arXiv subjects
Publications and source records attributed to Wei Hong.
Motivated by the extended deformation theory of complex manifolds, we give a combinatorial description of holomorphic polyvector fields on a smooth compact toric variety via Klyachko's filtrations. This yields dimension and formal equivariant-character formulas and recovers the descriptions of Demazure roots and anticanonical sections.
This work investigates the mean-field stochastic PDEs involving a class of pseudo-monotone kernels. We first study the well-posedness -- in both the strong and weak sense -- within the variational framework by introducing a notion of measure-dependent pseudo-monotone operators, which generalizes the classical framework due to Brézis. Furthermore, we establish the quantitative dimension-free propagation of chaos within a $p$-uniformly convex Banach space for general infinite-dimensional weakly interacting systems, obtaining convergence rates that are near-optimal in a suitable sense. Our results reveal a new insight: the convergence rate of the mean-field limit is intrinsically governed by the geometry of the underlying solution space, specifically its modulus of convexity. As applications, we study several finite- and infinite-dimensional interacting particle systems arising in machine learning and fluid mechanics, including stochastic Stein variational gradient descent, mean-field Allen-Cahn equations, and Lagrangian-averaged Burgers equations.
This work investigates the global existence, uniqueness, and Feller property for stochastic partial differential equations under generalized coercivity conditions, particularly in cases where the corresponding deterministic equations possess only local solutions. Furthermore, we reveal a novel phenomenon: for a potentially explosive deterministic system, the introduction of appropriate multiplicative noise not only prevents blow-up but also leads to the finite-time extinction of the stochastic dynamics. Our main results are applicable to a broad range of models, including stochastic 3D Navier-Stokes equations, stochastic surface growth models, and stochastic $p$-Laplace equations with heat sources.
On-chip inductive elements are pivotal in determining both the silicon footprint and performance of millimeter-wave (mmWave) integrated circuits. However, the layout-level synthesis of these passive devices is severely challenged by highly nonlinear geometry-to-performance mappings, computationally expensive full-wave electromagnetic simulations, topology-dependent design spaces, and the inherent non-uniqueness of inverse design. To overcome these bottlenecks, we propose a hybrid forward optimization and reverse design (HFORD) method for the target-to-layout synthesis of mmWave inductive elements. Utilizing a unified core to map device-level requirements to layout-level seeds, HFORD structures direct device targets and translates circuit specifications into a hierarchical synthesis flow. Specifically, sparse-fitting sampling is introduced to improve coverage across critical performance regions, while compact response-fitting coefficients significantly reduce training dimensionality. The HFORD core integrates a random forest for topology selection, a variational autoencoder for spectral feature generation, a mixture density network for probabilistic inverse mapping, and particle swarm optimization for latent space exploration. This integration improves the feasibility of the generated layout seeds under design rule check (DRC) constraints. Two design examples demonstrate that the proposed method accelerates the design cycle from hours to minutes compared to conventional optimization methods.
We study the impact of imposing an infinite-future condition on Gaussian-process (GP) reconstructions of $H(z)$ from 37 cosmic-chronometer measurements. Implementing the asymptotic limit $H(-1)=0$ expected in constant-$w$CDM with $w>-1$ as a pseudo-point at $z=-1$ with tunable uncertainty $σ_{-1}$ lowers the GP-inferred Hubble constant from $H_0=68.71\pm6.08$ to $H_0\simeq(64.67$--$65.86)\pm(4.45$--$4.85)~{\rm km\,s^{-1}\,Mpc^{-1}}$. The resulting $H_0$ remains within $\sim0.32$--$0.61\,σ$ of the \textit{Planck} $Λ$CDM value, while the separation from representative local distance-ladder measurements increases to $\sim1.45$--$1.83\,σ$. A scan over $σ_{-1}$ shows that the shift is governed by the effective pseudo-point weight, interpolating between the hard-condition and data-dominated limits. Finally, constant-$w$CDM Markov Chain Monte Carlo (MCMC) fits to the same $H(z)$ data with $H_0$ fixed to the GP-inferred values show that $Ω_m$ is only weakly affected, whereas lower $H_0$ shifts $w$ toward less negative values; allowing curvature broadens constraints and remains consistent with $Ω_k=0$.
Stochastic Unit Commitment (SUC) has been proposed to manage the uncertainties driven by renewable integration, but it leads to significant computational complexity. When accelerated by Benders Decomposition (BD), the master problem becomes binary integer programming, which is still NP-hard and computationally demanding for classical methods. Quantum Annealing (QA), known for efficiently solving Quadratic Unconstrained Binary Optimization (QUBO) problems, presents a potential solution. However, existing quantum algorithms rely on slack variables to handle linear binary inequality constraints, leading to increased qubit consumption and reduced computational efficiency. To solve the problem, this paper introduces the Powell-Hestenes-Rockafellar Augmented Lagrangian Multiplier (PHR-ALM) method to eliminate the need for slack variables, making qubit consumption independent of the increasing number of Benders cuts. To further reduce the qubit overhead, quantum ADMM is applied to break large-scale SUC into smaller blocks for sequential solutions, which does not scale with the number of generators. Finally, the simulation results on both 4-generator and the IEEE bus-118 systems demonstrate the feasibility and scalability of the proposed algorithm, indicating its superior qubit and runtime efficiency over classical and baseline quantum approaches on the D-Wave QPU platform.
Background: Type 2 diabetes mellitus (T2DM) is increasingly recognised as a systemic disease characterised by coordinated dysfunction across metabolic, renal, lipid, and inflammatory pathways. Existing clinical assessments often fail to capture this multi-dimensional burden. Methods: We conducted a retrospective study of 1,195 patients using routinely collected laboratory biomarkers. System-level abnormality indices were constructed to quantify organ-specific dysfunction, and multi-system involvement was defined as abnormalities in two or more systems. Supervised machine learning models, including logistic regression, random forest, and gradient boosting, were trained to predict multi-system dysregulation. Model interpretability was achieved using SHapley Additive exPlanations (SHAP). Results: The gradient boosting model demonstrated near-perfect discrimination (AUC = 1.000), significantly outperforming logistic regression (AUC = 0.925). Feature attribution analysis revealed that hyperglycaemia, renal impairment, dyslipidaemia, and inflammation were the dominant drivers of multi-system risk. Dose-response relationships observed in partial dependence analyses further supported the biological plausibility of model predictions. Conclusion: This study presents an interpretable, data-driven framework for quantifying systemic disease burden in T2DM. By linking routine biomarkers to multi-organ dysfunction, our approach provides both predictive accuracy and mechanistic insight, offering potential for improved risk stratification and precision medicine in diabetes care. The data and code used in this study are openly available on GitHub at: https://github.com/MiniHanWang/Type-2-Diabetes-1.git
Retinal imaging provides a non-invasive window into systemic microvascular health and has emerged as a potential biomarker for systemic diseases. However, whether retinal features encode biologically meaningful systemic signals that can be reliably interpreted using explainable artificial intelligence (XAI) remains unclear. An explainable multi-task deep learning framework was developed to investigate associations between retinal microvascular features and systemic abnormalities in Type 2 Diabetes Mellitus. A total of 11,011 fundus images from 2,719 individuals were analysed using a shared neural network with task-specific heads for glycaemic status, kidney abnormality, and multi-system involvement. Model interpretability was evaluated using Gradient-weighted Class Activation Mapping (Grad-CAM), anatomical masking, and vessel alignment analysis. The framework demonstrated task-dependent predictive performance, with the best discrimination observed for kidney abnormality (AUC up to 0.63), whereas glycaemic status prediction showed limited performance (AUC = 0.49-0.61). Explainability analyses consistently localized model attention to retinal vessels and peripapillary regions. Masking experiments showed that occlusion of vascular regions caused the greatest performance decline, indicating that retinal vessels were the primary predictive source. Different architectures exhibited heterogeneous attention patterns, suggesting multiple representational pathways for systemic signal encoding. This pilot study demonstrates that retinal microvascular features contain measurable signals associated with systemic abnormalities, particularly microvascular damage. By integrating multi-task learning with quantitative XAI validation, this framework advances retinal imaging toward interpretable digital biomarkers for systemic risk stratification in diabetes.
Gravitational waves (GWs) can resonate with magnetic fields through the Gertsenshtein-Zeldovich effect, producing electromagnetic signals at the same frequency. In pulsar magnetospheres, this conversion may yield a faint radio-band signal that could be detected. In this work, we focus on two specific pulsars, PSR J1856-3754 and PSR J0720-3125, and use numerical simulations to evaluate how well the FAST and SKA2-MID telescopes could detect such signals. We consider transient events, including primordial-black-hole-like mergers, as well as stochastic backgrounds, including primordial GWs. To improve detection sensitivity, we propose four observational methods to lower the detectable energy-density limit of very high-frequency (VHF) GWs; the "Multiple Pulsars with Multiple Telescopes" (MPMT) method performs best because it allows cross-validation and rejection of false candidates. Under the assumption of nearly 6000 hours of observation at 3 GHz and a $5σ$ detection threshold, the minimum detectable characteristic strain is projected to be $h_c \approx 10^{-23}$ for transient events and $h_c \approx 10^{-33}$ for stochastic backgrounds. Under optimistic assumptions on integration time and conversion efficiency, these projections suggest that radio-band searches may approach the sensitivity needed to begin testing representative VHF GW scenarios. More broadly, this conversion in pulsar magnetospheres could be relevant to the origin of some repeating fast radio bursts in the our galaxy.
Using the 37-point cosmic-chronometer subset of observational Hubble parameter (OHD) data, we develop a Bayesian Gaussian-process framework to reconstruct the normalized dark-energy density \(f(z)\) and equation of state \(w(z)\), focusing on how the choice of latent space affects the inference. We compare a Gaussian-process prior placed directly on \(f(z)\) with the conventional latent-\(H\) formulation, and also test a log-\(f\) branch that enforces \(f(z)>0\). We further analyze OHD-like mock data generated from fiducial \(Λ\)CDM and mildly evolving \(w_0w_a\) models, using both the observed redshift distribution and a higher-quality high-redshift setup. For real OHD, leave-one-out cross-validation shows no strong predictive preference between latent-\(f\) and latent-\(H\) reconstructions. The inferred \(f(z)\), \(w(z)\), and \(Om(z)\) remain consistent with \(Λ\)CDM across the tested external priors, while apparent \(Om(z)\) trends are prior sensitive and not robust evidence for dark-energy evolution. Residual differences between the two latent constructions are small, sign mixed, prior dependent, and mainly confined to the weakly constrained high-redshift tail. We therefore interpret the real-data results primarily as a methodological assessment. In mock tests, the framework responds to injected mild evolution in the reconstructed dark-energy quantities and \(Om(z)\), with detectability depending on method and data coverage. Improved high-redshift OHD reduces the discrepancy between latent constructions and makes the \(Om(z)\) response more consistently detectable. The latent-\(f\) approach is therefore a viable alternative to latent-\(H\), while current constraints are limited mainly by sparse high-redshift OHD and dependence on external priors.
The aim of this paper is to investigate the large deviations for a class of slow-fast mean-field diffusions, which extends some existing results to the case where the laws of fast process are also involved in the slow component. Due to the perturbations of fast process and its time marginal law, one cannot prove the large deviations based on verifying the powerful weak convergence criterion directly. To overcome this problem, we employ the functional occupation measure, which combined with the notion of the viable pair and the controls of feedback form to characterize the limits of controlled sequences and justify the upper and lower bounds of Laplace principle. As a consequence, the explicit representation formula of the rate function for large deviations is also presented.
In this work, we establish the small-noise asymptotic behaviour (namely, the functional law of large numbers and the large deviation principle) for multi-scale McKean--Vlasov diffusions with super-linear kernels. In this setting, the interaction depends on the laws of both the slow component and the fast oscillating process. Consequently, the frozen (parameterized) system exhibits McKean--Vlasov dynamics, forming a nonlinear Markov process and thereby rendering the analysis more complex compared to existing works. We develop a lifted semigroup argument and employ a generalized Khasminskii time discretization scheme to derive the small-noise limit of the slow variable, providing explicit convergence rates. Furthermore, we introduce the notion of a lifted viable pair and utilize a generalized functional occupation measure approach to establish the Laplace principle, which is equivalent to the large deviation principle. The main results of this work find broad applications in multi-scale models arising in fields such as machine learning and optimization theory. In particular, our results can be employed to analyze the dynamics of multi-scale consensus-based methods for multilevel optimization, where the coefficients typically satisfy local Lipschitz continuity on the interaction kernels.
The Hubble tension refers to the significant discrepancy in the Hubble constant $H_{0}$ obtained from two different measurement methods in cosmology. One method derives data from the Cosmic Microwave Background (CMB) observations by the Planck satellite, yielding a value of $67.4\pm{0.5} \ \mathrm{km\ s^{-1}} \mathrm{Mpc^{-1}} $, while the other method relies on direct measurements of Type Ia supernovae, producing a value $73.04\pm{1.04} \ \mathrm{km\ s^{-1}} \mathrm{Mpc^{-1}} $. This issue has persisted for several years. To theoretically explore potential solutions to this problem, this paper examines a model within the framework of Einstein-Cartan (EC) theory, where torsion is introduced with spin as the corresponding entity, allowing for the assumption $H = -αϕ$. By employing the Markov Chain Monte Carlo (MCMC) algorithm and utilizing Cosmic Chronometers (CC) data, we impose parameter constraints on various parameters in the Friedmann equations, particularly focusing on the curvature density parameter $Ω_k$, to assess whether the model remains stable under this assumption and whether the estimated parameters align more closely with either of the observational results. In conclusion, we find that the parameter constraints in the model incorporating torsion ($ H_0 = 67.6^{+2.1}_{-2.7} \ \mathrm{km\ s^{-1}\ Mpc^{-1}}$, obtained under the Big Bang Nucleosynthesis (BBN) constraint with $Ω_{k}=0$; $ H_0 = 66.2^{+4.4}_{-2.9} \ \mathrm{km\ s^{-1}\ Mpc^{-1}}$, obtained under same constraint but set $Ω_{k}$ as a free variable; $ H_0 = 68.8^{+2.9}_{-4.2} \ \mathrm{km\ s^{-1}\ Mpc^{-1}}$, obtained under the Planck constraint) are more consistent with the value derived from CMB data, favoring the lower $H_0$ value.
Context. Gamma-ray bursts (GRBs) reach redshifts beyond Type Ia supernovae (SNe Ia) and can extend distance measurements into the early Universe, but their use as distance indicators is limited by the circularity problem in calibrating empirical luminosity relations. Aims. We present a model-independent methodology to overcome this circularity by combining Pantheon$+$ SNe Ia, a distance reconstruction based on artificial neural networks (ANNs), and two GRB correlations (Amati and Combo) into a distance ladder from low to high redshift, with the goal of constraining cosmological parameters in $Λ\mathrm{CDM}$ and $w_0 w_a \mathrm{CDM}$. Methods. We use the ReFANN to reconstruct the luminosity distance $d_L(z)$ and distance modulus $μ(z)$ from the Pantheon$+$ dataset, with hyperparameters optimized via approximate Bayesian computation rejection and a risk function. This model-independent reconstruction calibrates the Amati and Combo relations using a low-redshift ($z<1$) GRB sample from Fermi GBM and Swift-XRT. The calibrated relations then provide distance estimates for GRBs at $z \geq 1$. Finally, a joint Bayesian analysis simultaneously constrains the cosmological and GRB correlation parameters, ensuring self-consistent uncertainty propagation. Results. We obtain consistent cosmological constraints from two independent GRB correlations. The Hubble constant $H_0$ agrees with SNe Ia values, though potentially influenced by Pantheon$+$ dataset. High-redshift GRBs favour a higher matter density $Ω_m$ than the Pantheon$+$ and hint at possible dark energy evolution.Conclusions. We present a framework that mitigates GRB cosmology's circularity problem, extending the distance ladder to $z \sim 9$ and establishing GRBs as a high-redshift probe.
In the classical work [FK], Fujita and Kato established the local existence of solutions to the 3D Navier-Stokes equations in the critical $\mathbb{H}^{1/2}$-space. In this paper, we are concerned with the global well-posedness of the stochastic forced 3D Navier-Stokes equations in the $\mathbb{H}^{1/2}$-space under general initial conditions, where the stochastic forcing comprises a transport forcing and a nonlocal turbulent forcing. In this setting, the random noise is shown to provide a regularization effect on the energy estimates, which we obtain by constructing suitable Lyapunov functions. However, its nonlocality also brings analytical challenges. We develop a bootstrap type estimate based on the kinematic viscosity together with a delicate stopping time argument to prove the global existence and uniqueness of solutions, as well as continuous dependence on the initial value. Furthermore, we also investigated the long-time behavior of the stochastic forced 3D Navier-Stokes equations.
Integrated Sensing and Communication (ISAC) has been identified as a key 6G application by ITU and 3GPP. Channel measurement and modeling is a prerequisite for ISAC system design and has attracted widespread attention from both academia and industry. 3GPP Release 19 initiated the ISAC channel study item in December 2023 and finalized its modeling specification in May 2025 after extensive technical discussions. However, a comprehensive survey that provides a systematic overview,from empirical channel features to modeling methodologies and standardized simulators,remains unavailable. In this paper, the key requirements and challenges in ISAC channel research are first analyzed, followed by a structured overview of the standardization workflow throughout the 3GPP Release 19 process. Then, critical aspects of ISAC channels, including physical objects, target channels, and background channels, are examined in depth, together with additional features such as spatial consistency, environment objects, Doppler characteristics, and shared clusters, supported by measurement-based analysis. To establish a unified ISAC channel modeling framework, an Extended Geometry-based Stochastic Model (E-GBSM) is proposed, incorporating all the aforementioned ISAC channel characteristics. Finally, a standardized simulator is developed based on E-GBSM, and a two-phase calibration procedure aligned with 3GPP Release 19 is conducted to validate both the model and the simulator, demonstrating close agreement with industrial reference results. Overall, this paper provides a systematic survey of 3GPP Release 19 ISAC channel standardization and offers insights into best practices for new feature characterization, unified modeling methodology, and standardized simulator implementation, which can effectively supporting ISAC technology evaluation and future 6G standardization.
We introduce LongCat-Flash-Omni, a state-of-the-art open-source omni-modal model with 560 billion parameters, excelling at real-time audio-visual interaction. By adopting a curriculum-inspired progressive training strategy that transitions from simpler to increasingly complex modality sequence modeling tasks, LongCat-Flash-Omni attains comprehensive multimodal capabilities while maintaining strong unimodal capability. Building upon LongCat-Flash, which adopts a high-performance Shortcut-connected Mixture-of-Experts (MoE) architecture with zero-computation experts, LongCat-Flash-Omni integrates efficient multimodal perception and speech reconstruction modules. Despite its immense size of 560B parameters (with 27B activated), LongCat-Flash-Omni achieves low-latency real-time audio-visual interaction. For training infrastructure, we developed a modality-decoupled parallelism scheme specifically designed to manage the data and model heterogeneity inherent in large-scale multimodal training. This innovative approach demonstrates exceptional efficiency by sustaining over 90% of the throughput achieved by text-only training. Extensive evaluations show that LongCat-Flash-Omni achieves state-of-the-art performance on omni-modal benchmarks among open-source models. Furthermore, it delivers highly competitive results across a wide range of modality-specific tasks, including text, image, and video understanding, as well as audio understanding and generation. We provide a comprehensive overview of the model architecture design, training procedures, and data strategies, and open-source the model to foster future research and development in the community.
In the context of fitting cosmological models, parameter degeneracy remains a central issue. This paper critically examines traditional methods for constraining parameters and focuses on the G factor as a tool for evaluating the quality of observational data. To ensure analytical independence, two datasets--Cosmic Chronometers (CC) and Baryon Acoustic Oscillations (BAO)--were utilized as samples for parameter fitting, supplemented by Markov Chain Monte Carlo (MCMC) simulations. The Figure of Merit (FoM) matrix served as the final criterion for assessing fitting performance. The results show that the G factor of the CC dataset increases linearly with redshift z, whereas the G factor of the BAO dataset follows a cubic relationship. Further analysis indicates that the FoM value for datasets with high G factors is significantly higher than that for datasets with low G factors, thereby validating the G factor's effectiveness as a tool for assessing observational data quality and reducing parameter degeneracy. This suggests that the G factor may serve as a diagnostic tool and selection criterion for optimizing observational datasets in future research.