that targeted immunization and degree-preferential rewiring substantially suppress epidemic prevalence, outperforming random strategies. These results demonstrate that higher-order interactions and adaptive group-level responses fundamentally reshape epidemic bifurcations and suggest principles for designing effective intervention policies in complex social systems.

physics.soc-ph↗

arXiv2026

Reconstructing Synthetic SDO/AIA 193 A EUV Images from He I 10830 A Observations with Diffusion Model Translator

Routine full-disk EUV imaging has been available only since the modern era, such as SOHO and SDO. To extend EUV coronal context into earlier periods, we leverage the multi-decade availability of full-disk \HeI{} observations, whose absorption is modulated by coronal irradiance and magnetic topology and is widely used as a proxy for open-field regions. We present a diffusion-based conditional image translation framework, Coronal Hole-aware Diffusion Model Translator (CH-aware DMT), to reconstruct synthetic SDO/AIA 193 \AA{} EUV images from \HeI{} inputs. The model is trained on temporally co-aligned SOLIS \HeI{} and AIA 193 \AA{} pairs spanning 2011--2015 using a month-based split, where January--October are used for training, November is used for validation, and December for testing. On the held-out test set, the reconstructions preserve dominant full-disk EUV morphology (CC=0.92) and recover CH-related low-intensity structure (CC=0.84). We further assess historical applicability by (1) comparing reconstructed AIA 193 \AA{} morphology with SOHO/EIT 195 \AA{} over 2005--2015; (2) comparing reconstructed AIA 193 \AA{} images generated from KPVT \HeI{} inputs against Yohkoh/SXT soft X-ray observations; and (3) evaluating long-term reconstructed disk-integrated emission statistics against observational EUV series and independent solar activity proxies (sunspot number and F10.7 radio flux over 1974--2015). These results indicate that CH-aware DMT conditioned on \HeI{} can provide a physically plausible synthetic AIA 193 \AA{} coronal proxy for historical studies, supporting multi-decade analyses of large-scale coronal evolution before the direct EUV imaging was available.

astro-ph.SR↗

arXiv2026

Optimal drift optimizer for non-convex optimization

We study a finite-horizon stochastic control criterion for non-convex optimization in which Brownian exploration is balanced against a quadratic control cost. Rather than emphasizing the classical Hopf--Cole representation, we isolate the exact drift selected by the criterion and reorganize it in a form adapted to optimization. The key object is the conditional terminal law of the optimal process. We show that this law is a Gibbs measure for a proximally penalized energy, yielding three exact representations of the drift: potential, averaged-gradient, and barycentric. We then analyze two asymptotic regimes relevant for optimization. As terminal time is approached, the drift recovers a scaled gradient-descent field. In the low-temperature regime, assuming a unique global minimizer, the conditional terminal law concentrates on it even in the presence of nonglobal local minima, and the drift converges to an affine attraction field toward it. In the nondegenerate case we also derive Laplace asymptotics for the drift, the value function, and the covariance of the conditional terminal law. Finally, we record a simple gradient-free discretization suggested by the barycentric formula.

math.OC↗

arXiv2026

Finding Koopman Invariant Subspaces via Personalized PageRank

Selecting a finite dictionary of observables whose span is Koopman-invariant is a central challenge in data-driven Koopman operator approximation. We address this problem by exploiting zero-block structure in Extended Dynamic Mode Decomposition (EDMD) matrices. We show that any sub-dictionary whose span is Koopman-invariant induces an exact zero block in the EDMD matrix, even for finite data. We then show that such blocks can be detected by applying PageRank to a row-normalized EDMD matrix constructed from a large initial dictionary. The theory extends to approximately invariant subspaces and yields stronger guarantees for personalized PageRank (PPR) when the seed observables lie inside the target block and reach all observables in that block. Combining EDMD concentration bounds with PageRank perturbation theory gives end-to-end detection guarantees with $O(1/\sqrt{M})$ finite-sample scaling and explicit constants. More generally, without assuming an invariant subspace exists, high PPR mass on a sub-dictionary controls discounted multi-step leakage from the seed observables. Numerical experiments on the Duffing oscillator, Van der Pol oscillator, Lorenz system, and a three-well Ramachandran potential suggest that the method identifies compact, interpretable dictionaries with accurate predictions.

math.DS↗

arXiv2026

Event-B Agent: Towards LLM Agent for Formal Model Synthesis and Repair

Building software that is correct by construction is a long-standing goal in software engineering, as it ensures reliability during design and development rather than after deployment. Formal methods realize this vision by enabling the expression of system behavior and requirements in mathematics, thereby guaranteeing correctness through formal verification, including theorem proving and model checking. However, the steep learning curve and demand for mathematical expertise hinder the widespread adoption of formal methods. Large language models (LLMs) have recently shown promise in bridging this gap through autoformalization. However, existing LLM-based approaches are largely limited to isolated tasks, such as theorem proving without formalization or model synthesis with insufficient verification. While valuable, these efforts do not fully exploit the potential of a more comprehensive framework in which models and proofs evolve together, a process that closely reflects real-world development practice. To address this gap, we propose Event-B Agent, a novel framework inspired by the interleaved nature of software design. Given natural language requirements, Event-B Agent constructs an initial model and iteratively repairs and refines it using formal verification feedback. Refinement simplifies proof discharge, while repair of models and proofs ensures the soundness of each refinement step. Together, these two components reinforce each other to progressively improve the model quality. Evaluation across systems of varying complexity demonstrates that Event-B Agent substantially outperforms baselines in end-to-end formal model synthesis and repair, while maintaining reasonable efficiency. These results suggest that Event-B Agent is a promising step toward correct-by-construction formal model synthesis and repair.

cs.SE↗

arXiv2026

Provable imitation learning for control of instability in partially-observed Vlasov--Poisson equations

We consider the stabilization of Vlasov--Poisson plasma dynamics, a central control problem in nuclear fusion. Our focus is the gap between what an ideal controller would use and what experiments can actually observe: while optimal policy may rely on the full phase-space state, practical feedback is typically limited to sparse macroscopic diagnostics. We therefore study imitation learning methods that distill a fully observed expert policy into controllers operating only on macroscopic measurements. We show the stability guarantees of the learned policy, where the error floor depends on the minimal behavior cloning loss achievable under the observation constraints. We further characterize this minimal loss in terms of a notion of entropy that quantifies the complexity of the initial distribution. Our results demonstrates the theoretical feasibility of learning stabilizing feedback policies for kinetic plasma dynamics from macroscopic observations, and exhibits the adaptivity of the learning approach to low-complexity structures. Through extensive numerical experiments, we validate our theory and show that the learned policies can stabilize the system using only macroscopic observations, within a significantly longer time horizon than non-adaptive baseline controllers.

cs.LG↗

arXiv2026

Rumor Propagation and Supervision during Confrontation: An Importance-Driven SIRQS Network Model

The societal impact of rumor spreading is becoming increasingly severe; yet, current research remains relatively one-sided, typically focusing on either rumor propagation or rumor control while neglecting the confrontational and dynamically evolving relationship between them. To address this gap, we propose a novel confrontation framework for rumor modeling. We extend the classical Susceptible-Infected-Recovered-Susceptible (SIRS) model into an Ignorant-Spreader-Stifler-Vigilant-Ignorant (SIRQS) framework by introducing a vigilant state and a confrontation mechanism, thereby capturing subtle differences in individual states during rumor propagation and in their confrontational behavior toward supervisors. At the same time, supervisors patrol the network through random walks guided by node propagation importance, enabling targeted monitoring of rumor spreaders and individuals with a high risk of spreading rumors. Using a microscopic Markov chain approach, we further characterize heterogeneous node behavior and individual differences, and couple the propagation and supervision processes to model node-state transition patterns. We conduct simulations on networks with three different sizes, various topologies, and a real-world network. The results show that the supervision subject, the preference effects associated with the number of supervisors, and the confrontation mechanism are key factors in supervision, and largely determine the effectiveness of rumor propagation control in the simulations, reflecting the substantial influence of these three mechanisms in real-world spreading scenarios. Finally, through multiple evaluation indicators, we provide references for determining the optimal number of supervisors.

physics.soc-ph↗

arXiv2026

Brane quantization and SYZ mirror symmetry

Coisotropic A-branes were introduced by Kapustin--Orlov to enlarge the Fukaya category of a symplectic manifold in a way that aligns with predictions from homological mirror symmetry. From a mathematical perspective, however, the categorical framework governing such branes remains largely undeveloped. On the other hand, Gukov--Witten's brane quantization suggests that a holomorphic deformation quantization of a holomorphic symplectic manifold $X$ arises from the endomorphism algebra $Hom_A(B_{cc},B_{cc})$ of a canonical coisotropic A-brane $B_{cc}$, which naturally acts on the morphism space $Hom_A(B,B_{cc})$ with a Lagrangian A-brane $B$ that in turn gives precisely the geometric quantization of $B$. In this paper, we consider a holomorphic symplectic manifold $X$ which admits an SYZ fibration and apply SYZ mirror symmetry to study its brane quantization. Given any semi-affine, space-filling coisotropic A-brane $B_{cc}$ on $X$, we construct the mirror B-brane $\check{B}_{cc}$ on the mirror manifold $\check{X}$ by an SYZ transform. We then present a mathematical definition of the endomorphism algebra $Hom_A(B_{cc},B_{cc})$ by constructing a distinguished non-formal holomorphic deformation quantization of $X$. Using a twisted family Toeplitz construction, we transform $Hom_A(B_{cc},B_{cc})$ to the mirror B-side and prove that this induces an isomorphism $Hom_A(B_{cc},B_{cc})\cong Hom_B(\check{B}_{cc},\check{B}_{cc})$ between the endomorphism algebras. Furthermore, taking any torus fiber of $X$ as the Lagrangian A-brane $B$, we fully realize Gukov--Witten's proposal, namely, there is a natural action of $Hom_A(B_{cc},B_{cc})$ on $Hom_A(B,B_{cc})$ which is precisely mirror to the natural action on the mirror B-side. This provides a mathematical framework which is compatible with Gukov--Witten's brane quantization proposal, SYZ mirror symmetry as well as family Floer theory.

math.DG↗

arXiv2026

High-Integration multimode waveguide grating based CWDM4 MUX/DEMUX with Flat Wide Passband and Ultra-Low Crosstalk for 2xFR4 Module Applications

This work presents a compact, low-crosstalk CWDM4 MUX/DEMUX utilizing cascaded multimode waveguide grating filters. The individual filters are designed with finite Gaussian apodization and positive dispersion, enabling strong unilateral sidelobe suppression while maintaining a minimum feature size compatible with UV lithography. By cascading these filters, we demonstrate a DEMUX that achieves channel crosstalk below -25 dB, insertion loss under 1 dB, and a flat-top bandwidth of approximately 18 nm. The entire device occupies a compact footprint of only 1.6 mm x 40 um, with a channel spacing compatible with commercial TIA and driver chips. Furthermore, a series-parallel hybrid cascade configuration can further suppress the crosstalk to -40 dB.

physics.optics↗

arXiv2026

Stochastic Modified Equations for Stochastic Gradient Descent in Infinite-Dimensional Hilbert Spaces

Inverse problems in scientific computing often require optimization over infinite-dimensional Hilbert spaces. A commonly used solver in such settings is stochastic gradient descent (SGD), where gradients are approximated using randomly sampled sub-objective functions. In this work we study the continuous-time limit of SGD in the small step-size regime. We show that the discrete dynamics can be approximated by a stochastic differential equation (SDE) driven by cylindrical Brownian motion. The analysis extends diffusion-approximation results previously established in Euclidean spaces to the infinite-dimensional setting. Two analytical difficulties arise in this extension. First, the cylindrical nature of the noise requires establishing well-posedness of the resulting stochastic evolution equation through appropriate structural conditions on the covariance operator. Second, since the randomness in SGD originates from discrete sampling while the limiting equation is driven by Gaussian noise, the comparison between the two dynamics must be carried out in a weak sense. We therefore introduce a suitable class of smooth functionals on the Hilbert space and prove that the discrepancy between SGD and the limiting SDE, when evaluated through these functionals, is of second order in the step size. Numerical experiments confirm the predicted convergence behavior.

math.OC↗