arXiv subjects

Yiming Jiang

Publications and source records attributed to Yiming Jiang.

At least 19 recordsLinked to original sources

arXiv2026

Stochastic Keller Segel System with Porous Medium Diffusion and Nonlinear Chemotactic Sensitivity

In this paper, we investigate a stochastic Keller--Segel system with porous medium diffusion and nonlinear chemotactic sensitivity on a bounded one-dimensional domain. The model describes cell aggregation in complex environments, where the dispersal of cells is governed by density-dependent diffusion $\Delta u^{[m]}$, reflecting the combined effects of porous media and population crowding, and the perception of chemoattractants follows Stevens' power law, leading to the nonlinear chemotactic sensitivity $\nabla\cdot(u\nabla v^{[a]})$. In addition, random environmental fluctuations are incorporated through multiplicative noise $u\,dW(t)$, which represents stochastic perturbations in population dynamics. For $a\geq1$ and $m\geq2a+1$, we establish the global existence of martingale solutions, uniform a priori estimates, and preservation of non-negativity. The condition $m\geq2a+1$ reveals a balance between nonlinear chemotactic aggregation and porous-medium diffusion: stronger sensing response requires stronger diffusion to prevent excessive aggregation. The proof combines a decoupled auxiliary system, energy estimates, and a stochastic Schauder--Tychonoff fixed point argument to overcome the difficulties caused by degenerate diffusion, nonlinear drift, and stochastic perturbations.

math.AP↗

arXiv2026

Stochastic Two-Species Chemotaxis Competition: Global Well Posedness and Continuous Dependence

In this paper, we investigate a stochastic two species competition Keller--Segel model. Chemotactic movement, interspecific competition, and environmental fluctuations may act simultaneously when two species respond to the same chemical signal. We consider a stochastic two-species chemotaxis--competition system on a bounded smooth domain $\mathcal O\subset\mathbb R^n$, $n\in\{1,2\}$. Both species contribute to the production of the signal and move along its gradient; their population equations also include nonlinear competition and multiplicative noise. If the self-damping exponents exceed two, we prove that the system has a unique global adapted nonnegative mild solution. We also establish continuous dependence in probability on admissible initial data over finite time intervals. The results prove the global well-posedness under the stated assumptions and we still show that small changes in the initial populations, in probability, to small changes in the solution. Due to the two coupled chemotactic fluxes and the stochastic terms, the $L^p$ estimates contain terms with no fixed sign. They are controlled by parabolic estimates for the signal equation, superquadratic self-damping, and stochastic convolution estimates.

math.AP↗

arXiv2026

From Score Learning to Discretized Sampling: An End-to-End Generalization Analysis of Diffusion Models

Despite the empirical success of score-based diffusion models, a complete theoretical understanding of how finite-sample learning, network parameterization, and numerical discretization jointly dictate generative quality remains underdeveloped. Existing sampling analyses often evaluate the generative performance conditional on an oracle score or a pre-specified error threshold. In this work, we establish a unified convergence and generalization framework for score-based diffusion models parameterized by practical ResNet-type architectures. We analyze the generalization and convergence properties from the practical finite-sample, discrete-time learning problem of the score function to the ideal continuous-time, population-level objective. Based on the generalization result of the learning problem of score function, we analyze the sampling process induced by the learned score function and provide an end-to-end total variation distance estimate for the generated terminal distribution. This estimate explicitly decomposes the overall generative error into four interpretable components: the truncation error of the forward process, the reverse-time discretization error, the generalization error incorporating both finite data and forward-time discretization, and the training optimization gap. Our results quantitatively characterize how the training sample size, temporal discretization grids, and optimization accuracy jointly control the final fidelity of samples generated by diffusion models.

cs.LG↗

arXiv2026

Mean field and N-agent games for optimal relative consumption-investment with jump risk and common noise

This paper studies an optimal consumption--investment problem for competitive agents in an $N$-player game and its associated mean field game. Each agent invests in an individual risky asset subject to idiosyncratic noise, common noise and downward jump risk, and the interaction among agents is induced by relative performance concerns in both consumption and terminal wealth. In the mean field limit, we characterize a deterministic mean field equilibrium in analytical form by using the stochastic maximum principle. Numerical experiments are presented to illustrate the resulting equilibrium and its financial implications. Finally, based on the obtained mean field equilibrium, we construct an approximate Nash equilibrium for the $N$-player game. This model is motivated by \cite{Merton1971} and \cite{Lacker2020}.

math.OC↗

arXiv2026

Well-posedness of the mean field game master equation on Carnot tori

We study the master equation for a second-order mean field game on Carnot tori, which means the generic player can move periodically only along admissible trajectories given by the family of vector fields generating the Carnot group. As examples of sub-Riemannian manifolds, Carnot groups represent a type of non-commutative groups characterized by stratified Lie algebra structures. In order to obtain the well-posedness of the master equation, we analyze the properties of its solution by investigating a degenerate mean field game system for which there exists an equivalent characterization with the master equation. The main part of this paper lies in leveraging the regularity properties of solutions to two classes of linear degenerate parabolic equations and a class of linear degenerate coupled systems to derive the existence of solutions to the master equation. The research in this paper is motivated by \cite{19CDLL,24MMM}.

math.AP↗

arXiv2026

FA-LAM: Focus-Aware Large Avatar Model for One-Shot 4D Animatable Gaussian Head

We propose FA-LAM, a Focus-Aware Large Avatar Model for one-shot animatable Gaussian head creation, while simultaneously enabling static 3D and dynamic 4D full-head recovery. The core of our method lies in a thorough analysis of the attention mechanisms and the entangled reconstruction and animation training pipeline adopted by prior state-of-the-art approaches. Our analysis identifies two main factors that compromise the quality of 3D full-head generation: (1) incorrect and noisy attention activations, and (2) conflicts between the tasks of reconstruction and animation. To address the first issue, we introduce a symmetric and semantic attention regularization strategy that leverages the inherent semantics and structural symmetry of human heads. To disentangle the objectives of reconstruction and animation, we develop a novel dual-phase training pipeline that separates the model's capabilities for large-view hallucination and animation into distinct modules. Moreover, we enhance our model to support multi-view and streaming 4D reconstruction in an efficient and memory-friendly manner through a core autoregressive modification with tailored visibility-aware token fusion. Collectively, these innovations enable FA-LAM to reconstruct animatable Gaussian full heads with superior quality, particularly in fine facial regions and large viewing angles.

cs.CV↗

arXiv2026

HiReFF: High-Resolution Feedforward Human Reconstruction from Uncalibrated Sparse-View Video

Uncalibrated volumetric video streaming for human reconstruction is essential for holographic communication and AR/VR, yet remains challenging due to the need for temporal consistency and computational efficiency from sparse-view inputs. Existing methods rely on per-scene optimization or calibrated cameras, while recent feed-forward models are limited to low-resolution (0.5K) single-frame synthesis. We present HiReFF, a feed-forward method for 2K-resolution 360{\deg} human video reconstruction from uncalibrated sparse-view videos. Our framework decomposes the problem into two key tasks: foreground 3D Gaussian reconstruction from sparse-view videos (four views separated by 90{\deg}) and computationally efficient high-resolution synthesis. To enable the former, we propose Scale-synchronized Camera Calibration to resolve scale ambiguity for multi-view supervision, and Gaussian-wise Foreground Masking to reconstruct clean foregrounds by modulating Gaussian parameters. For efficient high-resolution synthesis, our High-resolution Side-tuning achieves 2K rendering by augmenting the Gaussian head with supplementary features while keeping the backbone at 0.5K, drastically reducing computational overhead. Experiments demonstrate that HiReFF significantly outperforms existing methods in high-resolution streaming volumetric video reconstruction. https://iridescentjiang.github.io/HiReFF

cs.CV↗

arXiv2026

Regularity results for linear parabolic equations on Carnot tori via mollifier kernel construction

This paper first proves the existence, uniqueness and regularity of the solution to a class of linear backward parabolic equations on Carnot tori, namely the periodic linear parabolic equation on Carnot groups. Such groups are non-commutative and typical examples of sub-Riemannian manifolds. Moreover, we apply the results for this equation to its dual equation (i.e., the Fokker-Planck-Kolmogorov equation in the general form), and derive the existence, uniqueness and regularity of its weak solution. To obtain the regularity results for solutions to the linear parabolic equation and its dual equation, firstly, we construct several families of mollifiers adapted respectively to the H\"{o}rmander vector fields generating Carnot groups, Carnot tori and dual spaces of non-isotropic H\"{o}lder spaces; secondly, we use the theory of singular integral operators to establish stronger a priori regularity for the solutions.

math.AP↗

arXiv2026

TRACER: Texture-Robust Affordance Chain-of-Thought for Deformable-Object Refinement

The central challenge in robotic manipulation of deformable objects lies in aligning high-level semantic instructions with physical interaction points under complex appearance and texture variations. Due to near-infinite degrees of freedom, complex dynamics, and heterogeneous patterns, existing vision-based affordance prediction methods often suffer from boundary overflow and fragmented functional regions. To address these issues, we propose TRACER, a Texture-Robust Affordance Chain-of-thought with dEformable-object Refinement framework, which establishes a cross-hierarchical mapping from hierarchical semantic reasoning to appearance-robust and physically consistent functional region refinement. Specifically, a Tree-structured Affordance Chain-of-Thought (TA-CoT) is formulated to decompose high-level task intentions into hierarchical sub-task semantics, providing consistent guidance across various execution stages. To ensure spatial integrity, a Spatial-Constrained Boundary Refinement (SCBR) mechanism is introduced to suppress prediction spillover, guiding the perceptual response to converge toward authentic interaction manifolds. Furthermore, an Interactive Convergence Refinement Flow (ICRF) is developed to aggregate discrete pixels corrupted by appearance noise, significantly enhancing the spatial continuity and physical plausibility of the identified functional regions. Extensive experiments conducted on the Fine-AGDDO15 dataset and a real-world robotic platform demonstrate that TRACER significantly improves affordance grounding precision across diverse textures and patterns inherent to deformable objects. More importantly, it enhances the success rate of long-horizon tasks, effectively bridging the gap between high-level semantic reasoning and low-level physical execution. The source code and dataset will be made publicly available at https://github.com/Dikay1/TRACER.

cs.RO↗

arXiv2025

Mean-Field Game for Gene Expression of Beetles

In this paper, we investigate the probability of the expression of genes that control the size of beetles under competitive relationships. We use the mean field game (MFG) theory in multiple populations to characterize the different competitive pressures of large and small beetles in the population, and simulate the probability of gene expression in finite time $[0, T]$. Therefore, we prove the existence and uniqueness of the solution of the equation under some assumptions.

math.OC↗

arXiv2025

Cross-Layer-Optimized Link Selection for Hologram Video Streaming over Millimeter Wave Networks

Holographic-type communication brings an immersive tele-holography experience by delivering holographic contents to users. As the direct representation of holographic contents, hologram videos are naturally three-dimensional representation, which consist of a huge volume of data. Advanced multi-connectivity (MC) millimeter-wave (mmWave) networks are now available to transmit hologram videos by providing the necessary bandwidth. However, the existing link selection schemes in MC-based mmWave networks neglect the source content characteristics of hologram videos and the coordination among the parameters of different protocol layers in each link, leading to sub-optimal streaming performance. To address this issue, we propose a cross-layer-optimized link selection scheme for hologram video streaming over mmWave networks. This scheme optimizes link selection by jointly adjusting the video coding bitrate, the modulation and channel coding schemes (MCS), and link power allocation to minimize the end-to-end hologram distortion while guaranteeing the synchronization and quality balance between real and imaginary components of the hologram. Results show that the proposed scheme can effectively improve the hologram video streaming performance in terms of PSNR by 1.2dB to 6.4dB against the non-cross-layer scheme.

eess.SP↗

arXiv2025

One-Shot Affordance Grounding of Deformable Objects in Egocentric Organizing Scenes

Deformable object manipulation in robotics presents significant challenges due to uncertainties in component properties, diverse configurations, visual interference, and ambiguous prompts. These factors complicate both perception and control tasks. To address these challenges, we propose a novel method for One-Shot Affordance Grounding of Deformable Objects (OS-AGDO) in egocentric organizing scenes, enabling robots to recognize previously unseen deformable objects with varying colors and shapes using minimal samples. Specifically, we first introduce the Deformable Object Semantic Enhancement Module (DefoSEM), which enhances hierarchical understanding of the internal structure and improves the ability to accurately identify local features, even under conditions of weak component information. Next, we propose the ORB-Enhanced Keypoint Fusion Module (OEKFM), which optimizes feature extraction of key components by leveraging geometric constraints and improves adaptability to diversity and visual interference. Additionally, we propose an instance-conditional prompt based on image data and task context, which effectively mitigates the issue of region ambiguity caused by prompt words. To validate these methods, we construct a diverse real-world dataset, AGDDO15, which includes 15 common types of deformable objects and their associated organizational actions. Experimental results demonstrate that our approach significantly outperforms state-of-the-art methods, achieving improvements of 6.2%, 3.2%, and 2.9% in KLD, SIM, and NSS metrics, respectively, while exhibiting high generalization performance. Source code and benchmark dataset are made publicly available at https://github.com/Dikay1/OS-AGDO.

cs.CV↗

arXiv2024

Causal Inference in Social Platforms Under Approximate Interference Networks

Estimating the total treatment effect (TTE) of a new feature in social platforms is crucial for understanding its impact on user behavior. However, the presence of network interference, which arises from user interactions, often complicates this estimation process. Experimenters typically face challenges in fully capturing the intricate structure of this interference, leading to less reliable estimates. To address this issue, we propose a novel approach that leverages surrogate networks and the pseudo inverse estimator. Our contributions can be summarized as follows: (1) We introduce the surrogate network framework, which simulates the practical situation where experimenters build an approximation of the true interference network using observable data. (2) We investigate the performance of the pseudo inverse estimator within this framework, revealing a bias-variance trade-off introduced by the surrogate network. We demonstrate a tighter asymptotic variance bound compared to previous studies and propose an enhanced variance estimator outperforming the original estimator. (3) We apply the pseudo inverse estimator to a real experiment involving over 50 million users, demonstrating its effectiveness in detecting network interference when combined with the difference-in-means estimator. Our research aims to bridge the gap between theoretical literature and practical implementation, providing a solution for estimating TTE in the presence of network interference and unknown interference structures.

stat.AP↗

arXiv2024

Stackelberg games with the third party

In this paper, we introduce the third party to achieve the Stackelberg equilibrium with the time inconsistency in three different Stackelberg games, which are the discrete-time games, the dynamic games, and the mean field games. Here all followers are experiencing learning-by-doing. The role of a third party is similar to industry associations, they supervise the leader's implementation and impose penalties for the defection with the discount factor. Then we obtain different forms of discount factors in different models and effective conditions to prevent defection.These results are consistent and the third party intervention is effective and maneuverable in practice.

math.OC↗

arXiv2024

Fujita phenomena in nonlinear fractional Rayleigh-Stokes equations

This paper concerns the Cauchy problems for the nonlinear Rayleigh-Stokes equation and the corresponding system with time-fractional derivative of order $\alpha\in(0,1)$, which can be used to simulate the anomalous diffusion in viscoelastic fluids. It is shown that there exists the critical Fujita exponent which separates systematic blow-up of the solutions from possible global existence, and the critical exponent is independent of the parameter $\alpha$. Different from the general scaling argument for parabolic problems, the main ingredients of our proof are suitable decay estimates of the solution operator and the construction of the test function.

math.AP↗

arXiv2024

Distributed Estimation in Blockchain-aided Internet of Things in the Presence of Attacks

Distributed estimation in a blockchain-aided Internet of Things (BIoT) is considered, where the integrated blockchain secures data exchanges across the BIoT and the storage of data at BIoT agents. This paper focuses on developing a performance guarantee for the distributed estimation in a BIoT in the presence of malicious attacks which jointly exploits vulnerabilities present in both IoT devices and the employed blockchain within the BIoT. To achieve this, we adopt the Cramer-Rao Bound (CRB) as the performance metric, and maximize the CRB for estimating the parameter of interest over the attack domain. However, the maximization problem is inherently non-convex, making it infeasible to obtain the globally optimal solution in general. To address this issue, we develop a relaxation method capable of transforming the original non-convex optimization problem into a convex optimization problem. Moreover, we derive the analytical expression for the optimal solution to the relaxed optimization problem. The optimal value of the relaxed optimization problem can be used to provide a valid estimation performance guarantee for the BIoT in the presence of attacks.

eess.SP↗

arXiv2024

Wellposedness of the Master Equation for Mean Field Games with Grushin Type Diffusion

We study the wellposedness of the master equation for a second-order mean field games with the Grushin type diffusion. In order to do this, we obtain the properties of its solution by investigating a degenerate mean field games system for which there exists an equivalent characterization with the master equation. The crucial points of this paper are to explore some regularities of solutions to two types of linear degenerate partial differential equations and a kind of degenerate linear coupled system so as to derive the existence of solutions to the master equation.

math.AP↗

arXiv2024

Time-Restricted Double-Spending Attack on PoW-based Blockchains

Numerous blockchain applications are designed with tasks that naturally have finite durations, and hence, a double-spending attack (DSA) on such blockchain applications leans towards being conducted within a finite timeframe, specifically before the completion of their tasks. Furthermore, existing research suggests that practical attackers typically favor executing a DSA within a finite timeframe due to their limited computational resources. These observations serve as the impetus for this paper to investigate a time-restricted DSA (TR-DSA) model on Proof-of-Work based blockchains. In this TR-DSA model, an attacker only mines its branch within a finite timeframe, and the TR-DSA is considered unsuccessful if the attacker's branch fails to surpass the honest miners' branch when the honest miners' branch has grown by a specific number of blocks. First, we developed a general closed-form expression for the success probability of a TR-DSA. This developed probability not only can assist in evaluating the risk of a DSA on blockchain applications with timely tasks, but also can enable practical attackers with limited computational resources to assess the feasibility and expected reward of launching a TR-DSA. In addition, we provide rigorous proof that the success probability of a TR-DSA is no greater than that of a time-unrestricted DSA where the attacker indefinitely mines its branch. This result implies that blockchain applications with timely tasks are less vulnerable to DSAs than blockchain applications that provide attackers with an unlimited timeframe for their attacks. Furthermore, we show that the success probability of a TR-DSA is always smaller than one even though the attacker controls more than half of the hash rate in the network. This result alerts attackers that there is still a risk of failure in launching a TR-DSA even if they amass a majority of the hash rate in the network.

cs.CR↗